CSTA Standards
 1BAP09

Create programs that use variables to store and modify data. [See: Defining Values; Structures, Reactors, and Animations; Key Events; Your Own Drawing Functions; Build Your Own Animation; Adding Collisions.]
 1BAP10

Create programs that include sequences, events, loops, and conditionals. [See: Piecewise Functions and Conditionals; Functions for Character Animation; Player Animation; Custom Scatter Plots; Method Chaining; Structures, Reactors, and Animations; Key Events; Adding Collisions.]
 1BAP11

Decompose (break down) problems into smaller, manageable subproblems to facilitate the program development process. [See: Problem Decomposition; Choosing Your Dataset; Refactoring; Going Deeper: Nested Structures.]
 1BAP12

Modify, remix, or incorporate portions of an existing program into one’s own work, to develop something new or add more advanced features. [See: Piecewise Functions and Conditionals; Making Game Images; Player Animation; Custom Scatter Plots; Introduction to Data Structures; Structures, Reactors, and Animations; Key Events; Refactoring.]
 1BAP14

Observe intellectual property rights and give appropriate attribution when creating or remixing programs. [See: Making Game Images.]
 1BAP15

Test and debug (identify and fix errors) a program or algorithm to ensure it runs as intended. [See: Functions Make Life Easier!; Checking Your Work; Debugging; Refactoring.]
 1BAP17

Describe choices made during program development using code comments, presentations, and demonstrations. [See: Introduction to Data Structures; Functions That Ask Questions.]
 1BDA06

Organize and present collected data visually to highlight relationships and support a claim. [See: Visualizing the “Shape” of Data; Box Plots; Standard Deviation; Scatter Plots; Correlations; Linear Regression.]
 1BDA07

Use data to highlight or propose causeandeffect relationships, predict outcomes, or communicate an idea. [See: Scatter Plots; Linear Regression.]
 1BIC21

Use public domain or creative commons media, and refrain from copying or using material created by others without permission. [See: Making Game Images.]
 2AP10

Use flowcharts and/or pseudocode to address complex problems as algorithms [See: Structures, Reactors, and Animations.]
 2AP11

Create clearly named variables that represent different data types and perform operations on their values. [See: Piecewise Functions and Conditionals; Simple Data Types; Function Composition; Defining Values; Functions Make Life Easier!; Functions for Character Animation; Surface Area of a Rectangular Prism; Problem Decomposition; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality; Custom Scatter Plots; Grouped Samples; Introduction to Data Structures; Structures, Reactors, and Animations.]
 2AP12

Design and iteratively develop programs that combine control structures, including nested loops and compound conditionals [See: Build Your Own Animation; Adding Levels; Making Pong; Going Deeper: Nested Structures.]
 2AP13

Decompose problems and subproblems into parts to facilitate the design, implementation, and review of programs [See: Problem Decomposition; Method Chaining; Defining Table Functions; Refactoring; Going Deeper: Nested Structures.]
 2AP14

Create procedures with parameters to organize code and make it easier to reuse. [See: Functions Make Life Easier!; Defining Table Functions; Introduction to Data Structures; Functions That Ask Questions; Key Events; Refactoring; Your Own Drawing Functions; Scoring.]
 2AP16

Incorporate existing code, media, and libraries into original programs, and give attribution. [See: Making Game Images.]
 2AP17

Systematically test and refine programs using a range of test cases [See: Piecewise Functions and Conditionals; Function Composition; Functions Make Life Easier!; Functions for Character Animation; Surface Area of a Rectangular Prism; Problem Decomposition; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality; Custom Scatter Plots; Method Chaining; Defining Table Functions; Checking Your Work; Functions That Ask Questions; Key Events; Scoring; Making Pong.]
 2AP19

Document programs in order to make them easier to follow, test, and debug. [See: Piecewise Functions and Conditionals; Function Composition; Functions Make Life Easier!; Functions for Character Animation; Surface Area of a Rectangular Prism; Problem Decomposition; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality; Custom Scatter Plots.]
 2DA08

Collect data using computational tools and transform the data to make it more useful and reliable. [See: Bar and Pie Charts; Probability, Inference, and Sample Size; Custom Scatter Plots; Table Methods; Grouped Samples.]
 2DA09

Refine computational models based on the data they have generated. [See: Probability, Inference, and Sample Size; Scatter Plots; Grouped Samples; Correlations.]
 2IC21

Discuss issues of bias and accessibility in the design of existing technologies [See: Threats to Validity.]
 2IC23

Describe tradeoffs between allowing information to be public and keeping information private and secure. [See: Ethics, Privacy, and Bias.]
 3AAP15

Justify the selection of specific control structures when tradeoffs involve implementation, readability, and program performance, and explain the benefits and drawbacks of choices made. [See: Refactoring; Going Deeper: Nested Structures.]
 3AAP16

Design and iteratively develop computational artifacts for practical intent, personal expression, or to address a societal issue by using events to initiate instructions. [See: Functions for Character Animation; Player Animation; Choosing Your Dataset; Ethics, Privacy, and Bias; Your Own Drawing Functions; Build Your Own Animation.]
 3AAP17

Decompose problems into smaller components through systematic analysis, using constructs such as procedures, modules, and/or objects. [See: Problem Decomposition; Choosing Your Dataset; Method Chaining; Defining Table Functions; Refactoring; Going Deeper: Nested Structures.]
 3AAP18

Create artifacts by using procedures within a program, combinations of data and procedures, or independent but interrelated programs. [See: Making Flags; Making Game Images; Method Chaining; Defining Table Functions; Scoring; Adding Levels; Feature: Timers.]
 3AAP20

Evaluate licenses that limit or restrict use of computational artifacts when using resources such as libraries [See: Making Game Images.]
 3AAP23

Document design decisions using text, graphics, presentations, and/or demonstrations in the development of complex programs. [See: Choosing Your Dataset.]
 3ADA11

Create interactive data visualizations using software tools to help others better understand realworld phenomena. [See: Bar and Pie Charts; Choosing Your Dataset; Histograms; Visualizing the “Shape” of Data; Box Plots; Standard Deviation; Scatter Plots; Linear Regression.]
 3ADA12

Create computational models that represent the relationships among different elements of data collected from a phenomenon or process. [See: Scatter Plots; Linear Regression.]
 3AIC24

Evaluate the ways computing impacts personal, ethical, social, economic, and cultural practices [See: Ethics, Privacy, and Bias.]
 3AIC29

Explain the privacy concerns related to the collection and generation of data through automated processes that may not be evident to users. [See: Ethics, Privacy, and Bias.]
 3AIC30

Evaluate the social and economic implications of privacy in the context of safety, law, or ethics. [See: Ethics, Privacy, and Bias.]
 3BAP10

Use and adapt classic algorithms to solve computational problems. [See: Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Sam the Butterfly  Applying Inequalities; The Distance Formula.]
 3BAP13

Illustrate the flow of execution of a recursive algorithm [See: Structures, Reactors, and Animations.]
 3BAP14

Construct solutions to problems using studentcreated components, such as procedures, modules and/or objects. [See: Piecewise Functions and Conditionals; Functions Make Life Easier!; Functions for Character Animation; Problem Decomposition; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality; Choosing Your Dataset; Histograms; Visualizing the “Shape” of Data; Custom Scatter Plots; Adding Collisions; Adding Levels; Feature: Timers.]
 3BAP21

Develop and use a series of test cases to verify that a program performs according to its design specifications. [See: Piecewise Functions and Conditionals; Function Composition; Functions Make Life Easier!; Functions for Character Animation; Problem Decomposition; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality; Checking Your Work; Functions That Ask Questions.]
 3BAP22

Modify an existing program to add additional functionality and discuss intended and unintended implications (e.g., breaking other functionality). [See: Player Animation; Functions That Ask Questions; Scoring; Feature: Timers.]
 3BNI05

Use data analysis tools and techniques to identify patterns in data representing complex systems [See: Scatter Plots; Custom Scatter Plots; Correlations; Linear Regression.]
 3BNI07

Evaluate the ability of models and simulations to test and support the refinement of hypotheses. [See: Correlations; Threats to Validity.]
K12CS Standards
 68.Algorithms and Programming.Control

Programmers select and combine control structures, such as loops, event handlers, and conditionals, to create more complex program behavior. [See: Defining Values; Solving Word Problems with the Design Recipe; Functions for Character Animation; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality; Method Chaining; Introduction to Data Structures; Functions That Ask Questions; Key Events; Refactoring; Feature: Timers.]
 68.Algorithms and Programming.Modularity

Programs use procedures to organize code, hide implementation details, and make code easier to reuse. Procedures can be repurposed in new programs. Defining parameters for procedures can generalize behavior and increase reusability. [See: Functions Make Life Easier!; Sam the Butterfly  Applying Inequalities; Defining Table Functions; Refactoring.]
 68.Algorithms and Programming.Variables

Programmers create variables to store data values of selected types. A meaningful identifier is assigned to each variable to access and perform operations on the value by name. Variables enable the flexibility to represent different situations, process different sets of data, and produce varying outputs. [See: Defining Values; Solving Word Problems with the Design Recipe; Functions for Character Animation; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality; Introduction to Data Structures; Functions That Ask Questions; Key Events; Refactoring; Feature: Timers.]
 68.Computing Systems.Troubleshooting

Comprehensive troubleshooting requires knowledge of how computing devices and components work and interact. A systematic process will identify the source of a problem, whether within a device or in a larger system of connected devices. [See: Checking Your Work.]
 68.Data and Analysis.Collection

People design algorithms and tools to automate the collection of data by computers. When data collection is automated, data is sampled and converted into a form that a computer can process. For example, data from an analog sensor must be converted into a digital form. The method used to automate data collection is influenced by the availability of tools and the intended use of the data. [See: Collecting Data; Threats to Validity.]
 68.Data and Analysis.Inference and Models

People transform, generalize, simplify, and present large data sets in different ways to influence how other people interpret and understand the underlying information. Examples include visualization, aggregation, rearrangement, and application of mathematical operations. [See: Choosing Your Dataset; Measures of Center; Box Plots; Standard Deviation; Custom Scatter Plots.]
 68.Data and Analysis.Visualization and Transformation

Computer models can be used to simulate events, examine theories and inferences, or make predictions with either few or millions of data points. Computer models are abstractions that represent phenomena and use data and algorithms to emphasize key features and relationships within a system. As more data is automatically collected, models can be refined. [See: Scatter Plots; Correlations; Linear Regression.]
 912.Algorithms and Programming.Control

Programmers consider tradeoffs related to implementation, readability, and program performance when selecting and combining control structures. [See: Piecewise Functions and Conditionals; Custom Scatter Plots; Method Chaining.]
 912.Algorithms and Programming.Modularity

Complex programs are designed as systems of interacting modules, each with a specific role, coordinating for a common overall purpose. These modules can be procedures within a program; combinations of data and procedures; or independent, but interrelated, programs. Modules allow for better management of complex tasks. [See: Functions Make Life Easier!; Method Chaining; Defining Table Functions.]
 912.Algorithms and Programming.Variables

Data structures are used to manage program complexity. Programmers choose data structures based on functionality, storage, and performance tradeoffs. [See: Introduction to Data Structures; Going Deeper: Nested Structures.]
 912.Computing Systems.Troubleshooting

Troubleshooting complex problems involves the use of multiple sources when researching, evaluating, and implementing potential solutions. Troubleshooting also relies on experience, such as when people recognize that a problem is similar to one they have seen before or adapt solutions that have worked in the past. [See: Checking Your Work.]
 912.Data and Analysis.Collection

Data is constantly collected or generated through automated processes that are not always evident, raising privacy concerns. The different collection methods and tools that are used influence the amount and quality of the data that is observed and recorded. [See: Ethics, Privacy, and Bias; Collecting Data.]
 912.Data and Analysis.Inference and Models

The accuracy of predictions or inferences depends upon the limitations of the computer model and the data the model is built upon. The amount, quality, and diversity of data and the features chosen can affect the quality of a model and ability to understand a system. Predictions or inferences are tested to validate models. [See: Linear Regression; Threats to Validity.]
 912.Data and Analysis.Visualization and Transformation

Data can be transformed to remove errors, highlight or expose relationships, and/or make it easier for computers to process. [See: Choosing Your Dataset; Visualizing the “Shape” of Data; Box Plots; Standard Deviation; Scatter Plots.]
 912.Impacts of Computing.Culture

The design and use of computing technologies and artifacts can improve, worsen, or maintain inequitable access to information and opportunities. [See: Ethics, Privacy, and Bias.]
 912.Impacts of Computing.Safety, Law, and Ethics

Laws govern many aspects of computing, such as privacy, data, property, information, and identity. These laws can have beneficial and harmful effects, such as expediting or delaying advancements in computing and protecting or infringing upon people’s rights. International differences in laws and ethics have implications for computing. [See: Ethics, Privacy, and Bias.]
 912.Impacts of Computing.Social Interactions

Many aspects of society, especially careers, have been affected by the degree of communication afforded by computing. The increased connectivity between people in different cultures and in different career fields has changed the nature and content of many careers. [See: Computing Needs All Voices.]
Alabama Standards
 AL.5.G.A.1

Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., xaxis and xcoordinate, yaxis and ycoordinate). [See: Coordinates and Game Design.]
 AL.5.OA.A

Write and interpret numerical expressions. [See: Order of Operations.]
 AL.5.OA.A.1

Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. [See: Order of Operations.]
 AL.6.EE.B

Reason about and solve onevariable equations and inequalities. [See: Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 AL.6.EE.B.6

Use variables to represent numbers and write expressions when solving a realworld or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. [See: Piecewise Functions and Conditionals; Function Composition; Defining Values; Functions Make Life Easier!; Functions: Contracts, Examples & Definitions; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Surface Area of a Rectangular Prism; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality; Defining Table Functions; Grouped Samples; Linear Regression.]
 AL.6.EE.B.8

Write an inequality of the form x > c or x < c to represent a constraint or condition in a realworld or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. [See: Simple Inequalities; Sam the Butterfly  Applying Inequalities.]
 AL.6.G.A

Solve realworld and mathematical problems involving area, surface area, and volume. [See: Surface Area of a Rectangular Prism.]
 AL.6.G.A.4

Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [See: Surface Area of a Rectangular Prism.]
 AL.6.RP.A

Understand ratio concepts and use ratio reasoning to solve problems. [See: Making Flags; Bar and Pie Charts.]
 AL.6.RP.A.1

Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. [See: Making Flags.]
 AL.6.RP.A.3.D

Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. [See: Making Flags.]
 AL.6.SP.A

Develop understanding of statistical variability. [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 AL.6.SP.A.1

Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. [See: Introduction to Data Science; The Data Cycle; Choosing Your Dataset.]
 AL.6.SP.A.2

Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots; Standard Deviation.]
 AL.6.SP.A.3

Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. [See: Box Plots; Standard Deviation.]
 AL.6.SP.B

Summarize and describe distributions. [See: Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 AL.6.SP.B.4

Display numerical data in plots on a number line, including dot plots, histograms, and box plots. [See: Histograms; Visualizing the “Shape” of Data; Box Plots; Standard Deviation.]
 AL.6.SP.B.5

Summarize numerical data sets in relation to their context. [See: Measures of Center; Box Plots; Standard Deviation.]
 AL.6.SP.B.5.C

Summarize numerical data sets in relation to their context by giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. [See: Measures of Center; Box Plots; Standard Deviation.]
 AL.6.SP.B.5.D

Summarize numerical data sets in relation to their context by relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. [See: Measures of Center.]
 AL.7.EE.A.2

Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. [See: Problem Decomposition.]
 AL.7.EE.B

Solve reallife and mathematical problems using numerical and algebraic expressions and equations. [See: Piecewise Functions and Conditionals; Solving Word Problems with the Design Recipe; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Player Animation; The Distance Formula.]
 AL.7.EE.B.4

Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. [See: Defining Values; Functions Make Life Easier!; Solving Word Problems with the Design Recipe; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 AL.7.G.B.4

Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. [See: Solving Word Problems with the Design Recipe.]
 AL.7.G.B.6

Solve realworld and mathematical problems involving area, volume and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [See: Solving Word Problems with the Design Recipe; Surface Area of a Rectangular Prism.]
 AL.7.RP.A

Analyze proportional relationships and use them to solve realworld and mathematical problems. [See: Making Flags; Making Game Images.]
 AL.7.RP.A.1

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. [See: Making Flags.]
 AL.7.RP.A.2.A

Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. [See: Functions Can Be Linear; Defining Linear Functions.]
 AL.7.RP.A.2.B

Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. [See: Functions Can Be Linear; Defining Linear Functions.]
 AL.7.SP.A

Use random sampling to draw inferences about a population. [See: Probability, Inference, and Sample Size.]
 AL.7.SP.A.1

Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. [See: Probability, Inference, and Sample Size.]
 AL.7.SP.A.2

Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. [See: Probability, Inference, and Sample Size.]
 AL.7.SP.B

Draw informal comparative inferences about two populations. [See: Bar and Pie Charts.]
 AL.8.EE.B

Understand the connections between proportional relationships, lines, and linear equations. [See: Functions Can Be Linear; Defining Linear Functions.]
 AL.8.EE.B.5

Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [See: Functions Can Be Linear; Defining Linear Functions.]
 AL.8.F.A.1

Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. [See: Contracts; The Vertical Line Test.]
 AL.8.F.A.2

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [See: Functions Can Be Linear; Defining Linear Functions.]
 AL.8.F.A.3

Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. [See: Functions Can Be Linear; Defining Linear Functions.]
 AL.8.F.B

Use functions to model relationships between quantities. [See: Functions Make Life Easier!; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition.]
 AL.8.F.B.4

Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. [See: Functions Can Be Linear; Defining Linear Functions.]
 AL.8.F.B.5

Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. [See: Functions Can Be Linear; Defining Linear Functions.]
 AL.8.G.A.1

Verify experimentally the properties of rotations, reflections, and translations. [See: Making Game Images.]
 AL.8.G.B

Understand and apply the Pythagorean Theorem. [See: The Distance Formula.]
 AL.8.G.B.7

Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions. [See: The Distance Formula.]
 AL.8.G.B.8

Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. [See: The Distance Formula.]
 AL.8.SP.A.1

Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. [See: Scatter Plots; Grouped Samples; Correlations; Linear Regression.]
 AL.8.SP.A.2

Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. [See: Scatter Plots; Correlations; Linear Regression.]
 AL.8.SP.A.3

Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. [See: Linear Regression.]
 AL.HSA.CED.A

Create equations that describe numbers or relationships. [See: Solving Word Problems with the Design Recipe; Surface Area of a Rectangular Prism; Problem Decomposition; Sam the Butterfly  Applying Inequalities.]
 AL.HSA.CED.A.1

Create equations and inequalities in one variable and use them to solve problems. [See: Sam the Butterfly  Applying Inequalities.]
 AL.HSA.CED.A.2

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [See: Sam the Butterfly  Applying Inequalities.]
 AL.HSA.CED.A.3

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. [See: Sam the Butterfly  Applying Inequalities.]
 AL.HSA.SSE.A.1

Interpret expressions that represent a quantity in terms of its context. [See: Defining Values; Functions Make Life Easier!; Solving Word Problems with the Design Recipe.]
 AL.HSA.SSE.A.1.A

Interpret parts of an expression, such as terms, factors, and coefficients. [See: Piecewise Functions and Conditionals; Player Animation.]
 AL.HSA.SSE.A.1.B

Interpret complicated expressions by viewing one or more of their parts as a single entity. [See: Piecewise Functions and Conditionals; Player Animation; Custom Scatter Plots.]
 AL.HSA.SSE.A.2

Use the structure of an expression to identify ways to rewrite it. [See: Order of Operations.]
 AL.HSA.SSE.B

Write expressions in equivalent forms to solve problems. [See: Order of Operations.]
 AL.HSF.BF.A

Build a function that models a relationship between two quantities. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 AL.HSF.BF.A.1

Write a function that describes a relationship between two quantities. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 AL.HSF.BF.A.1.B

Combine standard function types using arithmetic operations. [See: Function Composition.]
 AL.HSF.BF.A.1.C

Compose functions. [See: Function Composition; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality.]
 AL.HSF.BF.B

Build new functions from existing functions. [See: Problem Decomposition; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality.]
 AL.HSF.IF.A

Understand the concept of a function and use function notation. [See: Functions Make Life Easier!; Function Notation.]
 AL.HSF.IF.A.1

Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). [See: Contracts; The Vertical Line Test.]
 AL.HSF.IF.A.2

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. [See: Contracts; Making Flags; Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 AL.HSF.IF.B

Interpret functions that arise in applications in terms of the context. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 AL.HSF.IF.B.5

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. [See: Functions Can Be Linear; Defining Linear Functions.]
 AL.HSF.IF.C

Analyze functions using different representations. [See: The Vertical Line Test; Functions: Contracts, Examples & Definitions; Functions Can Be Linear; Defining Linear Functions; Solving Word Problems with the Design Recipe.]
 AL.HSF.IF.C.9

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [See: Functions Can Be Linear; Defining Linear Functions; Problem Decomposition.]
 AL.HSN.Q.A

Reason quantitatively and use units to solve problems. [See: Making Flags.]
 AL.HSS.CP.A.1

Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ('or', 'and', 'not'). [See: Compound Inequalities: Solutions & NonSolutions.]
 AL.HSS.CP.B.9

Use permutations and combinations to compute probabilities of compound events and solve problems. [See: Permutations; Combinations.]
 AL.HSS.IC.A

Understand and evaluate random processes underlying statistical experiments. [See: Probability, Inference, and Sample Size.]
 AL.HSS.IC.A.1

Understand statistics as a process for making inferences about population parameters based on a random sample from that population. [See: Probability, Inference, and Sample Size.]
 AL.HSS.IC.B

Make inferences and justify conclusions from sample surveys, experiments, and observational studies. [See: Collecting Data.]
 AL.HSS.IC.B.3

Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. [See: Probability, Inference, and Sample Size; Collecting Data.]
 AL.HSS.IC.B.4

Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. [See: Collecting Data.]
 AL.HSS.IC.B.6

Evaluate reports based on data. [See: Threats to Validity.]
 AL.HSS.ID.A

Summarize, represent, and interpret data on a single count or measurement variable. [See: Bar and Pie Charts; Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 AL.HSS.ID.A.1

Represent data with plots on the real number line (dot plots, histograms, and box plots). [See: Histograms; Visualizing the “Shape” of Data; Box Plots; Standard Deviation.]
 AL.HSS.ID.A.2

Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. [See: Histograms; Measures of Center; Box Plots; Standard Deviation.]
 AL.HSS.ID.A.3

Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots; Standard Deviation.]
 AL.HSS.ID.B

Summarize, represent, and interpret data on two categorical and quantitative variables. [See: Scatter Plots; Correlations.]
 AL.HSS.ID.B.6

Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. [See: Scatter Plots; Correlations.]
 AL.HSS.ID.B.6.A

Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. [See: Linear Regression.]
 AL.HSS.ID.B.6.C

Fit a linear function for a scatter plot that suggests a linear association. [See: Linear Regression.]
 AL.HSS.ID.C

Interpret linear models. [See: Linear Regression.]
 AL.HSS.ID.C.7

Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. [See: Linear Regression.]
 AL.HSS.ID.C.8

Compute (using technology) and interpret the correlation coefficient of a linear fit. [See: Scatter Plots; Correlations; Linear Regression.]
 AL.HSS.ID.C.9

Distinguish between correlation and causation. [See: Correlations; Linear Regression.]
 AL.SL.910.1

Initiate and participate effectively in a range of collaborative discussions (oneonone, in groups, and teacherled) with diverse partners on grades 910 topics, texts, and issues, building on others' ideas and expressing their own clearly and persuasively. [See: Introduction to Data Science.]
Arkansas Standards
 AR.5.G.A.1

Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., xaxis and xcoordinate, yaxis and ycoordinate). [See: Coordinates and Game Design.]
 AR.5.OA.A

Write and interpret numerical expressions. [See: Order of Operations.]
 AR.5.OA.A.1

Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. [See: Order of Operations.]
 AR.6.EE.B

Reason about and solve onevariable equations and inequalities. [See: Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 AR.6.EE.B.6

Use variables to represent numbers and write expressions when solving a realworld or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. [See: Piecewise Functions and Conditionals; Function Composition; Defining Values; Functions Make Life Easier!; Functions: Contracts, Examples & Definitions; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Surface Area of a Rectangular Prism; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality; Defining Table Functions; Grouped Samples; Linear Regression.]
 AR.6.EE.B.8

Write an inequality of the form x > c or x < c to represent a constraint or condition in a realworld or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. [See: Simple Inequalities; Sam the Butterfly  Applying Inequalities.]
 AR.6.G.A

Solve realworld and mathematical problems involving area, surface area, and volume. [See: Surface Area of a Rectangular Prism.]
 AR.6.G.A.4

Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [See: Surface Area of a Rectangular Prism.]
 AR.6.RP.A

Understand ratio concepts and use ratio reasoning to solve problems. [See: Making Flags; Bar and Pie Charts.]
 AR.6.RP.A.1

Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. [See: Making Flags.]
 AR.6.RP.A.3.D

Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. [See: Making Flags.]
 AR.6.SP.A

Develop understanding of statistical variability. [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 AR.6.SP.A.1

Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. [See: Introduction to Data Science; The Data Cycle; Choosing Your Dataset.]
 AR.6.SP.A.2

Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots; Standard Deviation.]
 AR.6.SP.A.3

Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. [See: Box Plots; Standard Deviation.]
 AR.6.SP.B

Summarize and describe distributions. [See: Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 AR.6.SP.B.4

Display numerical data in plots on a number line, including dot plots, histograms, and box plots. [See: Histograms; Visualizing the “Shape” of Data; Box Plots; Standard Deviation.]
 AR.6.SP.B.5

Summarize numerical data sets in relation to their context. [See: Measures of Center; Box Plots; Standard Deviation.]
 AR.6.SP.B.5.C

Summarize numerical data sets in relation to their context by giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. [See: Measures of Center; Box Plots; Standard Deviation.]
 AR.6.SP.B.5.D

Summarize numerical data sets in relation to their context by relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. [See: Measures of Center.]
 AR.7.EE.A.2

Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. [See: Problem Decomposition.]
 AR.7.EE.B

Solve reallife and mathematical problems using numerical and algebraic expressions and equations. [See: Piecewise Functions and Conditionals; Solving Word Problems with the Design Recipe; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Player Animation; The Distance Formula.]
 AR.7.EE.B.4

Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. [See: Defining Values; Functions Make Life Easier!; Solving Word Problems with the Design Recipe; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 AR.7.G.B.4

Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. [See: Solving Word Problems with the Design Recipe.]
 AR.7.G.B.6

Solve realworld and mathematical problems involving area, volume and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [See: Solving Word Problems with the Design Recipe; Surface Area of a Rectangular Prism.]
 AR.7.RP.A

Analyze proportional relationships and use them to solve realworld and mathematical problems. [See: Making Flags; Making Game Images.]
 AR.7.RP.A.1

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. [See: Making Flags.]
 AR.7.RP.A.2.A

Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. [See: Functions Can Be Linear; Defining Linear Functions.]
 AR.7.RP.A.2.B

Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. [See: Functions Can Be Linear; Defining Linear Functions.]
 AR.7.SP.A

Use random sampling to draw inferences about a population. [See: Probability, Inference, and Sample Size.]
 AR.7.SP.A.1

Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. [See: Probability, Inference, and Sample Size.]
 AR.7.SP.A.2

Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. [See: Probability, Inference, and Sample Size.]
 AR.7.SP.B

Draw informal comparative inferences about two populations. [See: Bar and Pie Charts.]
 AR.8.EE.B

Understand the connections between proportional relationships, lines, and linear equations. [See: Functions Can Be Linear; Defining Linear Functions.]
 AR.8.EE.B.5

Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [See: Functions Can Be Linear; Defining Linear Functions.]
 AR.8.F.A.1

Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. [See: Contracts; The Vertical Line Test.]
 AR.8.F.A.2

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [See: Functions Can Be Linear; Defining Linear Functions.]
 AR.8.F.A.3

Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. [See: Functions Can Be Linear; Defining Linear Functions.]
 AR.8.F.B

Use functions to model relationships between quantities. [See: Functions Make Life Easier!; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition.]
 AR.8.F.B.4

Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. [See: Functions Can Be Linear; Defining Linear Functions.]
 AR.8.F.B.5

Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. [See: Functions Can Be Linear; Defining Linear Functions.]
 AR.8.G.A.1

Verify experimentally the properties of rotations, reflections, and translations. [See: Making Game Images.]
 AR.8.G.B

Understand and apply the Pythagorean Theorem. [See: The Distance Formula.]
 AR.8.G.B.7

Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions. [See: The Distance Formula.]
 AR.8.G.B.8

Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. [See: The Distance Formula.]
 AR.8.SP.A.1

Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. [See: Scatter Plots; Grouped Samples; Correlations; Linear Regression.]
 AR.8.SP.A.2

Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. [See: Scatter Plots; Correlations; Linear Regression.]
 AR.8.SP.A.3

Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. [See: Linear Regression.]
 AR.HSA.CED.A

Create equations that describe numbers or relationships. [See: Solving Word Problems with the Design Recipe; Surface Area of a Rectangular Prism; Problem Decomposition; Sam the Butterfly  Applying Inequalities.]
 AR.HSA.CED.A.1

Create equations and inequalities in one variable and use them to solve problems. [See: Sam the Butterfly  Applying Inequalities.]
 AR.HSA.CED.A.2

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [See: Sam the Butterfly  Applying Inequalities.]
 AR.HSA.CED.A.3

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. [See: Sam the Butterfly  Applying Inequalities.]
 AR.HSA.SSE.A.1

Interpret expressions that represent a quantity in terms of its context. [See: Defining Values; Functions Make Life Easier!; Solving Word Problems with the Design Recipe.]
 AR.HSA.SSE.A.1.A

Interpret parts of an expression, such as terms, factors, and coefficients. [See: Piecewise Functions and Conditionals; Player Animation.]
 AR.HSA.SSE.A.1.B

Interpret complicated expressions by viewing one or more of their parts as a single entity. [See: Piecewise Functions and Conditionals; Player Animation; Custom Scatter Plots.]
 AR.HSA.SSE.A.2

Use the structure of an expression to identify ways to rewrite it. [See: Order of Operations.]
 AR.HSA.SSE.B

Write expressions in equivalent forms to solve problems. [See: Order of Operations.]
 AR.HSF.BF.A

Build a function that models a relationship between two quantities. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 AR.HSF.BF.A.1

Write a function that describes a relationship between two quantities. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 AR.HSF.BF.A.1.B

Combine standard function types using arithmetic operations. [See: Function Composition.]
 AR.HSF.BF.A.1.C

Compose functions. [See: Function Composition; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality.]
 AR.HSF.BF.B

Build new functions from existing functions. [See: Problem Decomposition; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality.]
 AR.HSF.IF.A

Understand the concept of a function and use function notation. [See: Functions Make Life Easier!; Function Notation.]
 AR.HSF.IF.A.1

Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). [See: Contracts; The Vertical Line Test.]
 AR.HSF.IF.A.2

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. [See: Contracts; Making Flags; Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 AR.HSF.IF.B

Interpret functions that arise in applications in terms of the context. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 AR.HSF.IF.B.5

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. [See: Functions Can Be Linear; Defining Linear Functions.]
 AR.HSF.IF.C

Analyze functions using different representations. [See: The Vertical Line Test; Functions: Contracts, Examples & Definitions; Functions Can Be Linear; Defining Linear Functions; Solving Word Problems with the Design Recipe.]
 AR.HSF.IF.C.9

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [See: Functions Can Be Linear; Defining Linear Functions; Problem Decomposition.]
 AR.HSN.Q.A

Reason quantitatively and use units to solve problems. [See: Making Flags.]
 AR.HSS.CP.A.1

Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ('or', 'and', 'not'). [See: Compound Inequalities: Solutions & NonSolutions.]
 AR.HSS.CP.B.9

Use permutations and combinations to compute probabilities of compound events and solve problems. [See: Permutations; Combinations.]
 AR.HSS.IC.A

Understand and evaluate random processes underlying statistical experiments. [See: Probability, Inference, and Sample Size.]
 AR.HSS.IC.A.1

Understand statistics as a process for making inferences about population parameters based on a random sample from that population. [See: Probability, Inference, and Sample Size.]
 AR.HSS.IC.B

Make inferences and justify conclusions from sample surveys, experiments, and observational studies. [See: Collecting Data.]
 AR.HSS.IC.B.3

Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. [See: Probability, Inference, and Sample Size; Collecting Data.]
 AR.HSS.IC.B.4

Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. [See: Collecting Data.]
 AR.HSS.IC.B.6

Evaluate reports based on data. [See: Threats to Validity.]
 AR.HSS.ID.A

Summarize, represent, and interpret data on a single count or measurement variable. [See: Bar and Pie Charts; Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 AR.HSS.ID.A.1

Represent data with plots on the real number line (dot plots, histograms, and box plots). [See: Histograms; Visualizing the “Shape” of Data; Box Plots; Standard Deviation.]
 AR.HSS.ID.A.2

Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. [See: Histograms; Measures of Center; Box Plots; Standard Deviation.]
 AR.HSS.ID.A.3

Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots; Standard Deviation.]
 AR.HSS.ID.B

Summarize, represent, and interpret data on two categorical and quantitative variables. [See: Scatter Plots; Correlations.]
 AR.HSS.ID.B.6

Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. [See: Scatter Plots; Correlations.]
 AR.HSS.ID.B.6.A

Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. [See: Linear Regression.]
 AR.HSS.ID.B.6.C

Fit a linear function for a scatter plot that suggests a linear association. [See: Linear Regression.]
 AR.HSS.ID.C

Interpret linear models. [See: Linear Regression.]
 AR.HSS.ID.C.7

Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. [See: Linear Regression.]
 AR.HSS.ID.C.8

Compute (using technology) and interpret the correlation coefficient of a linear fit. [See: Scatter Plots; Correlations; Linear Regression.]
 AR.HSS.ID.C.9

Distinguish between correlation and causation. [See: Correlations; Linear Regression.]
 AR.SL.910.1

Initiate and participate effectively in a range of collaborative discussions (oneonone, in groups, and teacherled) with diverse partners on grades 910 topics, texts, and issues, building on others' ideas and expressing their own clearly and persuasively. [See: Introduction to Data Science.]
California Standards
 CA.5.G.A.1

Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., xaxis and xcoordinate, yaxis and ycoordinate). [See: Coordinates and Game Design.]
 CA.5.OA.A

Write and interpret numerical expressions. [See: Order of Operations.]
 CA.5.OA.A.1

Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. [See: Order of Operations.]
 CA.6.EE.B

Reason about and solve onevariable equations and inequalities. [See: Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 CA.6.EE.B.6

Use variables to represent numbers and write expressions when solving a realworld or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. [See: Piecewise Functions and Conditionals; Function Composition; Defining Values; Functions Make Life Easier!; Functions: Contracts, Examples & Definitions; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Surface Area of a Rectangular Prism; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality; Defining Table Functions; Grouped Samples; Linear Regression.]
 CA.6.EE.B.8

Write an inequality of the form x > c or x < c to represent a constraint or condition in a realworld or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. [See: Simple Inequalities; Sam the Butterfly  Applying Inequalities.]
 CA.6.G.A

Solve realworld and mathematical problems involving area, surface area, and volume. [See: Surface Area of a Rectangular Prism.]
 CA.6.G.A.4

Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [See: Surface Area of a Rectangular Prism.]
 CA.6.RP.A

Understand ratio concepts and use ratio reasoning to solve problems. [See: Making Flags; Bar and Pie Charts.]
 CA.6.RP.A.1

Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. [See: Making Flags.]
 CA.6.RP.A.3.D

Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. [See: Making Flags.]
 CA.6.SP.A

Develop understanding of statistical variability. [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 CA.6.SP.A.1

Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. [See: Introduction to Data Science; The Data Cycle; Choosing Your Dataset.]
 CA.6.SP.A.2

Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots; Standard Deviation.]
 CA.6.SP.A.3

Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. [See: Box Plots; Standard Deviation.]
 CA.6.SP.B

Summarize and describe distributions. [See: Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 CA.6.SP.B.4

Display numerical data in plots on a number line, including dot plots, histograms, and box plots. [See: Histograms; Visualizing the “Shape” of Data; Box Plots; Standard Deviation.]
 CA.6.SP.B.5

Summarize numerical data sets in relation to their context. [See: Measures of Center; Box Plots; Standard Deviation.]
 CA.6.SP.B.5.C

Summarize numerical data sets in relation to their context by giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. [See: Measures of Center; Box Plots; Standard Deviation.]
 CA.6.SP.B.5.D

Summarize numerical data sets in relation to their context by relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. [See: Measures of Center.]
 CA.7.EE.A.2

Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. [See: Problem Decomposition.]
 CA.7.EE.B

Solve reallife and mathematical problems using numerical and algebraic expressions and equations. [See: Piecewise Functions and Conditionals; Solving Word Problems with the Design Recipe; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Player Animation; The Distance Formula.]
 CA.7.EE.B.4

Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. [See: Defining Values; Functions Make Life Easier!; Solving Word Problems with the Design Recipe; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 CA.7.G.B.4

Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. [See: Solving Word Problems with the Design Recipe.]
 CA.7.G.B.6

Solve realworld and mathematical problems involving area, volume and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [See: Solving Word Problems with the Design Recipe; Surface Area of a Rectangular Prism.]
 CA.7.RP.A

Analyze proportional relationships and use them to solve realworld and mathematical problems. [See: Making Flags; Making Game Images.]
 CA.7.RP.A.1

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. [See: Making Flags.]
 CA.7.RP.A.2.A

Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. [See: Functions Can Be Linear; Defining Linear Functions.]
 CA.7.RP.A.2.B

Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. [See: Functions Can Be Linear; Defining Linear Functions.]
 CA.7.SP.A

Use random sampling to draw inferences about a population. [See: Probability, Inference, and Sample Size.]
 CA.7.SP.A.1

Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. [See: Probability, Inference, and Sample Size.]
 CA.7.SP.A.2

Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. [See: Probability, Inference, and Sample Size.]
 CA.7.SP.B

Draw informal comparative inferences about two populations. [See: Bar and Pie Charts.]
 CA.8.EE.B

Understand the connections between proportional relationships, lines, and linear equations. [See: Functions Can Be Linear; Defining Linear Functions.]
 CA.8.EE.B.5

Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [See: Functions Can Be Linear; Defining Linear Functions.]
 CA.8.F.A.1

Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. [See: Contracts; The Vertical Line Test.]
 CA.8.F.A.2

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [See: Functions Can Be Linear; Defining Linear Functions.]
 CA.8.F.A.3

Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. [See: Functions Can Be Linear; Defining Linear Functions.]
 CA.8.F.B

Use functions to model relationships between quantities. [See: Functions Make Life Easier!; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition.]
 CA.8.F.B.4

Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. [See: Functions Can Be Linear; Defining Linear Functions.]
 CA.8.F.B.5

Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. [See: Functions Can Be Linear; Defining Linear Functions.]
 CA.8.G.A.1

Verify experimentally the properties of rotations, reflections, and translations. [See: Making Game Images.]
 CA.8.G.B

Understand and apply the Pythagorean Theorem. [See: The Distance Formula.]
 CA.8.G.B.7

Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions. [See: The Distance Formula.]
 CA.8.G.B.8

Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. [See: The Distance Formula.]
 CA.8.SP.A.1

Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. [See: Scatter Plots; Grouped Samples; Correlations; Linear Regression.]
 CA.8.SP.A.2

Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. [See: Scatter Plots; Correlations; Linear Regression.]
 CA.8.SP.A.3

Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. [See: Linear Regression.]
 CA.HSA.CED.A

Create equations that describe numbers or relationships. [See: Solving Word Problems with the Design Recipe; Surface Area of a Rectangular Prism; Problem Decomposition; Sam the Butterfly  Applying Inequalities.]
 CA.HSA.CED.A.1

Create equations and inequalities in one variable and use them to solve problems. [See: Sam the Butterfly  Applying Inequalities.]
 CA.HSA.CED.A.2

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [See: Sam the Butterfly  Applying Inequalities.]
 CA.HSA.CED.A.3

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. [See: Sam the Butterfly  Applying Inequalities.]
 CA.HSA.SSE.A.1

Interpret expressions that represent a quantity in terms of its context. [See: Defining Values; Functions Make Life Easier!; Solving Word Problems with the Design Recipe.]
 CA.HSA.SSE.A.1.A

Interpret parts of an expression, such as terms, factors, and coefficients. [See: Piecewise Functions and Conditionals; Player Animation.]
 CA.HSA.SSE.A.1.B

Interpret complicated expressions by viewing one or more of their parts as a single entity. [See: Piecewise Functions and Conditionals; Player Animation; Custom Scatter Plots.]
 CA.HSA.SSE.A.2

Use the structure of an expression to identify ways to rewrite it. [See: Order of Operations.]
 CA.HSA.SSE.B

Write expressions in equivalent forms to solve problems. [See: Order of Operations.]
 CA.HSF.BF.A

Build a function that models a relationship between two quantities. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 CA.HSF.BF.A.1

Write a function that describes a relationship between two quantities. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 CA.HSF.BF.A.1.B

Combine standard function types using arithmetic operations. [See: Function Composition.]
 CA.HSF.BF.A.1.C

Compose functions. [See: Function Composition; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality.]
 CA.HSF.BF.B

Build new functions from existing functions. [See: Problem Decomposition; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality.]
 CA.HSF.IF.A

Understand the concept of a function and use function notation. [See: Functions Make Life Easier!; Function Notation.]
 CA.HSF.IF.A.1

Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). [See: Contracts; The Vertical Line Test.]
 CA.HSF.IF.A.2

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. [See: Contracts; Making Flags; Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 CA.HSF.IF.B

Interpret functions that arise in applications in terms of the context. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 CA.HSF.IF.B.5

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. [See: Functions Can Be Linear; Defining Linear Functions.]
 CA.HSF.IF.C

Analyze functions using different representations. [See: The Vertical Line Test; Functions: Contracts, Examples & Definitions; Functions Can Be Linear; Defining Linear Functions; Solving Word Problems with the Design Recipe.]
 CA.HSF.IF.C.9

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [See: Functions Can Be Linear; Defining Linear Functions; Problem Decomposition.]
 CA.HSN.Q.A

Reason quantitatively and use units to solve problems. [See: Making Flags.]
 CA.HSS.CP.A.1

Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ('or', 'and', 'not'). [See: Compound Inequalities: Solutions & NonSolutions.]
 CA.HSS.CP.B.9

Use permutations and combinations to compute probabilities of compound events and solve problems. [See: Permutations; Combinations.]
 CA.HSS.IC.A

Understand and evaluate random processes underlying statistical experiments. [See: Probability, Inference, and Sample Size.]
 CA.HSS.IC.A.1

Understand statistics as a process for making inferences about population parameters based on a random sample from that population. [See: Probability, Inference, and Sample Size.]
 CA.HSS.IC.B

Make inferences and justify conclusions from sample surveys, experiments, and observational studies. [See: Collecting Data.]
 CA.HSS.IC.B.3

Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. [See: Probability, Inference, and Sample Size; Collecting Data.]
 CA.HSS.IC.B.4

Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. [See: Collecting Data.]
 CA.HSS.IC.B.6

Evaluate reports based on data. [See: Threats to Validity.]
 CA.HSS.ID.A

Summarize, represent, and interpret data on a single count or measurement variable. [See: Bar and Pie Charts; Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 CA.HSS.ID.A.1

Represent data with plots on the real number line (dot plots, histograms, and box plots). [See: Histograms; Visualizing the “Shape” of Data; Box Plots; Standard Deviation.]
 CA.HSS.ID.A.2

Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. [See: Histograms; Measures of Center; Box Plots; Standard Deviation.]
 CA.HSS.ID.A.3

Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots; Standard Deviation.]
 CA.HSS.ID.B

Summarize, represent, and interpret data on two categorical and quantitative variables. [See: Scatter Plots; Correlations.]
 CA.HSS.ID.B.6

Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. [See: Scatter Plots; Correlations.]
 CA.HSS.ID.B.6.A

Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. [See: Linear Regression.]
 CA.HSS.ID.B.6.C

Fit a linear function for a scatter plot that suggests a linear association. [See: Linear Regression.]
 CA.HSS.ID.C

Interpret linear models. [See: Linear Regression.]
 CA.HSS.ID.C.7

Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. [See: Linear Regression.]
 CA.HSS.ID.C.8

Compute (using technology) and interpret the correlation coefficient of a linear fit. [See: Scatter Plots; Correlations; Linear Regression.]
 CA.HSS.ID.C.9

Distinguish between correlation and causation. [See: Correlations; Linear Regression.]
 CA.SL.910.1

Initiate and participate effectively in a range of collaborative discussions (oneonone, in groups, and teacherled) with diverse partners on grades 910 topics, texts, and issues, building on others' ideas and expressing their own clearly and persuasively. [See: Introduction to Data Science.]
Colorado Standards
 CO.5.G.A.1

Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., xaxis and xcoordinate, yaxis and ycoordinate). [See: Coordinates and Game Design.]
 CO.5.OA.A

Write and interpret numerical expressions. [See: Order of Operations.]
 CO.5.OA.A.1

Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. [See: Order of Operations.]
 CO.6.EE.B

Reason about and solve onevariable equations and inequalities. [See: Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 CO.6.EE.B.6

Use variables to represent numbers and write expressions when solving a realworld or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. [See: Piecewise Functions and Conditionals; Function Composition; Defining Values; Functions Make Life Easier!; Functions: Contracts, Examples & Definitions; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Surface Area of a Rectangular Prism; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality; Defining Table Functions; Grouped Samples; Linear Regression.]
 CO.6.EE.B.8

Write an inequality of the form x > c or x < c to represent a constraint or condition in a realworld or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. [See: Simple Inequalities; Sam the Butterfly  Applying Inequalities.]
 CO.6.G.A

Solve realworld and mathematical problems involving area, surface area, and volume. [See: Surface Area of a Rectangular Prism.]
 CO.6.G.A.4

Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [See: Surface Area of a Rectangular Prism.]
 CO.6.RP.A

Understand ratio concepts and use ratio reasoning to solve problems. [See: Making Flags; Bar and Pie Charts.]
 CO.6.RP.A.1

Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. [See: Making Flags.]
 CO.6.RP.A.3.D

Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. [See: Making Flags.]
 CO.6.SP.A

Develop understanding of statistical variability. [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 CO.6.SP.A.1

Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. [See: Introduction to Data Science; The Data Cycle; Choosing Your Dataset.]
 CO.6.SP.A.2

Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots; Standard Deviation.]
 CO.6.SP.A.3

Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. [See: Box Plots; Standard Deviation.]
 CO.6.SP.B

Summarize and describe distributions. [See: Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 CO.6.SP.B.4

Display numerical data in plots on a number line, including dot plots, histograms, and box plots. [See: Histograms; Visualizing the “Shape” of Data; Box Plots; Standard Deviation.]
 CO.6.SP.B.5

Summarize numerical data sets in relation to their context. [See: Measures of Center; Box Plots; Standard Deviation.]
 CO.6.SP.B.5.C

Summarize numerical data sets in relation to their context by giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. [See: Measures of Center; Box Plots; Standard Deviation.]
 CO.6.SP.B.5.D

Summarize numerical data sets in relation to their context by relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. [See: Measures of Center.]
 CO.7.EE.A.2

Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. [See: Problem Decomposition.]
 CO.7.EE.B

Solve reallife and mathematical problems using numerical and algebraic expressions and equations. [See: Piecewise Functions and Conditionals; Solving Word Problems with the Design Recipe; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Player Animation; The Distance Formula.]
 CO.7.EE.B.4

Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. [See: Defining Values; Functions Make Life Easier!; Solving Word Problems with the Design Recipe; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 CO.7.G.B.4

Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. [See: Solving Word Problems with the Design Recipe.]
 CO.7.G.B.6

Solve realworld and mathematical problems involving area, volume and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [See: Solving Word Problems with the Design Recipe; Surface Area of a Rectangular Prism.]
 CO.7.RP.A

Analyze proportional relationships and use them to solve realworld and mathematical problems. [See: Making Flags; Making Game Images.]
 CO.7.RP.A.1

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. [See: Making Flags.]
 CO.7.RP.A.2.A

Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. [See: Functions Can Be Linear; Defining Linear Functions.]
 CO.7.RP.A.2.B

Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. [See: Functions Can Be Linear; Defining Linear Functions.]
 CO.7.SP.A

Use random sampling to draw inferences about a population. [See: Probability, Inference, and Sample Size.]
 CO.7.SP.A.1

Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. [See: Probability, Inference, and Sample Size.]
 CO.7.SP.A.2

Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. [See: Probability, Inference, and Sample Size.]
 CO.7.SP.B

Draw informal comparative inferences about two populations. [See: Bar and Pie Charts.]
 CO.8.EE.B

Understand the connections between proportional relationships, lines, and linear equations. [See: Functions Can Be Linear; Defining Linear Functions.]
 CO.8.EE.B.5

Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [See: Functions Can Be Linear; Defining Linear Functions.]
 CO.8.F.A.1

Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. [See: Contracts; The Vertical Line Test.]
 CO.8.F.A.2

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [See: Functions Can Be Linear; Defining Linear Functions.]
 CO.8.F.A.3

Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. [See: Functions Can Be Linear; Defining Linear Functions.]
 CO.8.F.B

Use functions to model relationships between quantities. [See: Functions Make Life Easier!; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition.]
 CO.8.F.B.4

Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. [See: Functions Can Be Linear; Defining Linear Functions.]
 CO.8.F.B.5

Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. [See: Functions Can Be Linear; Defining Linear Functions.]
 CO.8.G.A.1

Verify experimentally the properties of rotations, reflections, and translations. [See: Making Game Images.]
 CO.8.G.B

Understand and apply the Pythagorean Theorem. [See: The Distance Formula.]
 CO.8.G.B.7

Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions. [See: The Distance Formula.]
 CO.8.G.B.8

Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. [See: The Distance Formula.]
 CO.8.SP.A.1

Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. [See: Scatter Plots; Grouped Samples; Correlations; Linear Regression.]
 CO.8.SP.A.2

Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. [See: Scatter Plots; Correlations; Linear Regression.]
 CO.8.SP.A.3

Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. [See: Linear Regression.]
 CO.HSA.CED.A

Create equations that describe numbers or relationships. [See: Solving Word Problems with the Design Recipe; Surface Area of a Rectangular Prism; Problem Decomposition; Sam the Butterfly  Applying Inequalities.]
 CO.HSA.CED.A.1

Create equations and inequalities in one variable and use them to solve problems. [See: Sam the Butterfly  Applying Inequalities.]
 CO.HSA.CED.A.2

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [See: Sam the Butterfly  Applying Inequalities.]
 CO.HSA.CED.A.3

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. [See: Sam the Butterfly  Applying Inequalities.]
 CO.HSA.SSE.A.1

Interpret expressions that represent a quantity in terms of its context. [See: Defining Values; Functions Make Life Easier!; Solving Word Problems with the Design Recipe.]
 CO.HSA.SSE.A.1.A

Interpret parts of an expression, such as terms, factors, and coefficients. [See: Piecewise Functions and Conditionals; Player Animation.]
 CO.HSA.SSE.A.1.B

Interpret complicated expressions by viewing one or more of their parts as a single entity. [See: Piecewise Functions and Conditionals; Player Animation; Custom Scatter Plots.]
 CO.HSA.SSE.A.2

Use the structure of an expression to identify ways to rewrite it. [See: Order of Operations.]
 CO.HSA.SSE.B

Write expressions in equivalent forms to solve problems. [See: Order of Operations.]
 CO.HSF.BF.A

Build a function that models a relationship between two quantities. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 CO.HSF.BF.A.1

Write a function that describes a relationship between two quantities. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 CO.HSF.BF.A.1.B

Combine standard function types using arithmetic operations. [See: Function Composition.]
 CO.HSF.BF.A.1.C

Compose functions. [See: Function Composition; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality.]
 CO.HSF.BF.B

Build new functions from existing functions. [See: Problem Decomposition; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality.]
 CO.HSF.IF.A

Understand the concept of a function and use function notation. [See: Functions Make Life Easier!; Function Notation.]
 CO.HSF.IF.A.1

Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). [See: Contracts; The Vertical Line Test.]
 CO.HSF.IF.A.2

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. [See: Contracts; Making Flags; Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 CO.HSF.IF.B

Interpret functions that arise in applications in terms of the context. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 CO.HSF.IF.B.5

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. [See: Functions Can Be Linear; Defining Linear Functions.]
 CO.HSF.IF.C

Analyze functions using different representations. [See: The Vertical Line Test; Functions: Contracts, Examples & Definitions; Functions Can Be Linear; Defining Linear Functions; Solving Word Problems with the Design Recipe.]
 CO.HSF.IF.C.9

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [See: Functions Can Be Linear; Defining Linear Functions; Problem Decomposition.]
 CO.HSN.Q.A

Reason quantitatively and use units to solve problems. [See: Making Flags.]
 CO.HSS.CP.A.1

Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ('or', 'and', 'not'). [See: Compound Inequalities: Solutions & NonSolutions.]
 CO.HSS.CP.B.9

Use permutations and combinations to compute probabilities of compound events and solve problems. [See: Permutations; Combinations.]
 CO.HSS.IC.A

Understand and evaluate random processes underlying statistical experiments. [See: Probability, Inference, and Sample Size.]
 CO.HSS.IC.A.1

Understand statistics as a process for making inferences about population parameters based on a random sample from that population. [See: Probability, Inference, and Sample Size.]
 CO.HSS.IC.B

Make inferences and justify conclusions from sample surveys, experiments, and observational studies. [See: Collecting Data.]
 CO.HSS.IC.B.3

Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. [See: Probability, Inference, and Sample Size; Collecting Data.]
 CO.HSS.IC.B.4

Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. [See: Collecting Data.]
 CO.HSS.IC.B.6

Evaluate reports based on data. [See: Threats to Validity.]
 CO.HSS.ID.A

Summarize, represent, and interpret data on a single count or measurement variable. [See: Bar and Pie Charts; Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 CO.HSS.ID.A.1

Represent data with plots on the real number line (dot plots, histograms, and box plots). [See: Histograms; Visualizing the “Shape” of Data; Box Plots; Standard Deviation.]
 CO.HSS.ID.A.2

Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. [See: Histograms; Measures of Center; Box Plots; Standard Deviation.]
 CO.HSS.ID.A.3

Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots; Standard Deviation.]
 CO.HSS.ID.B

Summarize, represent, and interpret data on two categorical and quantitative variables. [See: Scatter Plots; Correlations.]
 CO.HSS.ID.B.6

Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. [See: Scatter Plots; Correlations.]
 CO.HSS.ID.B.6.A

Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. [See: Linear Regression.]
 CO.HSS.ID.B.6.C

Fit a linear function for a scatter plot that suggests a linear association. [See: Linear Regression.]
 CO.HSS.ID.C

Interpret linear models. [See: Linear Regression.]
 CO.HSS.ID.C.7

Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. [See: Linear Regression.]
 CO.HSS.ID.C.8

Compute (using technology) and interpret the correlation coefficient of a linear fit. [See: Scatter Plots; Correlations; Linear Regression.]
 CO.HSS.ID.C.9

Distinguish between correlation and causation. [See: Correlations; Linear Regression.]
 CO.SL.910.1

Initiate and participate effectively in a range of collaborative discussions (oneonone, in groups, and teacherled) with diverse partners on grades 910 topics, texts, and issues, building on others' ideas and expressing their own clearly and persuasively. [See: Introduction to Data Science.]
Connecticut Standards
 CT.5.G.A.1

Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., xaxis and xcoordinate, yaxis and ycoordinate). [See: Coordinates and Game Design.]
 CT.5.OA.A

Write and interpret numerical expressions. [See: Order of Operations.]
 CT.5.OA.A.1

Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. [See: Order of Operations.]
 CT.6.EE.B

Reason about and solve onevariable equations and inequalities. [See: Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 CT.6.EE.B.6

Use variables to represent numbers and write expressions when solving a realworld or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. [See: Piecewise Functions and Conditionals; Function Composition; Defining Values; Functions Make Life Easier!; Functions: Contracts, Examples & Definitions; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Surface Area of a Rectangular Prism; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality; Defining Table Functions; Grouped Samples; Linear Regression.]
 CT.6.EE.B.8

Write an inequality of the form x > c or x < c to represent a constraint or condition in a realworld or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. [See: Simple Inequalities; Sam the Butterfly  Applying Inequalities.]
 CT.6.G.A

Solve realworld and mathematical problems involving area, surface area, and volume. [See: Surface Area of a Rectangular Prism.]
 CT.6.G.A.4

Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [See: Surface Area of a Rectangular Prism.]
 CT.6.RP.A

Understand ratio concepts and use ratio reasoning to solve problems. [See: Making Flags; Bar and Pie Charts.]
 CT.6.RP.A.1

Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. [See: Making Flags.]
 CT.6.RP.A.3.D

Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. [See: Making Flags.]
 CT.6.SP.A

Develop understanding of statistical variability. [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 CT.6.SP.A.1

Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. [See: Introduction to Data Science; The Data Cycle; Choosing Your Dataset.]
 CT.6.SP.A.2

Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots; Standard Deviation.]
 CT.6.SP.A.3

Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. [See: Box Plots; Standard Deviation.]
 CT.6.SP.B

Summarize and describe distributions. [See: Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 CT.6.SP.B.4

Display numerical data in plots on a number line, including dot plots, histograms, and box plots. [See: Histograms; Visualizing the “Shape” of Data; Box Plots; Standard Deviation.]
 CT.6.SP.B.5

Summarize numerical data sets in relation to their context. [See: Measures of Center; Box Plots; Standard Deviation.]
 CT.6.SP.B.5.C

Summarize numerical data sets in relation to their context by giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. [See: Measures of Center; Box Plots; Standard Deviation.]
 CT.6.SP.B.5.D

Summarize numerical data sets in relation to their context by relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. [See: Measures of Center.]
 CT.7.EE.A.2

Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. [See: Problem Decomposition.]
 CT.7.EE.B

Solve reallife and mathematical problems using numerical and algebraic expressions and equations. [See: Piecewise Functions and Conditionals; Solving Word Problems with the Design Recipe; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Player Animation; The Distance Formula.]
 CT.7.EE.B.4

Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. [See: Defining Values; Functions Make Life Easier!; Solving Word Problems with the Design Recipe; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 CT.7.G.B.4

Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. [See: Solving Word Problems with the Design Recipe.]
 CT.7.G.B.6

Solve realworld and mathematical problems involving area, volume and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [See: Solving Word Problems with the Design Recipe; Surface Area of a Rectangular Prism.]
 CT.7.RP.A

Analyze proportional relationships and use them to solve realworld and mathematical problems. [See: Making Flags; Making Game Images.]
 CT.7.RP.A.1

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. [See: Making Flags.]
 CT.7.RP.A.2.A

Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. [See: Functions Can Be Linear; Defining Linear Functions.]
 CT.7.RP.A.2.B

Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. [See: Functions Can Be Linear; Defining Linear Functions.]
 CT.7.SP.A

Use random sampling to draw inferences about a population. [See: Probability, Inference, and Sample Size.]
 CT.7.SP.A.1

Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. [See: Probability, Inference, and Sample Size.]
 CT.7.SP.A.2

Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. [See: Probability, Inference, and Sample Size.]
 CT.7.SP.B

Draw informal comparative inferences about two populations. [See: Bar and Pie Charts.]
 CT.8.EE.B

Understand the connections between proportional relationships, lines, and linear equations. [See: Functions Can Be Linear; Defining Linear Functions.]
 CT.8.EE.B.5

Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [See: Functions Can Be Linear; Defining Linear Functions.]
 CT.8.F.A.1

Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. [See: Contracts; The Vertical Line Test.]
 CT.8.F.A.2

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [See: Functions Can Be Linear; Defining Linear Functions.]
 CT.8.F.A.3

Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. [See: Functions Can Be Linear; Defining Linear Functions.]
 CT.8.F.B

Use functions to model relationships between quantities. [See: Functions Make Life Easier!; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition.]
 CT.8.F.B.4

Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. [See: Functions Can Be Linear; Defining Linear Functions.]
 CT.8.F.B.5

Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. [See: Functions Can Be Linear; Defining Linear Functions.]
 CT.8.G.A.1

Verify experimentally the properties of rotations, reflections, and translations. [See: Making Game Images.]
 CT.8.G.B

Understand and apply the Pythagorean Theorem. [See: The Distance Formula.]
 CT.8.G.B.7

Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions. [See: The Distance Formula.]
 CT.8.G.B.8

Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. [See: The Distance Formula.]
 CT.8.SP.A.1

Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. [See: Scatter Plots; Grouped Samples; Correlations; Linear Regression.]
 CT.8.SP.A.2

Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. [See: Scatter Plots; Correlations; Linear Regression.]
 CT.8.SP.A.3

Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. [See: Linear Regression.]
 CT.HSA.CED.A

Create equations that describe numbers or relationships. [See: Solving Word Problems with the Design Recipe; Surface Area of a Rectangular Prism; Problem Decomposition; Sam the Butterfly  Applying Inequalities.]
 CT.HSA.CED.A.1

Create equations and inequalities in one variable and use them to solve problems. [See: Sam the Butterfly  Applying Inequalities.]
 CT.HSA.CED.A.2

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [See: Sam the Butterfly  Applying Inequalities.]
 CT.HSA.CED.A.3

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. [See: Sam the Butterfly  Applying Inequalities.]
 CT.HSA.SSE.A.1

Interpret expressions that represent a quantity in terms of its context. [See: Defining Values; Functions Make Life Easier!; Solving Word Problems with the Design Recipe.]
 CT.HSA.SSE.A.1.A

Interpret parts of an expression, such as terms, factors, and coefficients. [See: Piecewise Functions and Conditionals; Player Animation.]
 CT.HSA.SSE.A.1.B

Interpret complicated expressions by viewing one or more of their parts as a single entity. [See: Piecewise Functions and Conditionals; Player Animation; Custom Scatter Plots.]
 CT.HSA.SSE.A.2

Use the structure of an expression to identify ways to rewrite it. [See: Order of Operations.]
 CT.HSA.SSE.B

Write expressions in equivalent forms to solve problems. [See: Order of Operations.]
 CT.HSF.BF.A

Build a function that models a relationship between two quantities. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 CT.HSF.BF.A.1

Write a function that describes a relationship between two quantities. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 CT.HSF.BF.A.1.B

Combine standard function types using arithmetic operations. [See: Function Composition.]
 CT.HSF.BF.A.1.C

Compose functions. [See: Function Composition; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality.]
 CT.HSF.BF.B

Build new functions from existing functions. [See: Problem Decomposition; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality.]
 CT.HSF.IF.A

Understand the concept of a function and use function notation. [See: Functions Make Life Easier!; Function Notation.]
 CT.HSF.IF.A.1

Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). [See: Contracts; The Vertical Line Test.]
 CT.HSF.IF.A.2

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. [See: Contracts; Making Flags; Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 CT.HSF.IF.B

Interpret functions that arise in applications in terms of the context. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 CT.HSF.IF.B.5

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. [See: Functions Can Be Linear; Defining Linear Functions.]
 CT.HSF.IF.C

Analyze functions using different representations. [See: The Vertical Line Test; Functions: Contracts, Examples & Definitions; Functions Can Be Linear; Defining Linear Functions; Solving Word Problems with the Design Recipe.]
 CT.HSF.IF.C.9

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [See: Functions Can Be Linear; Defining Linear Functions; Problem Decomposition.]
 CT.HSN.Q.A

Reason quantitatively and use units to solve problems. [See: Making Flags.]
 CT.HSS.CP.A.1

Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ('or', 'and', 'not'). [See: Compound Inequalities: Solutions & NonSolutions.]
 CT.HSS.CP.B.9

Use permutations and combinations to compute probabilities of compound events and solve problems. [See: Permutations; Combinations.]
 CT.HSS.IC.A

Understand and evaluate random processes underlying statistical experiments. [See: Probability, Inference, and Sample Size.]
 CT.HSS.IC.A.1

Understand statistics as a process for making inferences about population parameters based on a random sample from that population. [See: Probability, Inference, and Sample Size.]
 CT.HSS.IC.B

Make inferences and justify conclusions from sample surveys, experiments, and observational studies. [See: Collecting Data.]
 CT.HSS.IC.B.3

Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. [See: Probability, Inference, and Sample Size; Collecting Data.]
 CT.HSS.IC.B.4

Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. [See: Collecting Data.]
 CT.HSS.IC.B.6

Evaluate reports based on data. [See: Threats to Validity.]
 CT.HSS.ID.A

Summarize, represent, and interpret data on a single count or measurement variable. [See: Bar and Pie Charts; Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 CT.HSS.ID.A.1

Represent data with plots on the real number line (dot plots, histograms, and box plots). [See: Histograms; Visualizing the “Shape” of Data; Box Plots; Standard Deviation.]
 CT.HSS.ID.A.2

Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. [See: Histograms; Measures of Center; Box Plots; Standard Deviation.]
 CT.HSS.ID.A.3

Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots; Standard Deviation.]
 CT.HSS.ID.B

Summarize, represent, and interpret data on two categorical and quantitative variables. [See: Scatter Plots; Correlations.]
 CT.HSS.ID.B.6

Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. [See: Scatter Plots; Correlations.]
 CT.HSS.ID.B.6.A

Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. [See: Linear Regression.]
 CT.HSS.ID.B.6.C

Fit a linear function for a scatter plot that suggests a linear association. [See: Linear Regression.]
 CT.HSS.ID.C

Interpret linear models. [See: Linear Regression.]
 CT.HSS.ID.C.7

Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. [See: Linear Regression.]
 CT.HSS.ID.C.8

Compute (using technology) and interpret the correlation coefficient of a linear fit. [See: Scatter Plots; Correlations; Linear Regression.]
 CT.HSS.ID.C.9

Distinguish between correlation and causation. [See: Correlations; Linear Regression.]
 CT.SL.910.1

Initiate and participate effectively in a range of collaborative discussions (oneonone, in groups, and teacherled) with diverse partners on grades 910 topics, texts, and issues, building on others' ideas and expressing their own clearly and persuasively. [See: Introduction to Data Science.]
Delaware Standards
 DE.5.G.A.1

Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., xaxis and xcoordinate, yaxis and ycoordinate). [See: Coordinates and Game Design.]
 DE.5.OA.A

Write and interpret numerical expressions. [See: Order of Operations.]
 DE.5.OA.A.1

Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. [See: Order of Operations.]
 DE.6.EE.B

Reason about and solve onevariable equations and inequalities. [See: Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 DE.6.EE.B.6

Use variables to represent numbers and write expressions when solving a realworld or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. [See: Piecewise Functions and Conditionals; Function Composition; Defining Values; Functions Make Life Easier!; Functions: Contracts, Examples & Definitions; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Surface Area of a Rectangular Prism; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality; Defining Table Functions; Grouped Samples; Linear Regression.]
 DE.6.EE.B.8

Write an inequality of the form x > c or x < c to represent a constraint or condition in a realworld or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. [See: Simple Inequalities; Sam the Butterfly  Applying Inequalities.]
 DE.6.G.A

Solve realworld and mathematical problems involving area, surface area, and volume. [See: Surface Area of a Rectangular Prism.]
 DE.6.G.A.4

Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [See: Surface Area of a Rectangular Prism.]
 DE.6.RP.A

Understand ratio concepts and use ratio reasoning to solve problems. [See: Making Flags; Bar and Pie Charts.]
 DE.6.RP.A.1

Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. [See: Making Flags.]
 DE.6.RP.A.3.D

Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. [See: Making Flags.]
 DE.6.SP.A

Develop understanding of statistical variability. [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 DE.6.SP.A.1

Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. [See: Introduction to Data Science; The Data Cycle; Choosing Your Dataset.]
 DE.6.SP.A.2

Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots; Standard Deviation.]
 DE.6.SP.A.3

Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. [See: Box Plots; Standard Deviation.]
 DE.6.SP.B

Summarize and describe distributions. [See: Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 DE.6.SP.B.4

Display numerical data in plots on a number line, including dot plots, histograms, and box plots. [See: Histograms; Visualizing the “Shape” of Data; Box Plots; Standard Deviation.]
 DE.6.SP.B.5

Summarize numerical data sets in relation to their context. [See: Measures of Center; Box Plots; Standard Deviation.]
 DE.6.SP.B.5.C

Summarize numerical data sets in relation to their context by giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. [See: Measures of Center; Box Plots; Standard Deviation.]
 DE.6.SP.B.5.D

Summarize numerical data sets in relation to their context by relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. [See: Measures of Center.]
 DE.7.EE.A.2

Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. [See: Problem Decomposition.]
 DE.7.EE.B

Solve reallife and mathematical problems using numerical and algebraic expressions and equations. [See: Piecewise Functions and Conditionals; Solving Word Problems with the Design Recipe; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Player Animation; The Distance Formula.]
 DE.7.EE.B.4

Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. [See: Defining Values; Functions Make Life Easier!; Solving Word Problems with the Design Recipe; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 DE.7.G.B.4

Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. [See: Solving Word Problems with the Design Recipe.]
 DE.7.G.B.6

Solve realworld and mathematical problems involving area, volume and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [See: Solving Word Problems with the Design Recipe; Surface Area of a Rectangular Prism.]
 DE.7.RP.A

Analyze proportional relationships and use them to solve realworld and mathematical problems. [See: Making Flags; Making Game Images.]
 DE.7.RP.A.1

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. [See: Making Flags.]
 DE.7.RP.A.2.A

Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. [See: Functions Can Be Linear; Defining Linear Functions.]
 DE.7.RP.A.2.B

Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. [See: Functions Can Be Linear; Defining Linear Functions.]
 DE.7.SP.A

Use random sampling to draw inferences about a population. [See: Probability, Inference, and Sample Size.]
 DE.7.SP.A.1

Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. [See: Probability, Inference, and Sample Size.]
 DE.7.SP.A.2

Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. [See: Probability, Inference, and Sample Size.]
 DE.7.SP.B

Draw informal comparative inferences about two populations. [See: Bar and Pie Charts.]
 DE.8.EE.B

Understand the connections between proportional relationships, lines, and linear equations. [See: Functions Can Be Linear; Defining Linear Functions.]
 DE.8.EE.B.5

Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [See: Functions Can Be Linear; Defining Linear Functions.]
 DE.8.F.A.1

Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. [See: Contracts; The Vertical Line Test.]
 DE.8.F.A.2

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [See: Functions Can Be Linear; Defining Linear Functions.]
 DE.8.F.A.3

Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. [See: Functions Can Be Linear; Defining Linear Functions.]
 DE.8.F.B

Use functions to model relationships between quantities. [See: Functions Make Life Easier!; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition.]
 DE.8.F.B.4

Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. [See: Functions Can Be Linear; Defining Linear Functions.]
 DE.8.F.B.5

Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. [See: Functions Can Be Linear; Defining Linear Functions.]
 DE.8.G.A.1

Verify experimentally the properties of rotations, reflections, and translations. [See: Making Game Images.]
 DE.8.G.B

Understand and apply the Pythagorean Theorem. [See: The Distance Formula.]
 DE.8.G.B.7

Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions. [See: The Distance Formula.]
 DE.8.G.B.8

Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. [See: The Distance Formula.]
 DE.8.SP.A.1

Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. [See: Scatter Plots; Grouped Samples; Correlations; Linear Regression.]
 DE.8.SP.A.2

Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. [See: Scatter Plots; Correlations; Linear Regression.]
 DE.8.SP.A.3

Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. [See: Linear Regression.]
 DE.HSA.CED.A

Create equations that describe numbers or relationships. [See: Solving Word Problems with the Design Recipe; Surface Area of a Rectangular Prism; Problem Decomposition; Sam the Butterfly  Applying Inequalities.]
 DE.HSA.CED.A.1

Create equations and inequalities in one variable and use them to solve problems. [See: Sam the Butterfly  Applying Inequalities.]
 DE.HSA.CED.A.2

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [See: Sam the Butterfly  Applying Inequalities.]
 DE.HSA.CED.A.3

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. [See: Sam the Butterfly  Applying Inequalities.]
 DE.HSA.SSE.A.1

Interpret expressions that represent a quantity in terms of its context. [See: Defining Values; Functions Make Life Easier!; Solving Word Problems with the Design Recipe.]
 DE.HSA.SSE.A.1.A

Interpret parts of an expression, such as terms, factors, and coefficients. [See: Piecewise Functions and Conditionals; Player Animation.]
 DE.HSA.SSE.A.1.B

Interpret complicated expressions by viewing one or more of their parts as a single entity. [See: Piecewise Functions and Conditionals; Player Animation; Custom Scatter Plots.]
 DE.HSA.SSE.A.2

Use the structure of an expression to identify ways to rewrite it. [See: Order of Operations.]
 DE.HSA.SSE.B

Write expressions in equivalent forms to solve problems. [See: Order of Operations.]
 DE.HSF.BF.A

Build a function that models a relationship between two quantities. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 DE.HSF.BF.A.1

Write a function that describes a relationship between two quantities. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 DE.HSF.BF.A.1.B

Combine standard function types using arithmetic operations. [See: Function Composition.]
 DE.HSF.BF.A.1.C

Compose functions. [See: Function Composition; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality.]
 DE.HSF.BF.B

Build new functions from existing functions. [See: Problem Decomposition; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality.]
 DE.HSF.IF.A

Understand the concept of a function and use function notation. [See: Functions Make Life Easier!; Function Notation.]
 DE.HSF.IF.A.1

Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). [See: Contracts; The Vertical Line Test.]
 DE.HSF.IF.A.2

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. [See: Contracts; Making Flags; Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 DE.HSF.IF.B

Interpret functions that arise in applications in terms of the context. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 DE.HSF.IF.B.5

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. [See: Functions Can Be Linear; Defining Linear Functions.]
 DE.HSF.IF.C

Analyze functions using different representations. [See: The Vertical Line Test; Functions: Contracts, Examples & Definitions; Functions Can Be Linear; Defining Linear Functions; Solving Word Problems with the Design Recipe.]
 DE.HSF.IF.C.9

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [See: Functions Can Be Linear; Defining Linear Functions; Problem Decomposition.]
 DE.HSN.Q.A

Reason quantitatively and use units to solve problems. [See: Making Flags.]
 DE.HSS.CP.A.1

Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ('or', 'and', 'not'). [See: Compound Inequalities: Solutions & NonSolutions.]
 DE.HSS.CP.B.9

Use permutations and combinations to compute probabilities of compound events and solve problems. [See: Permutations; Combinations.]
 DE.HSS.IC.A

Understand and evaluate random processes underlying statistical experiments. [See: Probability, Inference, and Sample Size.]
 DE.HSS.IC.A.1

Understand statistics as a process for making inferences about population parameters based on a random sample from that population. [See: Probability, Inference, and Sample Size.]
 DE.HSS.IC.B

Make inferences and justify conclusions from sample surveys, experiments, and observational studies. [See: Collecting Data.]
 DE.HSS.IC.B.3

Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. [See: Probability, Inference, and Sample Size; Collecting Data.]
 DE.HSS.IC.B.4

Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. [See: Collecting Data.]
 DE.HSS.IC.B.6

Evaluate reports based on data. [See: Threats to Validity.]
 DE.HSS.ID.A

Summarize, represent, and interpret data on a single count or measurement variable. [See: Bar and Pie Charts; Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 DE.HSS.ID.A.1

Represent data with plots on the real number line (dot plots, histograms, and box plots). [See: Histograms; Visualizing the “Shape” of Data; Box Plots; Standard Deviation.]
 DE.HSS.ID.A.2

Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. [See: Histograms; Measures of Center; Box Plots; Standard Deviation.]
 DE.HSS.ID.A.3

Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots; Standard Deviation.]
 DE.HSS.ID.B

Summarize, represent, and interpret data on two categorical and quantitative variables. [See: Scatter Plots; Correlations.]
 DE.HSS.ID.B.6

Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. [See: Scatter Plots; Correlations.]
 DE.HSS.ID.B.6.A

Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. [See: Linear Regression.]
 DE.HSS.ID.B.6.C

Fit a linear function for a scatter plot that suggests a linear association. [See: Linear Regression.]
 DE.HSS.ID.C

Interpret linear models. [See: Linear Regression.]
 DE.HSS.ID.C.7

Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. [See: Linear Regression.]
 DE.HSS.ID.C.8

Compute (using technology) and interpret the correlation coefficient of a linear fit. [See: Scatter Plots; Correlations; Linear Regression.]
 DE.HSS.ID.C.9

Distinguish between correlation and causation. [See: Correlations; Linear Regression.]
 DE.SL.910.1

Initiate and participate effectively in a range of collaborative discussions (oneonone, in groups, and teacherled) with diverse partners on grades 910 topics, texts, and issues, building on others' ideas and expressing their own clearly and persuasively. [See: Introduction to Data Science.]
Delaware Standards
 GA.5.G.A.1

Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., xaxis and xcoordinate, yaxis and ycoordinate). [See: Coordinates and Game Design.]
 GA.5.OA.A

Write and interpret numerical expressions. [See: Order of Operations.]
 GA.5.OA.A.1

Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. [See: Order of Operations.]
 GA.6.EE.B

Reason about and solve onevariable equations and inequalities. [See: Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 GA.6.EE.B.6

Use variables to represent numbers and write expressions when solving a realworld or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. [See: Piecewise Functions and Conditionals; Function Composition; Defining Values; Functions Make Life Easier!; Functions: Contracts, Examples & Definitions; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Surface Area of a Rectangular Prism; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality; Defining Table Functions; Grouped Samples; Linear Regression.]
 GA.6.EE.B.8

Write an inequality of the form x > c or x < c to represent a constraint or condition in a realworld or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. [See: Simple Inequalities; Sam the Butterfly  Applying Inequalities.]
 GA.6.G.A

Solve realworld and mathematical problems involving area, surface area, and volume. [See: Surface Area of a Rectangular Prism.]
 GA.6.G.A.4

Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [See: Surface Area of a Rectangular Prism.]
 GA.6.RP.A

Understand ratio concepts and use ratio reasoning to solve problems. [See: Making Flags; Bar and Pie Charts.]
 GA.6.RP.A.1

Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. [See: Making Flags.]
 GA.6.RP.A.3.D

Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. [See: Making Flags.]
 GA.6.SP.A

Develop understanding of statistical variability. [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 GA.6.SP.A.1

Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. [See: Introduction to Data Science; The Data Cycle; Choosing Your Dataset.]
 GA.6.SP.A.2

Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots; Standard Deviation.]
 GA.6.SP.A.3

Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. [See: Box Plots; Standard Deviation.]
 GA.6.SP.B

Summarize and describe distributions. [See: Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 GA.6.SP.B.4

Display numerical data in plots on a number line, including dot plots, histograms, and box plots. [See: Histograms; Visualizing the “Shape” of Data; Box Plots; Standard Deviation.]
 GA.6.SP.B.5

Summarize numerical data sets in relation to their context. [See: Measures of Center; Box Plots; Standard Deviation.]
 GA.6.SP.B.5.C

Summarize numerical data sets in relation to their context by giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. [See: Measures of Center; Box Plots; Standard Deviation.]
 GA.6.SP.B.5.D

Summarize numerical data sets in relation to their context by relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. [See: Measures of Center.]
 GA.7.EE.A.2

Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. [See: Problem Decomposition.]
 GA.7.EE.B

Solve reallife and mathematical problems using numerical and algebraic expressions and equations. [See: Piecewise Functions and Conditionals; Solving Word Problems with the Design Recipe; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Player Animation; The Distance Formula.]
 GA.7.EE.B.4

Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. [See: Defining Values; Functions Make Life Easier!; Solving Word Problems with the Design Recipe; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 GA.7.G.B.4

Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. [See: Solving Word Problems with the Design Recipe.]
 GA.7.G.B.6

Solve realworld and mathematical problems involving area, volume and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [See: Solving Word Problems with the Design Recipe; Surface Area of a Rectangular Prism.]
 GA.7.RP.A

Analyze proportional relationships and use them to solve realworld and mathematical problems. [See: Making Flags; Making Game Images.]
 GA.7.RP.A.1

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. [See: Making Flags.]
 GA.7.RP.A.2.A

Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. [See: Functions Can Be Linear; Defining Linear Functions.]
 GA.7.RP.A.2.B

Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. [See: Functions Can Be Linear; Defining Linear Functions.]
 GA.7.SP.A

Use random sampling to draw inferences about a population. [See: Probability, Inference, and Sample Size.]
 GA.7.SP.A.1

Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. [See: Probability, Inference, and Sample Size.]
 GA.7.SP.A.2

Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. [See: Probability, Inference, and Sample Size.]
 GA.7.SP.B

Draw informal comparative inferences about two populations. [See: Bar and Pie Charts.]
 GA.8.EE.B

Understand the connections between proportional relationships, lines, and linear equations. [See: Functions Can Be Linear; Defining Linear Functions.]
 GA.8.EE.B.5

Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [See: Functions Can Be Linear; Defining Linear Functions.]
 GA.8.F.A.1

Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. [See: Contracts; The Vertical Line Test.]
 GA.8.F.A.2

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [See: Functions Can Be Linear; Defining Linear Functions.]
 GA.8.F.A.3

Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. [See: Functions Can Be Linear; Defining Linear Functions.]
 GA.8.F.B

Use functions to model relationships between quantities. [See: Functions Make Life Easier!; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition.]
 GA.8.F.B.4

Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. [See: Functions Can Be Linear; Defining Linear Functions.]
 GA.8.F.B.5

Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. [See: Functions Can Be Linear; Defining Linear Functions.]
 GA.8.G.A.1

Verify experimentally the properties of rotations, reflections, and translations. [See: Making Game Images.]
 GA.8.G.B

Understand and apply the Pythagorean Theorem. [See: The Distance Formula.]
 GA.8.G.B.7

Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions. [See: The Distance Formula.]
 GA.8.G.B.8

Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. [See: The Distance Formula.]
 GA.8.SP.A.1

Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. [See: Scatter Plots; Grouped Samples; Correlations; Linear Regression.]
 GA.8.SP.A.2

Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. [See: Scatter Plots; Correlations; Linear Regression.]
 GA.8.SP.A.3

Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. [See: Linear Regression.]
 GA.HSA.CED.A

Create equations that describe numbers or relationships. [See: Solving Word Problems with the Design Recipe; Surface Area of a Rectangular Prism; Problem Decomposition; Sam the Butterfly  Applying Inequalities.]
 GA.HSA.CED.A.1

Create equations and inequalities in one variable and use them to solve problems. [See: Sam the Butterfly  Applying Inequalities.]
 GA.HSA.CED.A.2

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [See: Sam the Butterfly  Applying Inequalities.]
 GA.HSA.CED.A.3

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. [See: Sam the Butterfly  Applying Inequalities.]
 GA.HSA.SSE.A.1

Interpret expressions that represent a quantity in terms of its context. [See: Defining Values; Functions Make Life Easier!; Solving Word Problems with the Design Recipe.]
 GA.HSA.SSE.A.1.A

Interpret parts of an expression, such as terms, factors, and coefficients. [See: Piecewise Functions and Conditionals; Player Animation.]
 GA.HSA.SSE.A.1.B

Interpret complicated expressions by viewing one or more of their parts as a single entity. [See: Piecewise Functions and Conditionals; Player Animation; Custom Scatter Plots.]
 GA.HSA.SSE.A.2

Use the structure of an expression to identify ways to rewrite it. [See: Order of Operations.]
 GA.HSA.SSE.B

Write expressions in equivalent forms to solve problems. [See: Order of Operations.]
 GA.HSF.BF.A

Build a function that models a relationship between two quantities. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 GA.HSF.BF.A.1

Write a function that describes a relationship between two quantities. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 GA.HSF.BF.A.1.B

Combine standard function types using arithmetic operations. [See: Function Composition.]
 GA.HSF.BF.A.1.C

Compose functions. [See: Function Composition; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality.]
 GA.HSF.BF.B

Build new functions from existing functions. [See: Problem Decomposition; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality.]
 GA.HSF.IF.A

Understand the concept of a function and use function notation. [See: Functions Make Life Easier!; Function Notation.]
 GA.HSF.IF.A.1

Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). [See: Contracts; The Vertical Line Test.]
 GA.HSF.IF.A.2

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. [See: Contracts; Making Flags; Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 GA.HSF.IF.B

Interpret functions that arise in applications in terms of the context. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 GA.HSF.IF.B.5

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. [See: Functions Can Be Linear; Defining Linear Functions.]
 GA.HSF.IF.C

Analyze functions using different representations. [See: The Vertical Line Test; Functions: Contracts, Examples & Definitions; Functions Can Be Linear; Defining Linear Functions; Solving Word Problems with the Design Recipe.]
 GA.HSF.IF.C.9

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [See: Functions Can Be Linear; Defining Linear Functions; Problem Decomposition.]
 GA.HSN.Q.A

Reason quantitatively and use units to solve problems. [See: Making Flags.]
 GA.HSS.CP.A.1

Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ('or', 'and', 'not'). [See: Compound Inequalities: Solutions & NonSolutions.]
 GA.HSS.CP.B.9

Use permutations and combinations to compute probabilities of compound events and solve problems. [See: Permutations; Combinations.]
 GA.HSS.IC.A

Understand and evaluate random processes underlying statistical experiments. [See: Probability, Inference, and Sample Size.]
 GA.HSS.IC.A.1

Understand statistics as a process for making inferences about population parameters based on a random sample from that population. [See: Probability, Inference, and Sample Size.]
 GA.HSS.IC.B

Make inferences and justify conclusions from sample surveys, experiments, and observational studies. [See: Collecting Data.]
 GA.HSS.IC.B.3

Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. [See: Probability, Inference, and Sample Size; Collecting Data.]
 GA.HSS.IC.B.4

Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. [See: Collecting Data.]
 GA.HSS.IC.B.6

Evaluate reports based on data. [See: Threats to Validity.]
 GA.HSS.ID.A

Summarize, represent, and interpret data on a single count or measurement variable. [See: Bar and Pie Charts; Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 GA.HSS.ID.A.1

Represent data with plots on the real number line (dot plots, histograms, and box plots). [See: Histograms; Visualizing the “Shape” of Data; Box Plots; Standard Deviation.]
 GA.HSS.ID.A.2

Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. [See: Histograms; Measures of Center; Box Plots; Standard Deviation.]
 GA.HSS.ID.A.3

Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots; Standard Deviation.]
 GA.HSS.ID.B

Summarize, represent, and interpret data on two categorical and quantitative variables. [See: Scatter Plots; Correlations.]
 GA.HSS.ID.B.6

Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. [See: Scatter Plots; Correlations.]
 GA.HSS.ID.B.6.A

Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. [See: Linear Regression.]
 GA.HSS.ID.B.6.C

Fit a linear function for a scatter plot that suggests a linear association. [See: Linear Regression.]
 GA.HSS.ID.C

Interpret linear models. [See: Linear Regression.]
 GA.HSS.ID.C.7

Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. [See: Linear Regression.]
 GA.HSS.ID.C.8

Compute (using technology) and interpret the correlation coefficient of a linear fit. [See: Scatter Plots; Correlations; Linear Regression.]
 GA.HSS.ID.C.9

Distinguish between correlation and causation. [See: Correlations; Linear Regression.]
 GA.SL.910.1

Initiate and participate effectively in a range of collaborative discussions (oneonone, in groups, and teacherled) with diverse partners on grades 910 topics, texts, and issues, building on others' ideas and expressing their own clearly and persuasively. [See: Introduction to Data Science.]
Hawaii Standards
 HI.5.G.A.1

Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., xaxis and xcoordinate, yaxis and ycoordinate). [See: Coordinates and Game Design.]
 HI.5.OA.A

Write and interpret numerical expressions. [See: Order of Operations.]
 HI.5.OA.A.1

Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. [See: Order of Operations.]
 HI.6.EE.B

Reason about and solve onevariable equations and inequalities. [See: Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 HI.6.EE.B.6

Use variables to represent numbers and write expressions when solving a realworld or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. [See: Piecewise Functions and Conditionals; Function Composition; Defining Values; Functions Make Life Easier!; Functions: Contracts, Examples & Definitions; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Surface Area of a Rectangular Prism; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality; Defining Table Functions; Grouped Samples; Linear Regression.]
 HI.6.EE.B.8

Write an inequality of the form x > c or x < c to represent a constraint or condition in a realworld or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. [See: Simple Inequalities; Sam the Butterfly  Applying Inequalities.]
 HI.6.G.A

Solve realworld and mathematical problems involving area, surface area, and volume. [See: Surface Area of a Rectangular Prism.]
 HI.6.G.A.4

Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [See: Surface Area of a Rectangular Prism.]
 HI.6.RP.A

Understand ratio concepts and use ratio reasoning to solve problems. [See: Making Flags; Bar and Pie Charts.]
 HI.6.RP.A.1

Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. [See: Making Flags.]
 HI.6.RP.A.3.D

Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. [See: Making Flags.]
 HI.6.SP.A

Develop understanding of statistical variability. [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 HI.6.SP.A.1

Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. [See: Introduction to Data Science; The Data Cycle; Choosing Your Dataset.]
 HI.6.SP.A.2

Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots; Standard Deviation.]
 HI.6.SP.A.3

Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. [See: Box Plots; Standard Deviation.]
 HI.6.SP.B

Summarize and describe distributions. [See: Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 HI.6.SP.B.4

Display numerical data in plots on a number line, including dot plots, histograms, and box plots. [See: Histograms; Visualizing the “Shape” of Data; Box Plots; Standard Deviation.]
 HI.6.SP.B.5

Summarize numerical data sets in relation to their context. [See: Measures of Center; Box Plots; Standard Deviation.]
 HI.6.SP.B.5.C

Summarize numerical data sets in relation to their context by giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. [See: Measures of Center; Box Plots; Standard Deviation.]
 HI.6.SP.B.5.D

Summarize numerical data sets in relation to their context by relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. [See: Measures of Center.]
 HI.7.EE.A.2

Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. [See: Problem Decomposition.]
 HI.7.EE.B

Solve reallife and mathematical problems using numerical and algebraic expressions and equations. [See: Piecewise Functions and Conditionals; Solving Word Problems with the Design Recipe; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Player Animation; The Distance Formula.]
 HI.7.EE.B.4

Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. [See: Defining Values; Functions Make Life Easier!; Solving Word Problems with the Design Recipe; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 HI.7.G.B.4

Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. [See: Solving Word Problems with the Design Recipe.]
 HI.7.G.B.6

Solve realworld and mathematical problems involving area, volume and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [See: Solving Word Problems with the Design Recipe; Surface Area of a Rectangular Prism.]
 HI.7.RP.A

Analyze proportional relationships and use them to solve realworld and mathematical problems. [See: Making Flags; Making Game Images.]
 HI.7.RP.A.1

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. [See: Making Flags.]
 HI.7.RP.A.2.A

Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. [See: Functions Can Be Linear; Defining Linear Functions.]
 HI.7.RP.A.2.B

Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. [See: Functions Can Be Linear; Defining Linear Functions.]
 HI.7.SP.A

Use random sampling to draw inferences about a population. [See: Probability, Inference, and Sample Size.]
 HI.7.SP.A.1

Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. [See: Probability, Inference, and Sample Size.]
 HI.7.SP.A.2

Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. [See: Probability, Inference, and Sample Size.]
 HI.7.SP.B

Draw informal comparative inferences about two populations. [See: Bar and Pie Charts.]
 HI.8.EE.B

Understand the connections between proportional relationships, lines, and linear equations. [See: Functions Can Be Linear; Defining Linear Functions.]
 HI.8.EE.B.5

Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [See: Functions Can Be Linear; Defining Linear Functions.]
 HI.8.F.A.1

Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. [See: Contracts; The Vertical Line Test.]
 HI.8.F.A.2

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [See: Functions Can Be Linear; Defining Linear Functions.]
 HI.8.F.A.3

Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. [See: Functions Can Be Linear; Defining Linear Functions.]
 HI.8.F.B

Use functions to model relationships between quantities. [See: Functions Make Life Easier!; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition.]
 HI.8.F.B.4

Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. [See: Functions Can Be Linear; Defining Linear Functions.]
 HI.8.F.B.5

Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. [See: Functions Can Be Linear; Defining Linear Functions.]
 HI.8.G.A.1

Verify experimentally the properties of rotations, reflections, and translations. [See: Making Game Images.]
 HI.8.G.B

Understand and apply the Pythagorean Theorem. [See: The Distance Formula.]
 HI.8.G.B.7

Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions. [See: The Distance Formula.]
 HI.8.G.B.8

Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. [See: The Distance Formula.]
 HI.8.SP.A.1

Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. [See: Scatter Plots; Grouped Samples; Correlations; Linear Regression.]
 HI.8.SP.A.2

Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. [See: Scatter Plots; Correlations; Linear Regression.]
 HI.8.SP.A.3

Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. [See: Linear Regression.]
 HI.HSA.CED.A

Create equations that describe numbers or relationships. [See: Solving Word Problems with the Design Recipe; Surface Area of a Rectangular Prism; Problem Decomposition; Sam the Butterfly  Applying Inequalities.]
 HI.HSA.CED.A.1

Create equations and inequalities in one variable and use them to solve problems. [See: Sam the Butterfly  Applying Inequalities.]
 HI.HSA.CED.A.2

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [See: Sam the Butterfly  Applying Inequalities.]
 HI.HSA.CED.A.3

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. [See: Sam the Butterfly  Applying Inequalities.]
 HI.HSA.SSE.A.1

Interpret expressions that represent a quantity in terms of its context. [See: Defining Values; Functions Make Life Easier!; Solving Word Problems with the Design Recipe.]
 HI.HSA.SSE.A.1.A

Interpret parts of an expression, such as terms, factors, and coefficients. [See: Piecewise Functions and Conditionals; Player Animation.]
 HI.HSA.SSE.A.1.B

Interpret complicated expressions by viewing one or more of their parts as a single entity. [See: Piecewise Functions and Conditionals; Player Animation; Custom Scatter Plots.]
 HI.HSA.SSE.A.2

Use the structure of an expression to identify ways to rewrite it. [See: Order of Operations.]
 HI.HSA.SSE.B

Write expressions in equivalent forms to solve problems. [See: Order of Operations.]
 HI.HSF.BF.A

Build a function that models a relationship between two quantities. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 HI.HSF.BF.A.1

Write a function that describes a relationship between two quantities. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 HI.HSF.BF.A.1.B

Combine standard function types using arithmetic operations. [See: Function Composition.]
 HI.HSF.BF.A.1.C

Compose functions. [See: Function Composition; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality.]
 HI.HSF.BF.B

Build new functions from existing functions. [See: Problem Decomposition; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality.]
 HI.HSF.IF.A

Understand the concept of a function and use function notation. [See: Functions Make Life Easier!; Function Notation.]
 HI.HSF.IF.A.1

Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). [See: Contracts; The Vertical Line Test.]
 HI.HSF.IF.A.2

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. [See: Contracts; Making Flags; Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 HI.HSF.IF.B

Interpret functions that arise in applications in terms of the context. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 HI.HSF.IF.B.5

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. [See: Functions Can Be Linear; Defining Linear Functions.]
 HI.HSF.IF.C

Analyze functions using different representations. [See: The Vertical Line Test; Functions: Contracts, Examples & Definitions; Functions Can Be Linear; Defining Linear Functions; Solving Word Problems with the Design Recipe.]
 HI.HSF.IF.C.9

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [See: Functions Can Be Linear; Defining Linear Functions; Problem Decomposition.]
 HI.HSN.Q.A

Reason quantitatively and use units to solve problems. [See: Making Flags.]
 HI.HSS.CP.A.1

Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ('or', 'and', 'not'). [See: Compound Inequalities: Solutions & NonSolutions.]
 HI.HSS.CP.B.9

Use permutations and combinations to compute probabilities of compound events and solve problems. [See: Permutations; Combinations.]
 HI.HSS.IC.A

Understand and evaluate random processes underlying statistical experiments. [See: Probability, Inference, and Sample Size.]
 HI.HSS.IC.A.1

Understand statistics as a process for making inferences about population parameters based on a random sample from that population. [See: Probability, Inference, and Sample Size.]
 HI.HSS.IC.B

Make inferences and justify conclusions from sample surveys, experiments, and observational studies. [See: Collecting Data.]
 HI.HSS.IC.B.3

Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. [See: Probability, Inference, and Sample Size; Collecting Data.]
 HI.HSS.IC.B.4

Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. [See: Collecting Data.]
 HI.HSS.IC.B.6

Evaluate reports based on data. [See: Threats to Validity.]
 HI.HSS.ID.A

Summarize, represent, and interpret data on a single count or measurement variable. [See: Bar and Pie Charts; Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 HI.HSS.ID.A.1

Represent data with plots on the real number line (dot plots, histograms, and box plots). [See: Histograms; Visualizing the “Shape” of Data; Box Plots; Standard Deviation.]
 HI.HSS.ID.A.2

Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. [See: Histograms; Measures of Center; Box Plots; Standard Deviation.]
 HI.HSS.ID.A.3

Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots; Standard Deviation.]
 HI.HSS.ID.B

Summarize, represent, and interpret data on two categorical and quantitative variables. [See: Scatter Plots; Correlations.]
 HI.HSS.ID.B.6

Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. [See: Scatter Plots; Correlations.]
 HI.HSS.ID.B.6.A

Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. [See: Linear Regression.]
 HI.HSS.ID.B.6.C

Fit a linear function for a scatter plot that suggests a linear association. [See: Linear Regression.]
 HI.HSS.ID.C

Interpret linear models. [See: Linear Regression.]
 HI.HSS.ID.C.7

Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. [See: Linear Regression.]
 HI.HSS.ID.C.8

Compute (using technology) and interpret the correlation coefficient of a linear fit. [See: Scatter Plots; Correlations; Linear Regression.]
 HI.HSS.ID.C.9

Distinguish between correlation and causation. [See: Correlations; Linear Regression.]
 HI.SL.910.1

Initiate and participate effectively in a range of collaborative discussions (oneonone, in groups, and teacherled) with diverse partners on grades 910 topics, texts, and issues, building on others' ideas and expressing their own clearly and persuasively. [See: Introduction to Data Science.]
Idaho Standards
 ID.5.G.A.1

Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., xaxis and xcoordinate, yaxis and ycoordinate). [See: Coordinates and Game Design.]
 ID.5.OA.A

Write and interpret numerical expressions. [See: Order of Operations.]
 ID.5.OA.A.1

Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. [See: Order of Operations.]
 ID.6.EE.B

Reason about and solve onevariable equations and inequalities. [See: Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 ID.6.EE.B.6

Use variables to represent numbers and write expressions when solving a realworld or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. [See: Piecewise Functions and Conditionals; Function Composition; Defining Values; Functions Make Life Easier!; Functions: Contracts, Examples & Definitions; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Surface Area of a Rectangular Prism; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality; Defining Table Functions; Grouped Samples; Linear Regression.]
 ID.6.EE.B.8

Write an inequality of the form x > c or x < c to represent a constraint or condition in a realworld or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. [See: Simple Inequalities; Sam the Butterfly  Applying Inequalities.]
 ID.6.G.A

Solve realworld and mathematical problems involving area, surface area, and volume. [See: Surface Area of a Rectangular Prism.]
 ID.6.G.A.4

Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [See: Surface Area of a Rectangular Prism.]
 ID.6.RP.A

Understand ratio concepts and use ratio reasoning to solve problems. [See: Making Flags; Bar and Pie Charts.]
 ID.6.RP.A.1

Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. [See: Making Flags.]
 ID.6.RP.A.3.D

Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. [See: Making Flags.]
 ID.6.SP.A

Develop understanding of statistical variability. [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 ID.6.SP.A.1

Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. [See: Introduction to Data Science; The Data Cycle; Choosing Your Dataset.]
 ID.6.SP.A.2

Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots; Standard Deviation.]
 ID.6.SP.A.3

Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. [See: Box Plots; Standard Deviation.]
 ID.6.SP.B

Summarize and describe distributions. [See: Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 ID.6.SP.B.4

Display numerical data in plots on a number line, including dot plots, histograms, and box plots. [See: Histograms; Visualizing the “Shape” of Data; Box Plots; Standard Deviation.]
 ID.6.SP.B.5

Summarize numerical data sets in relation to their context. [See: Measures of Center; Box Plots; Standard Deviation.]
 ID.6.SP.B.5.C

Summarize numerical data sets in relation to their context by giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. [See: Measures of Center; Box Plots; Standard Deviation.]
 ID.6.SP.B.5.D

Summarize numerical data sets in relation to their context by relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. [See: Measures of Center.]
 ID.7.EE.A.2

Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. [See: Problem Decomposition.]
 ID.7.EE.B

Solve reallife and mathematical problems using numerical and algebraic expressions and equations. [See: Piecewise Functions and Conditionals; Solving Word Problems with the Design Recipe; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Player Animation; The Distance Formula.]
 ID.7.EE.B.4

Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. [See: Defining Values; Functions Make Life Easier!; Solving Word Problems with the Design Recipe; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 ID.7.G.B.4

Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. [See: Solving Word Problems with the Design Recipe.]
 ID.7.G.B.6

Solve realworld and mathematical problems involving area, volume and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [See: Solving Word Problems with the Design Recipe; Surface Area of a Rectangular Prism.]
 ID.7.RP.A

Analyze proportional relationships and use them to solve realworld and mathematical problems. [See: Making Flags; Making Game Images.]
 ID.7.RP.A.1

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. [See: Making Flags.]
 ID.7.RP.A.2.A

Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. [See: Functions Can Be Linear; Defining Linear Functions.]
 ID.7.RP.A.2.B

Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. [See: Functions Can Be Linear; Defining Linear Functions.]
 ID.7.SP.A

Use random sampling to draw inferences about a population. [See: Probability, Inference, and Sample Size.]
 ID.7.SP.A.1

Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. [See: Probability, Inference, and Sample Size.]
 ID.7.SP.A.2

Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. [See: Probability, Inference, and Sample Size.]
 ID.7.SP.B

Draw informal comparative inferences about two populations. [See: Bar and Pie Charts.]
 ID.8.EE.B

Understand the connections between proportional relationships, lines, and linear equations. [See: Functions Can Be Linear; Defining Linear Functions.]
 ID.8.EE.B.5

Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [See: Functions Can Be Linear; Defining Linear Functions.]
 ID.8.F.A.1

Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. [See: Contracts; The Vertical Line Test.]
 ID.8.F.A.2

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [See: Functions Can Be Linear; Defining Linear Functions.]
 ID.8.F.A.3

Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. [See: Functions Can Be Linear; Defining Linear Functions.]
 ID.8.F.B

Use functions to model relationships between quantities. [See: Functions Make Life Easier!; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition.]
 ID.8.F.B.4

Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. [See: Functions Can Be Linear; Defining Linear Functions.]
 ID.8.F.B.5

Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. [See: Functions Can Be Linear; Defining Linear Functions.]
 ID.8.G.A.1

Verify experimentally the properties of rotations, reflections, and translations. [See: Making Game Images.]
 ID.8.G.B

Understand and apply the Pythagorean Theorem. [See: The Distance Formula.]
 ID.8.G.B.7

Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions. [See: The Distance Formula.]
 ID.8.G.B.8

Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. [See: The Distance Formula.]
 ID.8.SP.A.1

Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. [See: Scatter Plots; Grouped Samples; Correlations; Linear Regression.]
 ID.8.SP.A.2

Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. [See: Scatter Plots; Correlations; Linear Regression.]
 ID.8.SP.A.3

Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. [See: Linear Regression.]
 ID.HSA.CED.A

Create equations that describe numbers or relationships. [See: Solving Word Problems with the Design Recipe; Surface Area of a Rectangular Prism; Problem Decomposition; Sam the Butterfly  Applying Inequalities.]
 ID.HSA.CED.A.1

Create equations and inequalities in one variable and use them to solve problems. [See: Sam the Butterfly  Applying Inequalities.]
 ID.HSA.CED.A.2

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [See: Sam the Butterfly  Applying Inequalities.]
 ID.HSA.CED.A.3

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. [See: Sam the Butterfly  Applying Inequalities.]
 ID.HSA.SSE.A.1

Interpret expressions that represent a quantity in terms of its context. [See: Defining Values; Functions Make Life Easier!; Solving Word Problems with the Design Recipe.]
 ID.HSA.SSE.A.1.A

Interpret parts of an expression, such as terms, factors, and coefficients. [See: Piecewise Functions and Conditionals; Player Animation.]
 ID.HSA.SSE.A.1.B

Interpret complicated expressions by viewing one or more of their parts as a single entity. [See: Piecewise Functions and Conditionals; Player Animation; Custom Scatter Plots.]
 ID.HSA.SSE.A.2

Use the structure of an expression to identify ways to rewrite it. [See: Order of Operations.]
 ID.HSA.SSE.B

Write expressions in equivalent forms to solve problems. [See: Order of Operations.]
 ID.HSF.BF.A

Build a function that models a relationship between two quantities. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 ID.HSF.BF.A.1

Write a function that describes a relationship between two quantities. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 ID.HSF.BF.A.1.B

Combine standard function types using arithmetic operations. [See: Function Composition.]
 ID.HSF.BF.A.1.C

Compose functions. [See: Function Composition; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality.]
 ID.HSF.BF.B

Build new functions from existing functions. [See: Problem Decomposition; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality.]
 ID.HSF.IF.A

Understand the concept of a function and use function notation. [See: Functions Make Life Easier!; Function Notation.]
 ID.HSF.IF.A.1

Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). [See: Contracts; The Vertical Line Test.]
 ID.HSF.IF.A.2

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. [See: Contracts; Making Flags; Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 ID.HSF.IF.B

Interpret functions that arise in applications in terms of the context. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 ID.HSF.IF.B.5

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. [See: Functions Can Be Linear; Defining Linear Functions.]
 ID.HSF.IF.C

Analyze functions using different representations. [See: The Vertical Line Test; Functions: Contracts, Examples & Definitions; Functions Can Be Linear; Defining Linear Functions; Solving Word Problems with the Design Recipe.]
 ID.HSF.IF.C.9

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [See: Functions Can Be Linear; Defining Linear Functions; Problem Decomposition.]
 ID.HSN.Q.A

Reason quantitatively and use units to solve problems. [See: Making Flags.]
 ID.HSS.CP.A.1

Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ('or', 'and', 'not'). [See: Compound Inequalities: Solutions & NonSolutions.]
 ID.HSS.CP.B.9

Use permutations and combinations to compute probabilities of compound events and solve problems. [See: Permutations; Combinations.]
 ID.HSS.IC.A

Understand and evaluate random processes underlying statistical experiments. [See: Probability, Inference, and Sample Size.]
 ID.HSS.IC.A.1

Understand statistics as a process for making inferences about population parameters based on a random sample from that population. [See: Probability, Inference, and Sample Size.]
 ID.HSS.IC.B

Make inferences and justify conclusions from sample surveys, experiments, and observational studies. [See: Collecting Data.]
 ID.HSS.IC.B.3

Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. [See: Probability, Inference, and Sample Size; Collecting Data.]
 ID.HSS.IC.B.4

Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. [See: Collecting Data.]
 ID.HSS.IC.B.6

Evaluate reports based on data. [See: Threats to Validity.]
 ID.HSS.ID.A

Summarize, represent, and interpret data on a single count or measurement variable. [See: Bar and Pie Charts; Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 ID.HSS.ID.A.1

Represent data with plots on the real number line (dot plots, histograms, and box plots). [See: Histograms; Visualizing the “Shape” of Data; Box Plots; Standard Deviation.]
 ID.HSS.ID.A.2

Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. [See: Histograms; Measures of Center; Box Plots; Standard Deviation.]
 ID.HSS.ID.A.3

Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots; Standard Deviation.]
 ID.HSS.ID.B

Summarize, represent, and interpret data on two categorical and quantitative variables. [See: Scatter Plots; Correlations.]
 ID.HSS.ID.B.6

Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. [See: Scatter Plots; Correlations.]
 ID.HSS.ID.B.6.A

Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. [See: Linear Regression.]
 ID.HSS.ID.B.6.C

Fit a linear function for a scatter plot that suggests a linear association. [See: Linear Regression.]
 ID.HSS.ID.C

Interpret linear models. [See: Linear Regression.]
 ID.HSS.ID.C.7

Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. [See: Linear Regression.]
 ID.HSS.ID.C.8

Compute (using technology) and interpret the correlation coefficient of a linear fit. [See: Scatter Plots; Correlations; Linear Regression.]
 ID.HSS.ID.C.9

Distinguish between correlation and causation. [See: Correlations; Linear Regression.]
 ID.SL.910.1

Initiate and participate effectively in a range of collaborative discussions (oneonone, in groups, and teacherled) with diverse partners on grades 910 topics, texts, and issues, building on others' ideas and expressing their own clearly and persuasively. [See: Introduction to Data Science.]
Illinois Standards
 IL.5.G.A.1

Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., xaxis and xcoordinate, yaxis and ycoordinate). [See: Coordinates and Game Design.]
 IL.5.OA.A

Write and interpret numerical expressions. [See: Order of Operations.]
 IL.5.OA.A.1

Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. [See: Order of Operations.]
 IL.6.EE.B

Reason about and solve onevariable equations and inequalities. [See: Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 IL.6.EE.B.6

Use variables to represent numbers and write expressions when solving a realworld or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. [See: Piecewise Functions and Conditionals; Function Composition; Defining Values; Functions Make Life Easier!; Functions: Contracts, Examples & Definitions; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Surface Area of a Rectangular Prism; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality; Defining Table Functions; Grouped Samples; Linear Regression.]
 IL.6.EE.B.8

Write an inequality of the form x > c or x < c to represent a constraint or condition in a realworld or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. [See: Simple Inequalities; Sam the Butterfly  Applying Inequalities.]
 IL.6.G.A

Solve realworld and mathematical problems involving area, surface area, and volume. [See: Surface Area of a Rectangular Prism.]
 IL.6.G.A.4

Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [See: Surface Area of a Rectangular Prism.]
 IL.6.RP.A

Understand ratio concepts and use ratio reasoning to solve problems. [See: Making Flags; Bar and Pie Charts.]
 IL.6.RP.A.1

Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. [See: Making Flags.]
 IL.6.RP.A.3.D

Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. [See: Making Flags.]
 IL.6.SP.A

Develop understanding of statistical variability. [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 IL.6.SP.A.1

Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. [See: Introduction to Data Science; The Data Cycle; Choosing Your Dataset.]
 IL.6.SP.A.2

Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots; Standard Deviation.]
 IL.6.SP.A.3

Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. [See: Box Plots; Standard Deviation.]
 IL.6.SP.B

Summarize and describe distributions. [See: Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 IL.6.SP.B.4

Display numerical data in plots on a number line, including dot plots, histograms, and box plots. [See: Histograms; Visualizing the “Shape” of Data; Box Plots; Standard Deviation.]
 IL.6.SP.B.5

Summarize numerical data sets in relation to their context. [See: Measures of Center; Box Plots; Standard Deviation.]
 IL.6.SP.B.5.C

Summarize numerical data sets in relation to their context by giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. [See: Measures of Center; Box Plots; Standard Deviation.]
 IL.6.SP.B.5.D

Summarize numerical data sets in relation to their context by relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. [See: Measures of Center.]
 IL.7.EE.A.2

Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. [See: Problem Decomposition.]
 IL.7.EE.B

Solve reallife and mathematical problems using numerical and algebraic expressions and equations. [See: Piecewise Functions and Conditionals; Solving Word Problems with the Design Recipe; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Player Animation; The Distance Formula.]
 IL.7.EE.B.4

Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. [See: Defining Values; Functions Make Life Easier!; Solving Word Problems with the Design Recipe; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 IL.7.G.B.4

Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. [See: Solving Word Problems with the Design Recipe.]
 IL.7.G.B.6

Solve realworld and mathematical problems involving area, volume and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [See: Solving Word Problems with the Design Recipe; Surface Area of a Rectangular Prism.]
 IL.7.RP.A

Analyze proportional relationships and use them to solve realworld and mathematical problems. [See: Making Flags; Making Game Images.]
 IL.7.RP.A.1

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. [See: Making Flags.]
 IL.7.RP.A.2.A

Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. [See: Functions Can Be Linear; Defining Linear Functions.]
 IL.7.RP.A.2.B

Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. [See: Functions Can Be Linear; Defining Linear Functions.]
 IL.7.SP.A

Use random sampling to draw inferences about a population. [See: Probability, Inference, and Sample Size.]
 IL.7.SP.A.1

Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. [See: Probability, Inference, and Sample Size.]
 IL.7.SP.A.2

Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. [See: Probability, Inference, and Sample Size.]
 IL.7.SP.B

Draw informal comparative inferences about two populations. [See: Bar and Pie Charts.]
 IL.8.EE.B

Understand the connections between proportional relationships, lines, and linear equations. [See: Functions Can Be Linear; Defining Linear Functions.]
 IL.8.EE.B.5

Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [See: Functions Can Be Linear; Defining Linear Functions.]
 IL.8.F.A.1

Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. [See: Contracts; The Vertical Line Test.]
 IL.8.F.A.2

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [See: Functions Can Be Linear; Defining Linear Functions.]
 IL.8.F.A.3

Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. [See: Functions Can Be Linear; Defining Linear Functions.]
 IL.8.F.B

Use functions to model relationships between quantities. [See: Functions Make Life Easier!; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition.]
 IL.8.F.B.4

Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. [See: Functions Can Be Linear; Defining Linear Functions.]
 IL.8.F.B.5

Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. [See: Functions Can Be Linear; Defining Linear Functions.]
 IL.8.G.A.1

Verify experimentally the properties of rotations, reflections, and translations. [See: Making Game Images.]
 IL.8.G.B

Understand and apply the Pythagorean Theorem. [See: The Distance Formula.]
 IL.8.G.B.7

Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions. [See: The Distance Formula.]
 IL.8.G.B.8

Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. [See: The Distance Formula.]
 IL.8.SP.A.1

Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. [See: Scatter Plots; Grouped Samples; Correlations; Linear Regression.]
 IL.8.SP.A.2

Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. [See: Scatter Plots; Correlations; Linear Regression.]
 IL.8.SP.A.3

Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. [See: Linear Regression.]
 IL.HSA.CED.A

Create equations that describe numbers or relationships. [See: Solving Word Problems with the Design Recipe; Surface Area of a Rectangular Prism; Problem Decomposition; Sam the Butterfly  Applying Inequalities.]
 IL.HSA.CED.A.1

Create equations and inequalities in one variable and use them to solve problems. [See: Sam the Butterfly  Applying Inequalities.]
 IL.HSA.CED.A.2

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [See: Sam the Butterfly  Applying Inequalities.]
 IL.HSA.CED.A.3

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. [See: Sam the Butterfly  Applying Inequalities.]
 IL.HSA.SSE.A.1

Interpret expressions that represent a quantity in terms of its context. [See: Defining Values; Functions Make Life Easier!; Solving Word Problems with the Design Recipe.]
 IL.HSA.SSE.A.1.A

Interpret parts of an expression, such as terms, factors, and coefficients. [See: Piecewise Functions and Conditionals; Player Animation.]
 IL.HSA.SSE.A.1.B

Interpret complicated expressions by viewing one or more of their parts as a single entity. [See: Piecewise Functions and Conditionals; Player Animation; Custom Scatter Plots.]
 IL.HSA.SSE.A.2

Use the structure of an expression to identify ways to rewrite it. [See: Order of Operations.]
 IL.HSA.SSE.B

Write expressions in equivalent forms to solve problems. [See: Order of Operations.]
 IL.HSF.BF.A

Build a function that models a relationship between two quantities. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 IL.HSF.BF.A.1

Write a function that describes a relationship between two quantities. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 IL.HSF.BF.A.1.B

Combine standard function types using arithmetic operations. [See: Function Composition.]
 IL.HSF.BF.A.1.C

Compose functions. [See: Function Composition; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality.]
 IL.HSF.BF.B

Build new functions from existing functions. [See: Problem Decomposition; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality.]
 IL.HSF.IF.A

Understand the concept of a function and use function notation. [See: Functions Make Life Easier!; Function Notation.]
 IL.HSF.IF.A.1

Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). [See: Contracts; The Vertical Line Test.]
 IL.HSF.IF.A.2

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. [See: Contracts; Making Flags; Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 IL.HSF.IF.B

Interpret functions that arise in applications in terms of the context. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 IL.HSF.IF.B.5

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. [See: Functions Can Be Linear; Defining Linear Functions.]
 IL.HSF.IF.C

Analyze functions using different representations. [See: The Vertical Line Test; Functions: Contracts, Examples & Definitions; Functions Can Be Linear; Defining Linear Functions; Solving Word Problems with the Design Recipe.]
 IL.HSF.IF.C.9

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [See: Functions Can Be Linear; Defining Linear Functions; Problem Decomposition.]
 IL.HSN.Q.A

Reason quantitatively and use units to solve problems. [See: Making Flags.]
 IL.HSS.CP.A.1

Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ('or', 'and', 'not'). [See: Compound Inequalities: Solutions & NonSolutions.]
 IL.HSS.CP.B.9

Use permutations and combinations to compute probabilities of compound events and solve problems. [See: Permutations; Combinations.]
 IL.HSS.IC.A

Understand and evaluate random processes underlying statistical experiments. [See: Probability, Inference, and Sample Size.]
 IL.HSS.IC.A.1

Understand statistics as a process for making inferences about population parameters based on a random sample from that population. [See: Probability, Inference, and Sample Size.]
 IL.HSS.IC.B

Make inferences and justify conclusions from sample surveys, experiments, and observational studies. [See: Collecting Data.]
 IL.HSS.IC.B.3

Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. [See: Probability, Inference, and Sample Size; Collecting Data.]
 IL.HSS.IC.B.4

Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. [See: Collecting Data.]
 IL.HSS.IC.B.6

Evaluate reports based on data. [See: Threats to Validity.]
 IL.HSS.ID.A

Summarize, represent, and interpret data on a single count or measurement variable. [See: Bar and Pie Charts; Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 IL.HSS.ID.A.1

Represent data with plots on the real number line (dot plots, histograms, and box plots). [See: Histograms; Visualizing the “Shape” of Data; Box Plots; Standard Deviation.]
 IL.HSS.ID.A.2

Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. [See: Histograms; Measures of Center; Box Plots; Standard Deviation.]
 IL.HSS.ID.A.3

Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots; Standard Deviation.]
 IL.HSS.ID.B

Summarize, represent, and interpret data on two categorical and quantitative variables. [See: Scatter Plots; Correlations.]
 IL.HSS.ID.B.6

Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. [See: Scatter Plots; Correlations.]
 IL.HSS.ID.B.6.A

Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. [See: Linear Regression.]
 IL.HSS.ID.B.6.C

Fit a linear function for a scatter plot that suggests a linear association. [See: Linear Regression.]
 IL.HSS.ID.C

Interpret linear models. [See: Linear Regression.]
 IL.HSS.ID.C.7

Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. [See: Linear Regression.]
 IL.HSS.ID.C.8

Compute (using technology) and interpret the correlation coefficient of a linear fit. [See: Scatter Plots; Correlations; Linear Regression.]
 IL.HSS.ID.C.9

Distinguish between correlation and causation. [See: Correlations; Linear Regression.]
 IL.SL.910.1

Initiate and participate effectively in a range of collaborative discussions (oneonone, in groups, and teacherled) with diverse partners on grades 910 topics, texts, and issues, building on others' ideas and expressing their own clearly and persuasively. [See: Introduction to Data Science.]
Iowa Standards
 IA.5.G.A.1

Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., xaxis and xcoordinate, yaxis and ycoordinate). [See: Coordinates and Game Design.]
 IA.5.OA.A

Write and interpret numerical expressions. [See: Order of Operations.]
 IA.5.OA.A.1

Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. [See: Order of Operations.]
 IA.6.EE.B

Reason about and solve onevariable equations and inequalities. [See: Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 IA.6.EE.B.6

Use variables to represent numbers and write expressions when solving a realworld or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. [See: Piecewise Functions and Conditionals; Function Composition; Defining Values; Functions Make Life Easier!; Functions: Contracts, Examples & Definitions; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Surface Area of a Rectangular Prism; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality; Defining Table Functions; Grouped Samples; Linear Regression.]
 IA.6.EE.B.8

Write an inequality of the form x > c or x < c to represent a constraint or condition in a realworld or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. [See: Simple Inequalities; Sam the Butterfly  Applying Inequalities.]
 IA.6.G.A

Solve realworld and mathematical problems involving area, surface area, and volume. [See: Surface Area of a Rectangular Prism.]
 IA.6.G.A.4

Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [See: Surface Area of a Rectangular Prism.]
 IA.6.RP.A

Understand ratio concepts and use ratio reasoning to solve problems. [See: Making Flags; Bar and Pie Charts.]
 IA.6.RP.A.1

Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. [See: Making Flags.]
 IA.6.RP.A.3.D

Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. [See: Making Flags.]
 IA.6.SP.A

Develop understanding of statistical variability. [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 IA.6.SP.A.1

Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. [See: Introduction to Data Science; The Data Cycle; Choosing Your Dataset.]
 IA.6.SP.A.2

Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots; Standard Deviation.]
 IA.6.SP.A.3

Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. [See: Box Plots; Standard Deviation.]
 IA.6.SP.B

Summarize and describe distributions. [See: Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 IA.6.SP.B.4

Display numerical data in plots on a number line, including dot plots, histograms, and box plots. [See: Histograms; Visualizing the “Shape” of Data; Box Plots; Standard Deviation.]
 IA.6.SP.B.5

Summarize numerical data sets in relation to their context. [See: Measures of Center; Box Plots; Standard Deviation.]
 IA.6.SP.B.5.C

Summarize numerical data sets in relation to their context by giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. [See: Measures of Center; Box Plots; Standard Deviation.]
 IA.6.SP.B.5.D

Summarize numerical data sets in relation to their context by relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. [See: Measures of Center.]
 IA.7.EE.A.2

Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. [See: Problem Decomposition.]
 IA.7.EE.B

Solve reallife and mathematical problems using numerical and algebraic expressions and equations. [See: Piecewise Functions and Conditionals; Solving Word Problems with the Design Recipe; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Player Animation; The Distance Formula.]
 IA.7.EE.B.4

Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. [See: Defining Values; Functions Make Life Easier!; Solving Word Problems with the Design Recipe; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 IA.7.G.B.4

Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. [See: Solving Word Problems with the Design Recipe.]
 IA.7.G.B.6

Solve realworld and mathematical problems involving area, volume and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [See: Solving Word Problems with the Design Recipe; Surface Area of a Rectangular Prism.]
 IA.7.RP.A

Analyze proportional relationships and use them to solve realworld and mathematical problems. [See: Making Flags; Making Game Images.]
 IA.7.RP.A.1

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. [See: Making Flags.]
 IA.7.RP.A.2.A

Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. [See: Functions Can Be Linear; Defining Linear Functions.]
 IA.7.RP.A.2.B

Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. [See: Functions Can Be Linear; Defining Linear Functions.]
 IA.7.SP.A

Use random sampling to draw inferences about a population. [See: Probability, Inference, and Sample Size.]
 IA.7.SP.A.1

Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. [See: Probability, Inference, and Sample Size.]
 IA.7.SP.A.2

Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. [See: Probability, Inference, and Sample Size.]
 IA.7.SP.B

Draw informal comparative inferences about two populations. [See: Bar and Pie Charts.]
 IA.8.EE.B

Understand the connections between proportional relationships, lines, and linear equations. [See: Functions Can Be Linear; Defining Linear Functions.]
 IA.8.EE.B.5

Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [See: Functions Can Be Linear; Defining Linear Functions.]
 IA.8.F.A.1

Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. [See: Contracts; The Vertical Line Test.]
 IA.8.F.A.2

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [See: Functions Can Be Linear; Defining Linear Functions.]
 IA.8.F.A.3

Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. [See: Functions Can Be Linear; Defining Linear Functions.]
 IA.8.F.B

Use functions to model relationships between quantities. [See: Functions Make Life Easier!; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition.]
 IA.8.F.B.4

Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. [See: Functions Can Be Linear; Defining Linear Functions.]
 IA.8.F.B.5

Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. [See: Functions Can Be Linear; Defining Linear Functions.]
 IA.8.G.A.1

Verify experimentally the properties of rotations, reflections, and translations. [See: Making Game Images.]
 IA.8.G.B

Understand and apply the Pythagorean Theorem. [See: The Distance Formula.]
 IA.8.G.B.7

Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions. [See: The Distance Formula.]
 IA.8.G.B.8

Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. [See: The Distance Formula.]
 IA.8.SP.A.1

Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. [See: Scatter Plots; Grouped Samples; Correlations; Linear Regression.]
 IA.8.SP.A.2

Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. [See: Scatter Plots; Correlations; Linear Regression.]
 IA.8.SP.A.3

Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. [See: Linear Regression.]
 IA.HSA.CED.A

Create equations that describe numbers or relationships. [See: Solving Word Problems with the Design Recipe; Surface Area of a Rectangular Prism; Problem Decomposition; Sam the Butterfly  Applying Inequalities.]
 IA.HSA.CED.A.1

Create equations and inequalities in one variable and use them to solve problems. [See: Sam the Butterfly  Applying Inequalities.]
 IA.HSA.CED.A.2

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [See: Sam the Butterfly  Applying Inequalities.]
 IA.HSA.CED.A.3

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. [See: Sam the Butterfly  Applying Inequalities.]
 IA.HSA.SSE.A.1

Interpret expressions that represent a quantity in terms of its context. [See: Defining Values; Functions Make Life Easier!; Solving Word Problems with the Design Recipe.]
 IA.HSA.SSE.A.1.A

Interpret parts of an expression, such as terms, factors, and coefficients. [See: Piecewise Functions and Conditionals; Player Animation.]
 IA.HSA.SSE.A.1.B

Interpret complicated expressions by viewing one or more of their parts as a single entity. [See: Piecewise Functions and Conditionals; Player Animation; Custom Scatter Plots.]
 IA.HSA.SSE.A.2

Use the structure of an expression to identify ways to rewrite it. [See: Order of Operations.]
 IA.HSA.SSE.B

Write expressions in equivalent forms to solve problems. [See: Order of Operations.]
 IA.HSF.BF.A

Build a function that models a relationship between two quantities. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 IA.HSF.BF.A.1

Write a function that describes a relationship between two quantities. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 IA.HSF.BF.A.1.B

Combine standard function types using arithmetic operations. [See: Function Composition.]
 IA.HSF.BF.A.1.C

Compose functions. [See: Function Composition; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality.]
 IA.HSF.BF.B

Build new functions from existing functions. [See: Problem Decomposition; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality.]
 IA.HSF.IF.A

Understand the concept of a function and use function notation. [See: Functions Make Life Easier!; Function Notation.]
 IA.HSF.IF.A.1

Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). [See: Contracts; The Vertical Line Test.]
 IA.HSF.IF.A.2

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. [See: Contracts; Making Flags; Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 IA.HSF.IF.B

Interpret functions that arise in applications in terms of the context. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 IA.HSF.IF.B.5

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. [See: Functions Can Be Linear; Defining Linear Functions.]
 IA.HSF.IF.C

Analyze functions using different representations. [See: The Vertical Line Test; Functions: Contracts, Examples & Definitions; Functions Can Be Linear; Defining Linear Functions; Solving Word Problems with the Design Recipe.]
 IA.HSF.IF.C.9

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [See: Functions Can Be Linear; Defining Linear Functions; Problem Decomposition.]
 IA.HSN.Q.A

Reason quantitatively and use units to solve problems. [See: Making Flags.]
 IA.HSS.CP.A.1

Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ('or', 'and', 'not'). [See: Compound Inequalities: Solutions & NonSolutions.]
 IA.HSS.CP.B.9

Use permutations and combinations to compute probabilities of compound events and solve problems. [See: Permutations; Combinations.]
 IA.HSS.IC.A

Understand and evaluate random processes underlying statistical experiments. [See: Probability, Inference, and Sample Size.]
 IA.HSS.IC.A.1

Understand statistics as a process for making inferences about population parameters based on a random sample from that population. [See: Probability, Inference, and Sample Size.]
 IA.HSS.IC.B

Make inferences and justify conclusions from sample surveys, experiments, and observational studies. [See: Collecting Data.]
 IA.HSS.IC.B.3

Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. [See: Probability, Inference, and Sample Size; Collecting Data.]
 IA.HSS.IC.B.4

Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. [See: Collecting Data.]
 IA.HSS.IC.B.6

Evaluate reports based on data. [See: Threats to Validity.]
 IA.HSS.ID.A

Summarize, represent, and interpret data on a single count or measurement variable. [See: Bar and Pie Charts; Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 IA.HSS.ID.A.1

Represent data with plots on the real number line (dot plots, histograms, and box plots). [See: Histograms; Visualizing the “Shape” of Data; Box Plots; Standard Deviation.]
 IA.HSS.ID.A.2

Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. [See: Histograms; Measures of Center; Box Plots; Standard Deviation.]
 IA.HSS.ID.A.3

Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots; Standard Deviation.]
 IA.HSS.ID.B

Summarize, represent, and interpret data on two categorical and quantitative variables. [See: Scatter Plots; Correlations.]
 IA.HSS.ID.B.6

Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. [See: Scatter Plots; Correlations.]
 IA.HSS.ID.B.6.A

Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. [See: Linear Regression.]
 IA.HSS.ID.B.6.C

Fit a linear function for a scatter plot that suggests a linear association. [See: Linear Regression.]
 IA.HSS.ID.C

Interpret linear models. [See: Linear Regression.]
 IA.HSS.ID.C.7

Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. [See: Linear Regression.]
 IA.HSS.ID.C.8

Compute (using technology) and interpret the correlation coefficient of a linear fit. [See: Scatter Plots; Correlations; Linear Regression.]
 IA.HSS.ID.C.9

Distinguish between correlation and causation. [See: Correlations; Linear Regression.]
 IA.SL.910.1

Initiate and participate effectively in a range of collaborative discussions (oneonone, in groups, and teacherled) with diverse partners on grades 910 topics, texts, and issues, building on others' ideas and expressing their own clearly and persuasively. [See: Introduction to Data Science.]
Kansas Standards
 KS.5.G.A.1

Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., xaxis and xcoordinate, yaxis and ycoordinate). [See: Coordinates and Game Design.]
 KS.5.OA.A

Write and interpret numerical expressions. [See: Order of Operations.]
 KS.5.OA.A.1

Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. [See: Order of Operations.]
 KS.6.EE.B

Reason about and solve onevariable equations and inequalities. [See: Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 KS.6.EE.B.6

Use variables to represent numbers and write expressions when solving a realworld or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. [See: Piecewise Functions and Conditionals; Function Composition; Defining Values; Functions Make Life Easier!; Functions: Contracts, Examples & Definitions; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Surface Area of a Rectangular Prism; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality; Defining Table Functions; Grouped Samples; Linear Regression.]
 KS.6.EE.B.8

Write an inequality of the form x > c or x < c to represent a constraint or condition in a realworld or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. [See: Simple Inequalities; Sam the Butterfly  Applying Inequalities.]
 KS.6.G.A

Solve realworld and mathematical problems involving area, surface area, and volume. [See: Surface Area of a Rectangular Prism.]
 KS.6.G.A.4

Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [See: Surface Area of a Rectangular Prism.]
 KS.6.RP.A

Understand ratio concepts and use ratio reasoning to solve problems. [See: Making Flags; Bar and Pie Charts.]
 KS.6.RP.A.1

Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. [See: Making Flags.]
 KS.6.RP.A.3.D

Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. [See: Making Flags.]
 KS.6.SP.A

Develop understanding of statistical variability. [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 KS.6.SP.A.1

Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. [See: Introduction to Data Science; The Data Cycle; Choosing Your Dataset.]
 KS.6.SP.A.2

Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots; Standard Deviation.]
 KS.6.SP.A.3

Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. [See: Box Plots; Standard Deviation.]
 KS.6.SP.B

Summarize and describe distributions. [See: Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 KS.6.SP.B.4

Display numerical data in plots on a number line, including dot plots, histograms, and box plots. [See: Histograms; Visualizing the “Shape” of Data; Box Plots; Standard Deviation.]
 KS.6.SP.B.5

Summarize numerical data sets in relation to their context. [See: Measures of Center; Box Plots; Standard Deviation.]
 KS.6.SP.B.5.C

Summarize numerical data sets in relation to their context by giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. [See: Measures of Center; Box Plots; Standard Deviation.]
 KS.6.SP.B.5.D

Summarize numerical data sets in relation to their context by relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. [See: Measures of Center.]
 KS.7.EE.A.2

Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. [See: Problem Decomposition.]
 KS.7.EE.B

Solve reallife and mathematical problems using numerical and algebraic expressions and equations. [See: Piecewise Functions and Conditionals; Solving Word Problems with the Design Recipe; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Player Animation; The Distance Formula.]
 KS.7.EE.B.4

Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. [See: Defining Values; Functions Make Life Easier!; Solving Word Problems with the Design Recipe; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 KS.7.G.B.4

Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. [See: Solving Word Problems with the Design Recipe.]
 KS.7.G.B.6

Solve realworld and mathematical problems involving area, volume and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [See: Solving Word Problems with the Design Recipe; Surface Area of a Rectangular Prism.]
 KS.7.RP.A

Analyze proportional relationships and use them to solve realworld and mathematical problems. [See: Making Flags; Making Game Images.]
 KS.7.RP.A.1

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. [See: Making Flags.]
 KS.7.RP.A.2.A

Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. [See: Functions Can Be Linear; Defining Linear Functions.]
 KS.7.RP.A.2.B

Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. [See: Functions Can Be Linear; Defining Linear Functions.]
 KS.7.SP.A

Use random sampling to draw inferences about a population. [See: Probability, Inference, and Sample Size.]
 KS.7.SP.A.1

Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. [See: Probability, Inference, and Sample Size.]
 KS.7.SP.A.2

Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. [See: Probability, Inference, and Sample Size.]
 KS.7.SP.B

Draw informal comparative inferences about two populations. [See: Bar and Pie Charts.]
 KS.8.EE.B

Understand the connections between proportional relationships, lines, and linear equations. [See: Functions Can Be Linear; Defining Linear Functions.]
 KS.8.EE.B.5

Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [See: Functions Can Be Linear; Defining Linear Functions.]
 KS.8.F.A.1

Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. [See: Contracts; The Vertical Line Test.]
 KS.8.F.A.2

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [See: Functions Can Be Linear; Defining Linear Functions.]
 KS.8.F.A.3

Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. [See: Functions Can Be Linear; Defining Linear Functions.]
 KS.8.F.B

Use functions to model relationships between quantities. [See: Functions Make Life Easier!; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition.]
 KS.8.F.B.4

Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. [See: Functions Can Be Linear; Defining Linear Functions.]
 KS.8.F.B.5

Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. [See: Functions Can Be Linear; Defining Linear Functions.]
 KS.8.G.A.1

Verify experimentally the properties of rotations, reflections, and translations. [See: Making Game Images.]
 KS.8.G.B

Understand and apply the Pythagorean Theorem. [See: The Distance Formula.]
 KS.8.G.B.7

Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions. [See: The Distance Formula.]
 KS.8.G.B.8

Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. [See: The Distance Formula.]
 KS.8.SP.A.1

Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. [See: Scatter Plots; Grouped Samples; Correlations; Linear Regression.]
 KS.8.SP.A.2

Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. [See: Scatter Plots; Correlations; Linear Regression.]
 KS.8.SP.A.3

Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. [See: Linear Regression.]
 KS.HSA.CED.A

Create equations that describe numbers or relationships. [See: Solving Word Problems with the Design Recipe; Surface Area of a Rectangular Prism; Problem Decomposition; Sam the Butterfly  Applying Inequalities.]
 KS.HSA.CED.A.1

Create equations and inequalities in one variable and use them to solve problems. [See: Sam the Butterfly  Applying Inequalities.]
 KS.HSA.CED.A.2

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [See: Sam the Butterfly  Applying Inequalities.]
 KS.HSA.CED.A.3

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. [See: Sam the Butterfly  Applying Inequalities.]
 KS.HSA.SSE.A.1

Interpret expressions that represent a quantity in terms of its context. [See: Defining Values; Functions Make Life Easier!; Solving Word Problems with the Design Recipe.]
 KS.HSA.SSE.A.1.A

Interpret parts of an expression, such as terms, factors, and coefficients. [See: Piecewise Functions and Conditionals; Player Animation.]
 KS.HSA.SSE.A.1.B

Interpret complicated expressions by viewing one or more of their parts as a single entity. [See: Piecewise Functions and Conditionals; Player Animation; Custom Scatter Plots.]
 KS.HSA.SSE.A.2

Use the structure of an expression to identify ways to rewrite it. [See: Order of Operations.]
 KS.HSA.SSE.B

Write expressions in equivalent forms to solve problems. [See: Order of Operations.]
 KS.HSF.BF.A

Build a function that models a relationship between two quantities. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 KS.HSF.BF.A.1

Write a function that describes a relationship between two quantities. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 KS.HSF.BF.A.1.B

Combine standard function types using arithmetic operations. [See: Function Composition.]
 KS.HSF.BF.A.1.C

Compose functions. [See: Function Composition; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality.]
 KS.HSF.BF.B

Build new functions from existing functions. [See: Problem Decomposition; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality.]
 KS.HSF.IF.A

Understand the concept of a function and use function notation. [See: Functions Make Life Easier!; Function Notation.]
 KS.HSF.IF.A.1

Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). [See: Contracts; The Vertical Line Test.]
 KS.HSF.IF.A.2

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. [See: Contracts; Making Flags; Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 KS.HSF.IF.B

Interpret functions that arise in applications in terms of the context. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 KS.HSF.IF.B.5

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. [See: Functions Can Be Linear; Defining Linear Functions.]
 KS.HSF.IF.C

Analyze functions using different representations. [See: The Vertical Line Test; Functions: Contracts, Examples & Definitions; Functions Can Be Linear; Defining Linear Functions; Solving Word Problems with the Design Recipe.]
 KS.HSF.IF.C.9

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [See: Functions Can Be Linear; Defining Linear Functions; Problem Decomposition.]
 KS.HSN.Q.A

Reason quantitatively and use units to solve problems. [See: Making Flags.]
 KS.HSS.CP.A.1

Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ('or', 'and', 'not'). [See: Compound Inequalities: Solutions & NonSolutions.]
 KS.HSS.CP.B.9

Use permutations and combinations to compute probabilities of compound events and solve problems. [See: Permutations; Combinations.]
 KS.HSS.IC.A

Understand and evaluate random processes underlying statistical experiments. [See: Probability, Inference, and Sample Size.]
 KS.HSS.IC.A.1

Understand statistics as a process for making inferences about population parameters based on a random sample from that population. [See: Probability, Inference, and Sample Size.]
 KS.HSS.IC.B

Make inferences and justify conclusions from sample surveys, experiments, and observational studies. [See: Collecting Data.]
 KS.HSS.IC.B.3

Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. [See: Probability, Inference, and Sample Size; Collecting Data.]
 KS.HSS.IC.B.4

Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. [See: Collecting Data.]
 KS.HSS.IC.B.6

Evaluate reports based on data. [See: Threats to Validity.]
 KS.HSS.ID.A

Summarize, represent, and interpret data on a single count or measurement variable. [See: Bar and Pie Charts; Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 KS.HSS.ID.A.1

Represent data with plots on the real number line (dot plots, histograms, and box plots). [See: Histograms; Visualizing the “Shape” of Data; Box Plots; Standard Deviation.]
 KS.HSS.ID.A.2

Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. [See: Histograms; Measures of Center; Box Plots; Standard Deviation.]
 KS.HSS.ID.A.3

Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots; Standard Deviation.]
 KS.HSS.ID.B

Summarize, represent, and interpret data on two categorical and quantitative variables. [See: Scatter Plots; Correlations.]
 KS.HSS.ID.B.6

Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. [See: Scatter Plots; Correlations.]
 KS.HSS.ID.B.6.A

Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. [See: Linear Regression.]
 KS.HSS.ID.B.6.C

Fit a linear function for a scatter plot that suggests a linear association. [See: Linear Regression.]
 KS.HSS.ID.C

Interpret linear models. [See: Linear Regression.]
 KS.HSS.ID.C.7

Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. [See: Linear Regression.]
 KS.HSS.ID.C.8

Compute (using technology) and interpret the correlation coefficient of a linear fit. [See: Scatter Plots; Correlations; Linear Regression.]
 KS.HSS.ID.C.9

Distinguish between correlation and causation. [See: Correlations; Linear Regression.]
 KS.SL.910.1

Initiate and participate effectively in a range of collaborative discussions (oneonone, in groups, and teacherled) with diverse partners on grades 910 topics, texts, and issues, building on others' ideas and expressing their own clearly and persuasively. [See: Introduction to Data Science.]
Kentucky Standards
 KY.5.G.A.1

Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., xaxis and xcoordinate, yaxis and ycoordinate). [See: Coordinates and Game Design.]
 KY.5.OA.A

Write and interpret numerical expressions. [See: Order of Operations.]
 KY.5.OA.A.1

Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. [See: Order of Operations.]
 KY.6.EE.B

Reason about and solve onevariable equations and inequalities. [See: Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 KY.6.EE.B.6

Use variables to represent numbers and write expressions when solving a realworld or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. [See: Piecewise Functions and Conditionals; Function Composition; Defining Values; Functions Make Life Easier!; Functions: Contracts, Examples & Definitions; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Surface Area of a Rectangular Prism; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality; Defining Table Functions; Grouped Samples; Linear Regression.]
 KY.6.EE.B.8

Write an inequality of the form x > c or x < c to represent a constraint or condition in a realworld or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. [See: Simple Inequalities; Sam the Butterfly  Applying Inequalities.]
 KY.6.G.A

Solve realworld and mathematical problems involving area, surface area, and volume. [See: Surface Area of a Rectangular Prism.]
 KY.6.G.A.4

Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [See: Surface Area of a Rectangular Prism.]
 KY.6.RP.A

Understand ratio concepts and use ratio reasoning to solve problems. [See: Making Flags; Bar and Pie Charts.]
 KY.6.RP.A.1

Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. [See: Making Flags.]
 KY.6.RP.A.3.D

Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. [See: Making Flags.]
 KY.6.SP.A

Develop understanding of statistical variability. [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 KY.6.SP.A.1

Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. [See: Introduction to Data Science; The Data Cycle; Choosing Your Dataset.]
 KY.6.SP.A.2

Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots; Standard Deviation.]
 KY.6.SP.A.3

Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. [See: Box Plots; Standard Deviation.]
 KY.6.SP.B

Summarize and describe distributions. [See: Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 KY.6.SP.B.4

Display numerical data in plots on a number line, including dot plots, histograms, and box plots. [See: Histograms; Visualizing the “Shape” of Data; Box Plots; Standard Deviation.]
 KY.6.SP.B.5

Summarize numerical data sets in relation to their context. [See: Measures of Center; Box Plots; Standard Deviation.]
 KY.6.SP.B.5.C

Summarize numerical data sets in relation to their context by giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. [See: Measures of Center; Box Plots; Standard Deviation.]
 KY.6.SP.B.5.D

Summarize numerical data sets in relation to their context by relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. [See: Measures of Center.]
 KY.7.EE.A.2

Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. [See: Problem Decomposition.]
 KY.7.EE.B

Solve reallife and mathematical problems using numerical and algebraic expressions and equations. [See: Piecewise Functions and Conditionals; Solving Word Problems with the Design Recipe; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Player Animation; The Distance Formula.]
 KY.7.EE.B.4

Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. [See: Defining Values; Functions Make Life Easier!; Solving Word Problems with the Design Recipe; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 KY.7.G.B.4

Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. [See: Solving Word Problems with the Design Recipe.]
 KY.7.G.B.6

Solve realworld and mathematical problems involving area, volume and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [See: Solving Word Problems with the Design Recipe; Surface Area of a Rectangular Prism.]
 KY.7.RP.A

Analyze proportional relationships and use them to solve realworld and mathematical problems. [See: Making Flags; Making Game Images.]
 KY.7.RP.A.1

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. [See: Making Flags.]
 KY.7.RP.A.2.A

Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. [See: Functions Can Be Linear; Defining Linear Functions.]
 KY.7.RP.A.2.B

Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. [See: Functions Can Be Linear; Defining Linear Functions.]
 KY.7.SP.A

Use random sampling to draw inferences about a population. [See: Probability, Inference, and Sample Size.]
 KY.7.SP.A.1

Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. [See: Probability, Inference, and Sample Size.]
 KY.7.SP.A.2

Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. [See: Probability, Inference, and Sample Size.]
 KY.7.SP.B

Draw informal comparative inferences about two populations. [See: Bar and Pie Charts.]
 KY.8.EE.B

Understand the connections between proportional relationships, lines, and linear equations. [See: Functions Can Be Linear; Defining Linear Functions.]
 KY.8.EE.B.5

Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [See: Functions Can Be Linear; Defining Linear Functions.]
 KY.8.F.A.1

Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. [See: Contracts; The Vertical Line Test.]
 KY.8.F.A.2

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [See: Functions Can Be Linear; Defining Linear Functions.]
 KY.8.F.A.3

Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. [See: Functions Can Be Linear; Defining Linear Functions.]
 KY.8.F.B

Use functions to model relationships between quantities. [See: Functions Make Life Easier!; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition.]
 KY.8.F.B.4

Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. [See: Functions Can Be Linear; Defining Linear Functions.]
 KY.8.F.B.5

Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. [See: Functions Can Be Linear; Defining Linear Functions.]
 KY.8.G.A.1

Verify experimentally the properties of rotations, reflections, and translations. [See: Making Game Images.]
 KY.8.G.B

Understand and apply the Pythagorean Theorem. [See: The Distance Formula.]
 KY.8.G.B.7

Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions. [See: The Distance Formula.]
 KY.8.G.B.8

Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. [See: The Distance Formula.]
 KY.8.SP.A.1

Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. [See: Scatter Plots; Grouped Samples; Correlations; Linear Regression.]
 KY.8.SP.A.2

Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. [See: Scatter Plots; Correlations; Linear Regression.]
 KY.8.SP.A.3

Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. [See: Linear Regression.]
 KY.HSA.CED.A

Create equations that describe numbers or relationships. [See: Solving Word Problems with the Design Recipe; Surface Area of a Rectangular Prism; Problem Decomposition; Sam the Butterfly  Applying Inequalities.]
 KY.HSA.CED.A.1

Create equations and inequalities in one variable and use them to solve problems. [See: Sam the Butterfly  Applying Inequalities.]
 KY.HSA.CED.A.2

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [See: Sam the Butterfly  Applying Inequalities.]
 KY.HSA.CED.A.3

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. [See: Sam the Butterfly  Applying Inequalities.]
 KY.HSA.SSE.A.1

Interpret expressions that represent a quantity in terms of its context. [See: Defining Values; Functions Make Life Easier!; Solving Word Problems with the Design Recipe.]
 KY.HSA.SSE.A.1.A

Interpret parts of an expression, such as terms, factors, and coefficients. [See: Piecewise Functions and Conditionals; Player Animation.]
 KY.HSA.SSE.A.1.B

Interpret complicated expressions by viewing one or more of their parts as a single entity. [See: Piecewise Functions and Conditionals; Player Animation; Custom Scatter Plots.]
 KY.HSA.SSE.A.2

Use the structure of an expression to identify ways to rewrite it. [See: Order of Operations.]
 KY.HSA.SSE.B

Write expressions in equivalent forms to solve problems. [See: Order of Operations.]
 KY.HSF.BF.A

Build a function that models a relationship between two quantities. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 KY.HSF.BF.A.1

Write a function that describes a relationship between two quantities. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 KY.HSF.BF.A.1.B

Combine standard function types using arithmetic operations. [See: Function Composition.]
 KY.HSF.BF.A.1.C

Compose functions. [See: Function Composition; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality.]
 KY.HSF.BF.B

Build new functions from existing functions. [See: Problem Decomposition; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality.]
 KY.HSF.IF.A

Understand the concept of a function and use function notation. [See: Functions Make Life Easier!; Function Notation.]
 KY.HSF.IF.A.1

Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). [See: Contracts; The Vertical Line Test.]
 KY.HSF.IF.A.2

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. [See: Contracts; Making Flags; Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 KY.HSF.IF.B

Interpret functions that arise in applications in terms of the context. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 KY.HSF.IF.B.5

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. [See: Functions Can Be Linear; Defining Linear Functions.]
 KY.HSF.IF.C

Analyze functions using different representations. [See: The Vertical Line Test; Functions: Contracts, Examples & Definitions; Functions Can Be Linear; Defining Linear Functions; Solving Word Problems with the Design Recipe.]
 KY.HSF.IF.C.9

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [See: Functions Can Be Linear; Defining Linear Functions; Problem Decomposition.]
 KY.HSN.Q.A

Reason quantitatively and use units to solve problems. [See: Making Flags.]
 KY.HSS.CP.A.1

Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ('or', 'and', 'not'). [See: Compound Inequalities: Solutions & NonSolutions.]
 KY.HSS.CP.B.9

Use permutations and combinations to compute probabilities of compound events and solve problems. [See: Permutations; Combinations.]
 KY.HSS.IC.A

Understand and evaluate random processes underlying statistical experiments. [See: Probability, Inference, and Sample Size.]
 KY.HSS.IC.A.1

Understand statistics as a process for making inferences about population parameters based on a random sample from that population. [See: Probability, Inference, and Sample Size.]
 KY.HSS.IC.B

Make inferences and justify conclusions from sample surveys, experiments, and observational studies. [See: Collecting Data.]
 KY.HSS.IC.B.3

Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. [See: Probability, Inference, and Sample Size; Collecting Data.]
 KY.HSS.IC.B.4

Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. [See: Collecting Data.]
 KY.HSS.IC.B.6

Evaluate reports based on data. [See: Threats to Validity.]
 KY.HSS.ID.A

Summarize, represent, and interpret data on a single count or measurement variable. [See: Bar and Pie Charts; Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 KY.HSS.ID.A.1

Represent data with plots on the real number line (dot plots, histograms, and box plots). [See: Histograms; Visualizing the “Shape” of Data; Box Plots; Standard Deviation.]
 KY.HSS.ID.A.2

Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. [See: Histograms; Measures of Center; Box Plots; Standard Deviation.]
 KY.HSS.ID.A.3

Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots; Standard Deviation.]
 KY.HSS.ID.B

Summarize, represent, and interpret data on two categorical and quantitative variables. [See: Scatter Plots; Correlations.]
 KY.HSS.ID.B.6

Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. [See: Scatter Plots; Correlations.]
 KY.HSS.ID.B.6.A

Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. [See: Linear Regression.]
 KY.HSS.ID.B.6.C

Fit a linear function for a scatter plot that suggests a linear association. [See: Linear Regression.]
 KY.HSS.ID.C

Interpret linear models. [See: Linear Regression.]
 KY.HSS.ID.C.7

Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. [See: Linear Regression.]
 KY.HSS.ID.C.8

Compute (using technology) and interpret the correlation coefficient of a linear fit. [See: Scatter Plots; Correlations; Linear Regression.]
 KY.HSS.ID.C.9

Distinguish between correlation and causation. [See: Correlations; Linear Regression.]
 KY.SL.910.1

Initiate and participate effectively in a range of collaborative discussions (oneonone, in groups, and teacherled) with diverse partners on grades 910 topics, texts, and issues, building on others' ideas and expressing their own clearly and persuasively. [See: Introduction to Data Science.]
Louisiana Standards
 LA.5.G.A.1

Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., xaxis and xcoordinate, yaxis and ycoordinate). [See: Coordinates and Game Design.]
 LA.5.OA.A

Write and interpret numerical expressions. [See: Order of Operations.]
 LA.5.OA.A.1

Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. [See: Order of Operations.]
 LA.6.EE.B

Reason about and solve onevariable equations and inequalities. [See: Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 LA.6.EE.B.6

Use variables to represent numbers and write expressions when solving a realworld or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. [See: Piecewise Functions and Conditionals; Function Composition; Defining Values; Functions Make Life Easier!; Functions: Contracts, Examples & Definitions; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Surface Area of a Rectangular Prism; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality; Defining Table Functions; Grouped Samples; Linear Regression.]
 LA.6.EE.B.8

Write an inequality of the form x > c or x < c to represent a constraint or condition in a realworld or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. [See: Simple Inequalities; Sam the Butterfly  Applying Inequalities.]
 LA.6.G.A

Solve realworld and mathematical problems involving area, surface area, and volume. [See: Surface Area of a Rectangular Prism.]
 LA.6.G.A.4

Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [See: Surface Area of a Rectangular Prism.]
 LA.6.RP.A

Understand ratio concepts and use ratio reasoning to solve problems. [See: Making Flags; Bar and Pie Charts.]
 LA.6.RP.A.1

Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. [See: Making Flags.]
 LA.6.RP.A.3.D

Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. [See: Making Flags.]
 LA.6.SP.A

Develop understanding of statistical variability. [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 LA.6.SP.A.1

Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. [See: Introduction to Data Science; The Data Cycle; Choosing Your Dataset.]
 LA.6.SP.A.2

Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots; Standard Deviation.]
 LA.6.SP.A.3

Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. [See: Box Plots; Standard Deviation.]
 LA.6.SP.B

Summarize and describe distributions. [See: Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 LA.6.SP.B.4

Display numerical data in plots on a number line, including dot plots, histograms, and box plots. [See: Histograms; Visualizing the “Shape” of Data; Box Plots; Standard Deviation.]
 LA.6.SP.B.5

Summarize numerical data sets in relation to their context. [See: Measures of Center; Box Plots; Standard Deviation.]
 LA.6.SP.B.5.C

Summarize numerical data sets in relation to their context by giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. [See: Measures of Center; Box Plots; Standard Deviation.]
 LA.6.SP.B.5.D

Summarize numerical data sets in relation to their context by relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. [See: Measures of Center.]
 LA.7.EE.A.2

Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. [See: Problem Decomposition.]
 LA.7.EE.B

Solve reallife and mathematical problems using numerical and algebraic expressions and equations. [See: Piecewise Functions and Conditionals; Solving Word Problems with the Design Recipe; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Player Animation; The Distance Formula.]
 LA.7.EE.B.4

Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. [See: Defining Values; Functions Make Life Easier!; Solving Word Problems with the Design Recipe; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 LA.7.G.B.4

Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. [See: Solving Word Problems with the Design Recipe.]
 LA.7.G.B.6

Solve realworld and mathematical problems involving area, volume and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [See: Solving Word Problems with the Design Recipe; Surface Area of a Rectangular Prism.]
 LA.7.RP.A

Analyze proportional relationships and use them to solve realworld and mathematical problems. [See: Making Flags; Making Game Images.]
 LA.7.RP.A.1

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. [See: Making Flags.]
 LA.7.RP.A.2.A

Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. [See: Functions Can Be Linear; Defining Linear Functions.]
 LA.7.RP.A.2.B

Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. [See: Functions Can Be Linear; Defining Linear Functions.]
 LA.7.SP.A

Use random sampling to draw inferences about a population. [See: Probability, Inference, and Sample Size.]
 LA.7.SP.A.1

Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. [See: Probability, Inference, and Sample Size.]
 LA.7.SP.A.2

Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. [See: Probability, Inference, and Sample Size.]
 LA.7.SP.B

Draw informal comparative inferences about two populations. [See: Bar and Pie Charts.]
 LA.8.EE.B

Understand the connections between proportional relationships, lines, and linear equations. [See: Functions Can Be Linear; Defining Linear Functions.]
 LA.8.EE.B.5

Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [See: Functions Can Be Linear; Defining Linear Functions.]
 LA.8.F.A.1

Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. [See: Contracts; The Vertical Line Test.]
 LA.8.F.A.2

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [See: Functions Can Be Linear; Defining Linear Functions.]
 LA.8.F.A.3

Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. [See: Functions Can Be Linear; Defining Linear Functions.]
 LA.8.F.B

Use functions to model relationships between quantities. [See: Functions Make Life Easier!; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition.]
 LA.8.F.B.4

Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. [See: Functions Can Be Linear; Defining Linear Functions.]
 LA.8.F.B.5

Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. [See: Functions Can Be Linear; Defining Linear Functions.]
 LA.8.G.A.1

Verify experimentally the properties of rotations, reflections, and translations. [See: Making Game Images.]
 LA.8.G.B

Understand and apply the Pythagorean Theorem. [See: The Distance Formula.]
 LA.8.G.B.7

Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions. [See: The Distance Formula.]
 LA.8.G.B.8

Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. [See: The Distance Formula.]
 LA.8.SP.A.1

Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. [See: Scatter Plots; Grouped Samples; Correlations; Linear Regression.]
 LA.8.SP.A.2

Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. [See: Scatter Plots; Correlations; Linear Regression.]
 LA.8.SP.A.3

Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. [See: Linear Regression.]
 LA.HSA.CED.A

Create equations that describe numbers or relationships. [See: Solving Word Problems with the Design Recipe; Surface Area of a Rectangular Prism; Problem Decomposition; Sam the Butterfly  Applying Inequalities.]
 LA.HSA.CED.A.1

Create equations and inequalities in one variable and use them to solve problems. [See: Sam the Butterfly  Applying Inequalities.]
 LA.HSA.CED.A.2

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [See: Sam the Butterfly  Applying Inequalities.]
 LA.HSA.CED.A.3

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. [See: Sam the Butterfly  Applying Inequalities.]
 LA.HSA.SSE.A.1

Interpret expressions that represent a quantity in terms of its context. [See: Defining Values; Functions Make Life Easier!; Solving Word Problems with the Design Recipe.]
 LA.HSA.SSE.A.1.A

Interpret parts of an expression, such as terms, factors, and coefficients. [See: Piecewise Functions and Conditionals; Player Animation.]
 LA.HSA.SSE.A.1.B

Interpret complicated expressions by viewing one or more of their parts as a single entity. [See: Piecewise Functions and Conditionals; Player Animation; Custom Scatter Plots.]
 LA.HSA.SSE.A.2

Use the structure of an expression to identify ways to rewrite it. [See: Order of Operations.]
 LA.HSA.SSE.B

Write expressions in equivalent forms to solve problems. [See: Order of Operations.]
 LA.HSF.BF.A

Build a function that models a relationship between two quantities. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 LA.HSF.BF.A.1

Write a function that describes a relationship between two quantities. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 LA.HSF.BF.A.1.B

Combine standard function types using arithmetic operations. [See: Function Composition.]
 LA.HSF.BF.A.1.C

Compose functions. [See: Function Composition; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality.]
 LA.HSF.BF.B

Build new functions from existing functions. [See: Problem Decomposition; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality.]
 LA.HSF.IF.A

Understand the concept of a function and use function notation. [See: Functions Make Life Easier!; Function Notation.]
 LA.HSF.IF.A.1

Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). [See: Contracts; The Vertical Line Test.]
 LA.HSF.IF.A.2

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. [See: Contracts; Making Flags; Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 LA.HSF.IF.B

Interpret functions that arise in applications in terms of the context. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 LA.HSF.IF.B.5

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. [See: Functions Can Be Linear; Defining Linear Functions.]
 LA.HSF.IF.C

Analyze functions using different representations. [See: The Vertical Line Test; Functions: Contracts, Examples & Definitions; Functions Can Be Linear; Defining Linear Functions; Solving Word Problems with the Design Recipe.]
 LA.HSF.IF.C.9

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [See: Functions Can Be Linear; Defining Linear Functions; Problem Decomposition.]
 LA.HSN.Q.A

Reason quantitatively and use units to solve problems. [See: Making Flags.]
 LA.HSS.CP.A.1

Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ('or', 'and', 'not'). [See: Compound Inequalities: Solutions & NonSolutions.]
 LA.HSS.CP.B.9

Use permutations and combinations to compute probabilities of compound events and solve problems. [See: Permutations; Combinations.]
 LA.HSS.IC.A

Understand and evaluate random processes underlying statistical experiments. [See: Probability, Inference, and Sample Size.]
 LA.HSS.IC.A.1

Understand statistics as a process for making inferences about population parameters based on a random sample from that population. [See: Probability, Inference, and Sample Size.]
 LA.HSS.IC.B

Make inferences and justify conclusions from sample surveys, experiments, and observational studies. [See: Collecting Data.]
 LA.HSS.IC.B.3

Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. [See: Probability, Inference, and Sample Size; Collecting Data.]
 LA.HSS.IC.B.4

Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. [See: Collecting Data.]
 LA.HSS.IC.B.6

Evaluate reports based on data. [See: Threats to Validity.]
 LA.HSS.ID.A

Summarize, represent, and interpret data on a single count or measurement variable. [See: Bar and Pie Charts; Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 LA.HSS.ID.A.1

Represent data with plots on the real number line (dot plots, histograms, and box plots). [See: Histograms; Visualizing the “Shape” of Data; Box Plots; Standard Deviation.]
 LA.HSS.ID.A.2

Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. [See: Histograms; Measures of Center; Box Plots; Standard Deviation.]
 LA.HSS.ID.A.3

Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots; Standard Deviation.]
 LA.HSS.ID.B

Summarize, represent, and interpret data on two categorical and quantitative variables. [See: Scatter Plots; Correlations.]
 LA.HSS.ID.B.6

Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. [See: Scatter Plots; Correlations.]
 LA.HSS.ID.B.6.A

Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. [See: Linear Regression.]
 LA.HSS.ID.B.6.C

Fit a linear function for a scatter plot that suggests a linear association. [See: Linear Regression.]
 LA.HSS.ID.C

Interpret linear models. [See: Linear Regression.]
 LA.HSS.ID.C.7

Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. [See: Linear Regression.]
 LA.HSS.ID.C.8

Compute (using technology) and interpret the correlation coefficient of a linear fit. [See: Scatter Plots; Correlations; Linear Regression.]
 LA.HSS.ID.C.9

Distinguish between correlation and causation. [See: Correlations; Linear Regression.]
 LA.SL.910.1

Initiate and participate effectively in a range of collaborative discussions (oneonone, in groups, and teacherled) with diverse partners on grades 910 topics, texts, and issues, building on others' ideas and expressing their own clearly and persuasively. [See: Introduction to Data Science.]
Maine Standards
 ME.5.G.A.1

Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., xaxis and xcoordinate, yaxis and ycoordinate). [See: Coordinates and Game Design.]
 ME.5.OA.A

Write and interpret numerical expressions. [See: Order of Operations.]
 ME.5.OA.A.1

Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. [See: Order of Operations.]
 ME.6.EE.B

Reason about and solve onevariable equations and inequalities. [See: Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 ME.6.EE.B.6

Use variables to represent numbers and write expressions when solving a realworld or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. [See: Piecewise Functions and Conditionals; Function Composition; Defining Values; Functions Make Life Easier!; Functions: Contracts, Examples & Definitions; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Surface Area of a Rectangular Prism; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality; Defining Table Functions; Grouped Samples; Linear Regression.]
 ME.6.EE.B.8

Write an inequality of the form x > c or x < c to represent a constraint or condition in a realworld or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. [See: Simple Inequalities; Sam the Butterfly  Applying Inequalities.]
 ME.6.G.A

Solve realworld and mathematical problems involving area, surface area, and volume. [See: Surface Area of a Rectangular Prism.]
 ME.6.G.A.4

Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [See: Surface Area of a Rectangular Prism.]
 ME.6.RP.A

Understand ratio concepts and use ratio reasoning to solve problems. [See: Making Flags; Bar and Pie Charts.]
 ME.6.RP.A.1

Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. [See: Making Flags.]
 ME.6.RP.A.3.D

Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. [See: Making Flags.]
 ME.6.SP.A

Develop understanding of statistical variability. [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 ME.6.SP.A.1

Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. [See: Introduction to Data Science; The Data Cycle; Choosing Your Dataset.]
 ME.6.SP.A.2

Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots; Standard Deviation.]
 ME.6.SP.A.3

Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. [See: Box Plots; Standard Deviation.]
 ME.6.SP.B

Summarize and describe distributions. [See: Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 ME.6.SP.B.4

Display numerical data in plots on a number line, including dot plots, histograms, and box plots. [See: Histograms; Visualizing the “Shape” of Data; Box Plots; Standard Deviation.]
 ME.6.SP.B.5

Summarize numerical data sets in relation to their context. [See: Measures of Center; Box Plots; Standard Deviation.]
 ME.6.SP.B.5.C

Summarize numerical data sets in relation to their context by giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. [See: Measures of Center; Box Plots; Standard Deviation.]
 ME.6.SP.B.5.D

Summarize numerical data sets in relation to their context by relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. [See: Measures of Center.]
 ME.7.EE.A.2

Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. [See: Problem Decomposition.]
 ME.7.EE.B

Solve reallife and mathematical problems using numerical and algebraic expressions and equations. [See: Piecewise Functions and Conditionals; Solving Word Problems with the Design Recipe; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Player Animation; The Distance Formula.]
 ME.7.EE.B.4

Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. [See: Defining Values; Functions Make Life Easier!; Solving Word Problems with the Design Recipe; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 ME.7.G.B.4

Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. [See: Solving Word Problems with the Design Recipe.]
 ME.7.G.B.6

Solve realworld and mathematical problems involving area, volume and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [See: Solving Word Problems with the Design Recipe; Surface Area of a Rectangular Prism.]
 ME.7.RP.A

Analyze proportional relationships and use them to solve realworld and mathematical problems. [See: Making Flags; Making Game Images.]
 ME.7.RP.A.1

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. [See: Making Flags.]
 ME.7.RP.A.2.A

Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. [See: Functions Can Be Linear; Defining Linear Functions.]
 ME.7.RP.A.2.B

Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. [See: Functions Can Be Linear; Defining Linear Functions.]
 ME.7.SP.A

Use random sampling to draw inferences about a population. [See: Probability, Inference, and Sample Size.]
 ME.7.SP.A.1

Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. [See: Probability, Inference, and Sample Size.]
 ME.7.SP.A.2

Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. [See: Probability, Inference, and Sample Size.]
 ME.7.SP.B

Draw informal comparative inferences about two populations. [See: Bar and Pie Charts.]
 ME.8.EE.B

Understand the connections between proportional relationships, lines, and linear equations. [See: Functions Can Be Linear; Defining Linear Functions.]
 ME.8.EE.B.5

Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [See: Functions Can Be Linear; Defining Linear Functions.]
 ME.8.F.A.1

Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. [See: Contracts; The Vertical Line Test.]
 ME.8.F.A.2

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [See: Functions Can Be Linear; Defining Linear Functions.]
 ME.8.F.A.3

Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. [See: Functions Can Be Linear; Defining Linear Functions.]
 ME.8.F.B

Use functions to model relationships between quantities. [See: Functions Make Life Easier!; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition.]
 ME.8.F.B.4

Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. [See: Functions Can Be Linear; Defining Linear Functions.]
 ME.8.F.B.5

Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. [See: Functions Can Be Linear; Defining Linear Functions.]
 ME.8.G.A.1

Verify experimentally the properties of rotations, reflections, and translations. [See: Making Game Images.]
 ME.8.G.B

Understand and apply the Pythagorean Theorem. [See: The Distance Formula.]
 ME.8.G.B.7

Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions. [See: The Distance Formula.]
 ME.8.G.B.8

Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. [See: The Distance Formula.]
 ME.8.SP.A.1

Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. [See: Scatter Plots; Grouped Samples; Correlations; Linear Regression.]
 ME.8.SP.A.2

Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. [See: Scatter Plots; Correlations; Linear Regression.]
 ME.8.SP.A.3

Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. [See: Linear Regression.]
 ME.HSA.CED.A

Create equations that describe numbers or relationships. [See: Solving Word Problems with the Design Recipe; Surface Area of a Rectangular Prism; Problem Decomposition; Sam the Butterfly  Applying Inequalities.]
 ME.HSA.CED.A.1

Create equations and inequalities in one variable and use them to solve problems. [See: Sam the Butterfly  Applying Inequalities.]
 ME.HSA.CED.A.2

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [See: Sam the Butterfly  Applying Inequalities.]
 ME.HSA.CED.A.3

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. [See: Sam the Butterfly  Applying Inequalities.]
 ME.HSA.SSE.A.1

Interpret expressions that represent a quantity in terms of its context. [See: Defining Values; Functions Make Life Easier!; Solving Word Problems with the Design Recipe.]
 ME.HSA.SSE.A.1.A

Interpret parts of an expression, such as terms, factors, and coefficients. [See: Piecewise Functions and Conditionals; Player Animation.]
 ME.HSA.SSE.A.1.B

Interpret complicated expressions by viewing one or more of their parts as a single entity. [See: Piecewise Functions and Conditionals; Player Animation; Custom Scatter Plots.]
 ME.HSA.SSE.A.2

Use the structure of an expression to identify ways to rewrite it. [See: Order of Operations.]
 ME.HSA.SSE.B

Write expressions in equivalent forms to solve problems. [See: Order of Operations.]
 ME.HSF.BF.A

Build a function that models a relationship between two quantities. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 ME.HSF.BF.A.1

Write a function that describes a relationship between two quantities. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 ME.HSF.BF.A.1.B

Combine standard function types using arithmetic operations. [See: Function Composition.]
 ME.HSF.BF.A.1.C

Compose functions. [See: Function Composition; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality.]
 ME.HSF.BF.B

Build new functions from existing functions. [See: Problem Decomposition; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality.]
 ME.HSF.IF.A

Understand the concept of a function and use function notation. [See: Functions Make Life Easier!; Function Notation.]
 ME.HSF.IF.A.1

Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). [See: Contracts; The Vertical Line Test.]
 ME.HSF.IF.A.2

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. [See: Contracts; Making Flags; Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 ME.HSF.IF.B

Interpret functions that arise in applications in terms of the context. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 ME.HSF.IF.B.5

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. [See: Functions Can Be Linear; Defining Linear Functions.]
 ME.HSF.IF.C

Analyze functions using different representations. [See: The Vertical Line Test; Functions: Contracts, Examples & Definitions; Functions Can Be Linear; Defining Linear Functions; Solving Word Problems with the Design Recipe.]
 ME.HSF.IF.C.9

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [See: Functions Can Be Linear; Defining Linear Functions; Problem Decomposition.]
 ME.HSN.Q.A

Reason quantitatively and use units to solve problems. [See: Making Flags.]
 ME.HSS.CP.A.1

Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ('or', 'and', 'not'). [See: Compound Inequalities: Solutions & NonSolutions.]
 ME.HSS.CP.B.9

Use permutations and combinations to compute probabilities of compound events and solve problems. [See: Permutations; Combinations.]
 ME.HSS.IC.A

Understand and evaluate random processes underlying statistical experiments. [See: Probability, Inference, and Sample Size.]
 ME.HSS.IC.A.1

Understand statistics as a process for making inferences about population parameters based on a random sample from that population. [See: Probability, Inference, and Sample Size.]
 ME.HSS.IC.B

Make inferences and justify conclusions from sample surveys, experiments, and observational studies. [See: Collecting Data.]
 ME.HSS.IC.B.3

Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. [See: Probability, Inference, and Sample Size; Collecting Data.]
 ME.HSS.IC.B.4

Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. [See: Collecting Data.]
 ME.HSS.IC.B.6

Evaluate reports based on data. [See: Threats to Validity.]
 ME.HSS.ID.A

Summarize, represent, and interpret data on a single count or measurement variable. [See: Bar and Pie Charts; Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 ME.HSS.ID.A.1

Represent data with plots on the real number line (dot plots, histograms, and box plots). [See: Histograms; Visualizing the “Shape” of Data; Box Plots; Standard Deviation.]
 ME.HSS.ID.A.2

Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. [See: Histograms; Measures of Center; Box Plots; Standard Deviation.]
 ME.HSS.ID.A.3

Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots; Standard Deviation.]
 ME.HSS.ID.B

Summarize, represent, and interpret data on two categorical and quantitative variables. [See: Scatter Plots; Correlations.]
 ME.HSS.ID.B.6

Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. [See: Scatter Plots; Correlations.]
 ME.HSS.ID.B.6.A

Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. [See: Linear Regression.]
 ME.HSS.ID.B.6.C

Fit a linear function for a scatter plot that suggests a linear association. [See: Linear Regression.]
 ME.HSS.ID.C

Interpret linear models. [See: Linear Regression.]
 ME.HSS.ID.C.7

Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. [See: Linear Regression.]
 ME.HSS.ID.C.8

Compute (using technology) and interpret the correlation coefficient of a linear fit. [See: Scatter Plots; Correlations; Linear Regression.]
 ME.HSS.ID.C.9

Distinguish between correlation and causation. [See: Correlations; Linear Regression.]
 ME.SL.910.1

Initiate and participate effectively in a range of collaborative discussions (oneonone, in groups, and teacherled) with diverse partners on grades 910 topics, texts, and issues, building on others' ideas and expressing their own clearly and persuasively. [See: Introduction to Data Science.]
Michigan Standards
 MI.5.G.A.1

Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., xaxis and xcoordinate, yaxis and ycoordinate). [See: Coordinates and Game Design.]
 MI.5.OA.A

Write and interpret numerical expressions. [See: Order of Operations.]
 MI.5.OA.A.1

Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. [See: Order of Operations.]
 MI.6.EE.B

Reason about and solve onevariable equations and inequalities. [See: Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 MI.6.EE.B.6

Use variables to represent numbers and write expressions when solving a realworld or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. [See: Piecewise Functions and Conditionals; Function Composition; Defining Values; Functions Make Life Easier!; Functions: Contracts, Examples & Definitions; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Surface Area of a Rectangular Prism; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality; Defining Table Functions; Grouped Samples; Linear Regression.]
 MI.6.EE.B.8

Write an inequality of the form x > c or x < c to represent a constraint or condition in a realworld or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. [See: Simple Inequalities; Sam the Butterfly  Applying Inequalities.]
 MI.6.G.A

Solve realworld and mathematical problems involving area, surface area, and volume. [See: Surface Area of a Rectangular Prism.]
 MI.6.G.A.4

Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [See: Surface Area of a Rectangular Prism.]
 MI.6.RP.A

Understand ratio concepts and use ratio reasoning to solve problems. [See: Making Flags; Bar and Pie Charts.]
 MI.6.RP.A.1

Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. [See: Making Flags.]
 MI.6.RP.A.3.D

Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. [See: Making Flags.]
 MI.6.SP.A

Develop understanding of statistical variability. [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 MI.6.SP.A.1

Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. [See: Introduction to Data Science; The Data Cycle; Choosing Your Dataset.]
 MI.6.SP.A.2

Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots; Standard Deviation.]
 MI.6.SP.A.3

Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. [See: Box Plots; Standard Deviation.]
 MI.6.SP.B

Summarize and describe distributions. [See: Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 MI.6.SP.B.4

Display numerical data in plots on a number line, including dot plots, histograms, and box plots. [See: Histograms; Visualizing the “Shape” of Data; Box Plots; Standard Deviation.]
 MI.6.SP.B.5

Summarize numerical data sets in relation to their context. [See: Measures of Center; Box Plots; Standard Deviation.]
 MI.6.SP.B.5.C

Summarize numerical data sets in relation to their context by giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. [See: Measures of Center; Box Plots; Standard Deviation.]
 MI.6.SP.B.5.D

Summarize numerical data sets in relation to their context by relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. [See: Measures of Center.]
 MI.7.EE.A.2

Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. [See: Problem Decomposition.]
 MI.7.EE.B

Solve reallife and mathematical problems using numerical and algebraic expressions and equations. [See: Piecewise Functions and Conditionals; Solving Word Problems with the Design Recipe; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Player Animation; The Distance Formula.]
 MI.7.EE.B.4

Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. [See: Defining Values; Functions Make Life Easier!; Solving Word Problems with the Design Recipe; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 MI.7.G.B.4

Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. [See: Solving Word Problems with the Design Recipe.]
 MI.7.G.B.6

Solve realworld and mathematical problems involving area, volume and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [See: Solving Word Problems with the Design Recipe; Surface Area of a Rectangular Prism.]
 MI.7.RP.A

Analyze proportional relationships and use them to solve realworld and mathematical problems. [See: Making Flags; Making Game Images.]
 MI.7.RP.A.1

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. [See: Making Flags.]
 MI.7.RP.A.2.A

Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. [See: Functions Can Be Linear; Defining Linear Functions.]
 MI.7.RP.A.2.B

Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. [See: Functions Can Be Linear; Defining Linear Functions.]
 MI.7.SP.A

Use random sampling to draw inferences about a population. [See: Probability, Inference, and Sample Size.]
 MI.7.SP.A.1

Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. [See: Probability, Inference, and Sample Size.]
 MI.7.SP.A.2

Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. [See: Probability, Inference, and Sample Size.]
 MI.7.SP.B

Draw informal comparative inferences about two populations. [See: Bar and Pie Charts.]
 MI.8.EE.B

Understand the connections between proportional relationships, lines, and linear equations. [See: Functions Can Be Linear; Defining Linear Functions.]
 MI.8.EE.B.5

Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [See: Functions Can Be Linear; Defining Linear Functions.]
 MI.8.F.A.1

Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. [See: Contracts; The Vertical Line Test.]
 MI.8.F.A.2

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [See: Functions Can Be Linear; Defining Linear Functions.]
 MI.8.F.A.3

Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. [See: Functions Can Be Linear; Defining Linear Functions.]
 MI.8.F.B

Use functions to model relationships between quantities. [See: Functions Make Life Easier!; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition.]
 MI.8.F.B.4

Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. [See: Functions Can Be Linear; Defining Linear Functions.]
 MI.8.F.B.5

Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. [See: Functions Can Be Linear; Defining Linear Functions.]
 MI.8.G.A.1

Verify experimentally the properties of rotations, reflections, and translations. [See: Making Game Images.]
 MI.8.G.B

Understand and apply the Pythagorean Theorem. [See: The Distance Formula.]
 MI.8.G.B.7

Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions. [See: The Distance Formula.]
 MI.8.G.B.8

Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. [See: The Distance Formula.]
 MI.8.SP.A.1

Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. [See: Scatter Plots; Grouped Samples; Correlations; Linear Regression.]
 MI.8.SP.A.2

Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. [See: Scatter Plots; Correlations; Linear Regression.]
 MI.8.SP.A.3

Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. [See: Linear Regression.]
 MI.HSA.CED.A

Create equations that describe numbers or relationships. [See: Solving Word Problems with the Design Recipe; Surface Area of a Rectangular Prism; Problem Decomposition; Sam the Butterfly  Applying Inequalities.]
 MI.HSA.CED.A.1

Create equations and inequalities in one variable and use them to solve problems. [See: Sam the Butterfly  Applying Inequalities.]
 MI.HSA.CED.A.2

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [See: Sam the Butterfly  Applying Inequalities.]
 MI.HSA.CED.A.3

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. [See: Sam the Butterfly  Applying Inequalities.]
 MI.HSA.SSE.A.1

Interpret expressions that represent a quantity in terms of its context. [See: Defining Values; Functions Make Life Easier!; Solving Word Problems with the Design Recipe.]
 MI.HSA.SSE.A.1.A

Interpret parts of an expression, such as terms, factors, and coefficients. [See: Piecewise Functions and Conditionals; Player Animation.]
 MI.HSA.SSE.A.1.B

Interpret complicated expressions by viewing one or more of their parts as a single entity. [See: Piecewise Functions and Conditionals; Player Animation; Custom Scatter Plots.]
 MI.HSA.SSE.A.2

Use the structure of an expression to identify ways to rewrite it. [See: Order of Operations.]
 MI.HSA.SSE.B

Write expressions in equivalent forms to solve problems. [See: Order of Operations.]
 MI.HSF.BF.A

Build a function that models a relationship between two quantities. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 MI.HSF.BF.A.1

Write a function that describes a relationship between two quantities. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 MI.HSF.BF.A.1.B

Combine standard function types using arithmetic operations. [See: Function Composition.]
 MI.HSF.BF.A.1.C

Compose functions. [See: Function Composition; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality.]
 MI.HSF.BF.B

Build new functions from existing functions. [See: Problem Decomposition; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality.]
 MI.HSF.IF.A

Understand the concept of a function and use function notation. [See: Functions Make Life Easier!; Function Notation.]
 MI.HSF.IF.A.1

Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). [See: Contracts; The Vertical Line Test.]
 MI.HSF.IF.A.2

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. [See: Contracts; Making Flags; Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 MI.HSF.IF.B

Interpret functions that arise in applications in terms of the context. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 MI.HSF.IF.B.5

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. [See: Functions Can Be Linear; Defining Linear Functions.]
 MI.HSF.IF.C

Analyze functions using different representations. [See: The Vertical Line Test; Functions: Contracts, Examples & Definitions; Functions Can Be Linear; Defining Linear Functions; Solving Word Problems with the Design Recipe.]
 MI.HSF.IF.C.9

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [See: Functions Can Be Linear; Defining Linear Functions; Problem Decomposition.]
 MI.HSN.Q.A

Reason quantitatively and use units to solve problems. [See: Making Flags.]
 MI.HSS.CP.A.1

Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ('or', 'and', 'not'). [See: Compound Inequalities: Solutions & NonSolutions.]
 MI.HSS.CP.B.9

Use permutations and combinations to compute probabilities of compound events and solve problems. [See: Permutations; Combinations.]
 MI.HSS.IC.A

Understand and evaluate random processes underlying statistical experiments. [See: Probability, Inference, and Sample Size.]
 MI.HSS.IC.A.1

Understand statistics as a process for making inferences about population parameters based on a random sample from that population. [See: Probability, Inference, and Sample Size.]
 MI.HSS.IC.B

Make inferences and justify conclusions from sample surveys, experiments, and observational studies. [See: Collecting Data.]
 MI.HSS.IC.B.3

Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. [See: Probability, Inference, and Sample Size; Collecting Data.]
 MI.HSS.IC.B.4

Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. [See: Collecting Data.]
 MI.HSS.IC.B.6

Evaluate reports based on data. [See: Threats to Validity.]
 MI.HSS.ID.A

Summarize, represent, and interpret data on a single count or measurement variable. [See: Bar and Pie Charts; Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 MI.HSS.ID.A.1

Represent data with plots on the real number line (dot plots, histograms, and box plots). [See: Histograms; Visualizing the “Shape” of Data; Box Plots; Standard Deviation.]
 MI.HSS.ID.A.2

Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. [See: Histograms; Measures of Center; Box Plots; Standard Deviation.]
 MI.HSS.ID.A.3

Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots; Standard Deviation.]
 MI.HSS.ID.B

Summarize, represent, and interpret data on two categorical and quantitative variables. [See: Scatter Plots; Correlations.]
 MI.HSS.ID.B.6

Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. [See: Scatter Plots; Correlations.]
 MI.HSS.ID.B.6.A

Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. [See: Linear Regression.]
 MI.HSS.ID.B.6.C

Fit a linear function for a scatter plot that suggests a linear association. [See: Linear Regression.]
 MI.HSS.ID.C

Interpret linear models. [See: Linear Regression.]
 MI.HSS.ID.C.7

Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. [See: Linear Regression.]
 MI.HSS.ID.C.8

Compute (using technology) and interpret the correlation coefficient of a linear fit. [See: Scatter Plots; Correlations; Linear Regression.]
 MI.HSS.ID.C.9

Distinguish between correlation and causation. [See: Correlations; Linear Regression.]
 MI.SL.910.1

Initiate and participate effectively in a range of collaborative discussions (oneonone, in groups, and teacherled) with diverse partners on grades 910 topics, texts, and issues, building on others' ideas and expressing their own clearly and persuasively. [See: Introduction to Data Science.]
Maryland Standards
 MD.5.G.A.1

Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., xaxis and xcoordinate, yaxis and ycoordinate). [See: Coordinates and Game Design.]
 MD.5.OA.A

Write and interpret numerical expressions. [See: Order of Operations.]
 MD.5.OA.A.1

Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. [See: Order of Operations.]
 MD.6.EE.B

Reason about and solve onevariable equations and inequalities. [See: Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 MD.6.EE.B.6

Use variables to represent numbers and write expressions when solving a realworld or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. [See: Piecewise Functions and Conditionals; Function Composition; Defining Values; Functions Make Life Easier!; Functions: Contracts, Examples & Definitions; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Surface Area of a Rectangular Prism; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality; Defining Table Functions; Grouped Samples; Linear Regression.]
 MD.6.EE.B.8

Write an inequality of the form x > c or x < c to represent a constraint or condition in a realworld or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. [See: Simple Inequalities; Sam the Butterfly  Applying Inequalities.]
 MD.6.G.A

Solve realworld and mathematical problems involving area, surface area, and volume. [See: Surface Area of a Rectangular Prism.]
 MD.6.G.A.4

Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [See: Surface Area of a Rectangular Prism.]
 MD.6.RP.A

Understand ratio concepts and use ratio reasoning to solve problems. [See: Making Flags; Bar and Pie Charts.]
 MD.6.RP.A.1

Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. [See: Making Flags.]
 MD.6.RP.A.3.D

Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. [See: Making Flags.]
 MD.6.SP.A

Develop understanding of statistical variability. [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 MD.6.SP.A.1

Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. [See: Introduction to Data Science; The Data Cycle; Choosing Your Dataset.]
 MD.6.SP.A.2

Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots; Standard Deviation.]
 MD.6.SP.A.3

Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. [See: Box Plots; Standard Deviation.]
 MD.6.SP.B

Summarize and describe distributions. [See: Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 MD.6.SP.B.4

Display numerical data in plots on a number line, including dot plots, histograms, and box plots. [See: Histograms; Visualizing the “Shape” of Data; Box Plots; Standard Deviation.]
 MD.6.SP.B.5

Summarize numerical data sets in relation to their context. [See: Measures of Center; Box Plots; Standard Deviation.]
 MD.6.SP.B.5.C

Summarize numerical data sets in relation to their context by giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. [See: Measures of Center; Box Plots; Standard Deviation.]
 MD.6.SP.B.5.D

Summarize numerical data sets in relation to their context by relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. [See: Measures of Center.]
 MD.7.EE.A.2

Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. [See: Problem Decomposition.]
 MD.7.EE.B

Solve reallife and mathematical problems using numerical and algebraic expressions and equations. [See: Piecewise Functions and Conditionals; Solving Word Problems with the Design Recipe; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Player Animation; The Distance Formula.]
 MD.7.EE.B.4

Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. [See: Defining Values; Functions Make Life Easier!; Solving Word Problems with the Design Recipe; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 MD.7.G.B.4

Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. [See: Solving Word Problems with the Design Recipe.]
 MD.7.G.B.6

Solve realworld and mathematical problems involving area, volume and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [See: Solving Word Problems with the Design Recipe; Surface Area of a Rectangular Prism.]
 MD.7.RP.A

Analyze proportional relationships and use them to solve realworld and mathematical problems. [See: Making Flags; Making Game Images.]
 MD.7.RP.A.1

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. [See: Making Flags.]
 MD.7.RP.A.2.A

Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. [See: Functions Can Be Linear; Defining Linear Functions.]
 MD.7.RP.A.2.B

Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. [See: Functions Can Be Linear; Defining Linear Functions.]
 MD.7.SP.A

Use random sampling to draw inferences about a population. [See: Probability, Inference, and Sample Size.]
 MD.7.SP.A.1

Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. [See: Probability, Inference, and Sample Size.]
 MD.7.SP.A.2

Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. [See: Probability, Inference, and Sample Size.]
 MD.7.SP.B

Draw informal comparative inferences about two populations. [See: Bar and Pie Charts.]
 MD.8.EE.B

Understand the connections between proportional relationships, lines, and linear equations. [See: Functions Can Be Linear; Defining Linear Functions.]
 MD.8.EE.B.5

Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [See: Functions Can Be Linear; Defining Linear Functions.]
 MD.8.F.A.1

Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. [See: Contracts; The Vertical Line Test.]
 MD.8.F.A.2

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [See: Functions Can Be Linear; Defining Linear Functions.]
 MD.8.F.A.3

Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. [See: Functions Can Be Linear; Defining Linear Functions.]
 MD.8.F.B

Use functions to model relationships between quantities. [See: Functions Make Life Easier!; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition.]
 MD.8.F.B.4

Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. [See: Functions Can Be Linear; Defining Linear Functions.]
 MD.8.F.B.5

Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. [See: Functions Can Be Linear; Defining Linear Functions.]
 MD.8.G.A.1

Verify experimentally the properties of rotations, reflections, and translations. [See: Making Game Images.]
 MD.8.G.B

Understand and apply the Pythagorean Theorem. [See: The Distance Formula.]
 MD.8.G.B.7

Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions. [See: The Distance Formula.]
 MD.8.G.B.8

Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. [See: The Distance Formula.]
 MD.8.SP.A.1

Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. [See: Scatter Plots; Grouped Samples; Correlations; Linear Regression.]
 MD.8.SP.A.2

Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. [See: Scatter Plots; Correlations; Linear Regression.]
 MD.8.SP.A.3

Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. [See: Linear Regression.]
 MD.HSA.CED.A

Create equations that describe numbers or relationships. [See: Solving Word Problems with the Design Recipe; Surface Area of a Rectangular Prism; Problem Decomposition; Sam the Butterfly  Applying Inequalities.]
 MD.HSA.CED.A.1

Create equations and inequalities in one variable and use them to solve problems. [See: Sam the Butterfly  Applying Inequalities.]
 MD.HSA.CED.A.2

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [See: Sam the Butterfly  Applying Inequalities.]
 MD.HSA.CED.A.3

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. [See: Sam the Butterfly  Applying Inequalities.]
 MD.HSA.SSE.A.1

Interpret expressions that represent a quantity in terms of its context. [See: Defining Values; Functions Make Life Easier!; Solving Word Problems with the Design Recipe.]
 MD.HSA.SSE.A.1.A

Interpret parts of an expression, such as terms, factors, and coefficients. [See: Piecewise Functions and Conditionals; Player Animation.]
 MD.HSA.SSE.A.1.B

Interpret complicated expressions by viewing one or more of their parts as a single entity. [See: Piecewise Functions and Conditionals; Player Animation; Custom Scatter Plots.]
 MD.HSA.SSE.A.2

Use the structure of an expression to identify ways to rewrite it. [See: Order of Operations.]
 MD.HSA.SSE.B

Write expressions in equivalent forms to solve problems. [See: Order of Operations.]
 MD.HSF.BF.A

Build a function that models a relationship between two quantities. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 MD.HSF.BF.A.1

Write a function that describes a relationship between two quantities. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 MD.HSF.BF.A.1.B

Combine standard function types using arithmetic operations. [See: Function Composition.]
 MD.HSF.BF.A.1.C

Compose functions. [See: Function Composition; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality.]
 MD.HSF.BF.B

Build new functions from existing functions. [See: Problem Decomposition; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality.]
 MD.HSF.IF.A

Understand the concept of a function and use function notation. [See: Functions Make Life Easier!; Function Notation.]
 MD.HSF.IF.A.1

Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). [See: Contracts; The Vertical Line Test.]
 MD.HSF.IF.A.2

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. [See: Contracts; Making Flags; Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 MD.HSF.IF.B

Interpret functions that arise in applications in terms of the context. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 MD.HSF.IF.B.5

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. [See: Functions Can Be Linear; Defining Linear Functions.]
 MD.HSF.IF.C

Analyze functions using different representations. [See: The Vertical Line Test; Functions: Contracts, Examples & Definitions; Functions Can Be Linear; Defining Linear Functions; Solving Word Problems with the Design Recipe.]
 MD.HSF.IF.C.9

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [See: Functions Can Be Linear; Defining Linear Functions; Problem Decomposition.]
 MD.HSN.Q.A

Reason quantitatively and use units to solve problems. [See: Making Flags.]
 MD.HSS.CP.A.1

Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ('or', 'and', 'not'). [See: Compound Inequalities: Solutions & NonSolutions.]
 MD.HSS.CP.B.9

Use permutations and combinations to compute probabilities of compound events and solve problems. [See: Permutations; Combinations.]
 MD.HSS.IC.A

Understand and evaluate random processes underlying statistical experiments. [See: Probability, Inference, and Sample Size.]
 MD.HSS.IC.A.1

Understand statistics as a process for making inferences about population parameters based on a random sample from that population. [See: Probability, Inference, and Sample Size.]
 MD.HSS.IC.B

Make inferences and justify conclusions from sample surveys, experiments, and observational studies. [See: Collecting Data.]
 MD.HSS.IC.B.3

Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. [See: Probability, Inference, and Sample Size; Collecting Data.]
 MD.HSS.IC.B.4

Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. [See: Collecting Data.]
 MD.HSS.IC.B.6

Evaluate reports based on data. [See: Threats to Validity.]
 MD.HSS.ID.A

Summarize, represent, and interpret data on a single count or measurement variable. [See: Bar and Pie Charts; Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 MD.HSS.ID.A.1

Represent data with plots on the real number line (dot plots, histograms, and box plots). [See: Histograms; Visualizing the “Shape” of Data; Box Plots; Standard Deviation.]
 MD.HSS.ID.A.2

Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. [See: Histograms; Measures of Center; Box Plots; Standard Deviation.]
 MD.HSS.ID.A.3

Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots; Standard Deviation.]
 MD.HSS.ID.B

Summarize, represent, and interpret data on two categorical and quantitative variables. [See: Scatter Plots; Correlations.]
 MD.HSS.ID.B.6

Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. [See: Scatter Plots; Correlations.]
 MD.HSS.ID.B.6.A

Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. [See: Linear Regression.]
 MD.HSS.ID.B.6.C

Fit a linear function for a scatter plot that suggests a linear association. [See: Linear Regression.]
 MD.HSS.ID.C

Interpret linear models. [See: Linear Regression.]
 MD.HSS.ID.C.7

Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. [See: Linear Regression.]
 MD.HSS.ID.C.8

Compute (using technology) and interpret the correlation coefficient of a linear fit. [See: Scatter Plots; Correlations; Linear Regression.]
 MD.HSS.ID.C.9

Distinguish between correlation and causation. [See: Correlations; Linear Regression.]
 MD.SL.910.1

Initiate and participate effectively in a range of collaborative discussions (oneonone, in groups, and teacherled) with diverse partners on grades 910 topics, texts, and issues, building on others' ideas and expressing their own clearly and persuasively. [See: Introduction to Data Science.]
Massachusetts Standards
 MA.35.CAS.b.2

Describe the difference between digital artifacts that are open or free and those that are protected by copyright. [See: Making Game Images.]
 MA.5.G.A.1

Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., xaxis and xcoordinate, yaxis and ycoordinate). [See: Coordinates and Game Design.]
 MA.5.OA.A

Write and interpret numerical expressions. [See: Order of Operations.]
 MA.5.OA.A.1

Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. [See: Order of Operations.]
 MA.68.CAS.b.1

Explain how copyright law and licensing protect the owner of intellectual property. [See: Making Game Images.]
 MA.68.CAS.c.4

Evaluate how media and technology can be used to distort, exaggerate, and misrepresent information. [See: Measures of Center; Threats to Validity.]
 MA.68.CT.a.2

Define a simple function that represents a more complex task/problem and can be reused to solve similar tasks/problems. [See: Functions Make Life Easier!; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Sam the Butterfly  Applying Inequalities; Introduction to Data Structures; Structures, Reactors, and Animations; Functions That Ask Questions; Key Events; Refactoring; Scoring; Going Deeper: Nested Structures; Feature: Timers.]
 MA.68.CT.b.1

Design solutions that use repetition and conditionals. [See: Piecewise Functions and Conditionals; Player Animation; Table Methods; Defining Table Functions.]
 MA.68.CT.b.2

Use logical reasoning to predict outputs given varying inputs. [See: Functions Make Life Easier!; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Sam the Butterfly  Applying Inequalities; Introduction to Data Structures; Structures, Reactors, and Animations; Functions That Ask Questions; Key Events; Refactoring; Scoring; Going Deeper: Nested Structures; Feature: Timers.]
 MA.68.CT.b.3

Individually and collaboratively decompose a problem and create a subsolution for each of its parts (e.g., video game, robot obstacle course, making dinner). [See: Problem Decomposition; Collision Detection  Distance and Inequality.]
 MA.68.CT.b.5

Recognize that boundaries need to be taken into account for an algorithm to produce correct results. [See: Sam the Butterfly  Applying Inequalities.]
 MA.68.CT.c.4

Perform a variety of operations such as sorting, filtering, and searching in a database to organize and display information in a variety of ways such as number formats (scientific notation and percentages), charts, tables, and graphs. [See: Table Methods.]
 MA.68.CT.c.5

Select and use datacollection technology (e.g., probes, handheld devices, geographic mapping systems) to individually and collaboratively gather, view, organize, analyze, and report results for contentrelated problems. [See: Collecting Data.]
 MA.68.CT.d.2

Use functions to hide the detail in a program. [See: Functions Make Life Easier!; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Sam the Butterfly  Applying Inequalities; Introduction to Data Structures; Structures, Reactors, and Animations; Functions That Ask Questions; Key Events; Refactoring; Scoring; Going Deeper: Nested Structures; Feature: Timers.]
 MA.68.CT.d.4

Implement problem solutions using a programming language, including all of the following: looping behavior, conditional statements, expressions, variables, and functions. [See: Piecewise Functions and Conditionals; Player Animation.]
 MA.68.CT.d.5

Trace programs stepbystep in order to predict their behavior. [See: Functions Make Life Easier!; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Sam the Butterfly  Applying Inequalities; Introduction to Data Structures; Structures, Reactors, and Animations; Functions That Ask Questions; Key Events; Refactoring; Scoring; Going Deeper: Nested Structures; Feature: Timers.]
 MA.68.CT.d.6

Use an iterative approach in development and debugging to understand the dimensions of a problem clearly. [See: Debugging.]
 MA.68.DTC.a.4

Individually and collaboratively use advanced tools to design and create online content (e.g., digital portfolio, multimedia, blog, webpage). [See: Making Game Images; Functions for Character Animation; Sam the Butterfly  Applying Inequalities; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality.]
 MA.68.DTC.a.5

Individually and collaboratively develop and conduct an online survey. [See: Collecting Data.]
 MA.6.EE.B

Reason about and solve onevariable equations and inequalities. [See: Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 MA.6.EE.B.6

Use variables to represent numbers and write expressions when solving a realworld or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. [See: Piecewise Functions and Conditionals; Function Composition; Defining Values; Functions Make Life Easier!; Functions: Contracts, Examples & Definitions; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Surface Area of a Rectangular Prism; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality; Defining Table Functions; Grouped Samples; Linear Regression.]
 MA.6.EE.B.8

Write an inequality of the form x > c or x < c to represent a constraint or condition in a realworld or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. [See: Simple Inequalities; Sam the Butterfly  Applying Inequalities.]
 MA.6.G.A

Solve realworld and mathematical problems involving area, surface area, and volume. [See: Surface Area of a Rectangular Prism.]
 MA.6.G.A.4

Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [See: Surface Area of a Rectangular Prism.]
 MA.6.RP.A

Understand ratio concepts and use ratio reasoning to solve problems. [See: Making Flags; Bar and Pie Charts.]
 MA.6.RP.A.1

Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. [See: Making Flags.]
 MA.6.RP.A.3.D

Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. [See: Making Flags.]
 MA.6.SP.A

Develop understanding of statistical variability. [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 MA.6.SP.A.1

Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. [See: Introduction to Data Science; The Data Cycle; Choosing Your Dataset.]
 MA.6.SP.A.2

Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots; Standard Deviation.]
 MA.6.SP.A.3

Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. [See: Box Plots; Standard Deviation.]
 MA.6.SP.B

Summarize and describe distributions. [See: Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 MA.6.SP.B.4

Display numerical data in plots on a number line, including dot plots, histograms, and box plots. [See: Histograms; Visualizing the “Shape” of Data; Box Plots; Standard Deviation.]
 MA.6.SP.B.5

Summarize numerical data sets in relation to their context. [See: Measures of Center; Box Plots; Standard Deviation.]
 MA.6.SP.B.5.C

Summarize numerical data sets in relation to their context by giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. [See: Measures of Center; Box Plots; Standard Deviation.]
 MA.6.SP.B.5.D

Summarize numerical data sets in relation to their context by relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. [See: Measures of Center.]
 MA.7.EE.A.2

Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. [See: Problem Decomposition.]
 MA.7.EE.B

Solve reallife and mathematical problems using numerical and algebraic expressions and equations. [See: Piecewise Functions and Conditionals; Solving Word Problems with the Design Recipe; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Player Animation; The Distance Formula.]
 MA.7.EE.B.4

Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. [See: Defining Values; Functions Make Life Easier!; Solving Word Problems with the Design Recipe; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 MA.7.G.B.4

Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. [See: Solving Word Problems with the Design Recipe.]
 MA.7.G.B.6

Solve realworld and mathematical problems involving area, volume and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [See: Solving Word Problems with the Design Recipe; Surface Area of a Rectangular Prism.]
 MA.7.RP.A

Analyze proportional relationships and use them to solve realworld and mathematical problems. [See: Making Flags; Making Game Images.]
 MA.7.RP.A.1

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. [See: Making Flags.]
 MA.7.RP.A.2.A

Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. [See: Functions Can Be Linear; Defining Linear Functions.]
 MA.7.RP.A.2.B

Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. [See: Functions Can Be Linear; Defining Linear Functions.]
 MA.7.SP.A

Use random sampling to draw inferences about a population. [See: Probability, Inference, and Sample Size.]
 MA.7.SP.A.1

Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. [See: Probability, Inference, and Sample Size.]
 MA.7.SP.A.2

Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. [See: Probability, Inference, and Sample Size.]
 MA.7.SP.B

Draw informal comparative inferences about two populations. [See: Bar and Pie Charts.]
 MA.8.EE.B

Understand the connections between proportional relationships, lines, and linear equations. [See: Functions Can Be Linear; Defining Linear Functions.]
 MA.8.EE.B.5

Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [See: Functions Can Be Linear; Defining Linear Functions.]
 MA.8.F.A.1

Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. [See: Contracts; The Vertical Line Test.]
 MA.8.F.A.2

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [See: Functions Can Be Linear; Defining Linear Functions.]
 MA.8.F.A.3

Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. [See: Functions Can Be Linear; Defining Linear Functions.]
 MA.8.F.B

Use functions to model relationships between quantities. [See: Functions Make Life Easier!; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition.]
 MA.8.F.B.4

Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. [See: Functions Can Be Linear; Defining Linear Functions.]
 MA.8.F.B.5

Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. [See: Functions Can Be Linear; Defining Linear Functions.]
 MA.8.G.A.1

Verify experimentally the properties of rotations, reflections, and translations. [See: Making Game Images.]
 MA.8.G.B

Understand and apply the Pythagorean Theorem. [See: The Distance Formula.]
 MA.8.G.B.7

Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions. [See: The Distance Formula.]
 MA.8.G.B.8

Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. [See: The Distance Formula.]
 MA.8.SP.A.1

Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. [See: Scatter Plots; Grouped Samples; Correlations; Linear Regression.]
 MA.8.SP.A.2

Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. [See: Scatter Plots; Correlations; Linear Regression.]
 MA.8.SP.A.3

Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. [See: Linear Regression.]
 MA.912.CT.a.1

Discuss and give an example of the value of generalizing and decomposing aspects of a problem in order to solve it more effectively. [See: Problem Decomposition; Collision Detection  Distance and Inequality; Going Deeper: Nested Structures.]
 MA.912.CT.b.2

Represent algorithms using structured language, such as pseudocode. [See: Functions Make Life Easier!; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Sam the Butterfly  Applying Inequalities; Introduction to Data Structures; Structures, Reactors, and Animations; Functions That Ask Questions; Key Events; Refactoring; Scoring; Going Deeper: Nested Structures; Feature: Timers.]
 MA.912.CT.c.2

Create an appropriate multidimensional data structure that can be filtered, sorted, and searched (e.g., array, list, record). [See: Table Methods; Defining Table Functions.]
 MA.912.CT.c.3

Create, evaluate, and revise data visualization for communication and knowledge. [See: Bar and Pie Charts; Histograms; Visualizing the “Shape” of Data; Box Plots; Scatter Plots; Custom Scatter Plots; Correlations; Linear Regression.]
 MA.912.CT.c.4

Analyze a complex data set to answer a question or test a hypothesis (e.g., analyze a large set of weather or financial data to predict future patterns). [See: Visualizing the “Shape” of Data; Measures of Center; Linear Regression.]
 MA.912.CT.d.10

Use an iterative design process, including learning from making mistakes, to gain a better understanding of the problem domain. [See: Making Flags.]
 MA.912.CT.d.11

Engage in systematic testing and debugging methods to ensure program correctness. [See: Debugging.]
 MA.912.CT.d.12

Demonstrate how to document a program so that others can understand its design and implementation. [See: Solving Word Problems with the Design Recipe.]
 MA.912.CT.d.3

Select the appropriate data structure to represent information for a given problem (e.g., records, arrays, lists). [See: Table Methods; Defining Table Functions.]
 MA.912.CT.d.5

Use appropriate looping structures in programs (e.g., FOR, WHILE, RECURSION). [See: Table Methods; Defining Table Functions.]
 MA.912.CT.d.6

Use appropriate conditional structures in programs (e.g., IFTHEN, IFTHENELSE, SWITCH). [See: Piecewise Functions and Conditionals; Player Animation; Key Events.]
 MA.912.CT.d.7

Use a programming language or tool feature correctly to enforce operator precedence. [See: Order of Operations.]
 MA.912.CT.d.8

Use global and local scope appropriately in program design (e.g., for variables). [See: Making Flags.]
 MA.912.DTC.c.1

Generate, evaluate, and prioritize questions that can be researched through digital resources or tools. [See: Introduction to Data Science.]
 MA.912.DTC.c.4

Gather, organize, analyze, and synthesize information using a variety of digital tools. [See: Collecting Data.]
 MA.HSA.CED.A

Create equations that describe numbers or relationships. [See: Solving Word Problems with the Design Recipe; Surface Area of a Rectangular Prism; Problem Decomposition; Sam the Butterfly  Applying Inequalities.]
 MA.HSA.CED.A.1

Create equations and inequalities in one variable and use them to solve problems. [See: Sam the Butterfly  Applying Inequalities.]
 MA.HSA.CED.A.2

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [See: Sam the Butterfly  Applying Inequalities.]
 MA.HSA.CED.A.3

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. [See: Sam the Butterfly  Applying Inequalities.]
 MA.HSA.SSE.A.1

Interpret expressions that represent a quantity in terms of its context. [See: Defining Values; Functions Make Life Easier!; Solving Word Problems with the Design Recipe.]
 MA.HSA.SSE.A.1.A

Interpret parts of an expression, such as terms, factors, and coefficients. [See: Piecewise Functions and Conditionals; Player Animation.]
 MA.HSA.SSE.A.1.B

Interpret complicated expressions by viewing one or more of their parts as a single entity. [See: Piecewise Functions and Conditionals; Player Animation; Custom Scatter Plots.]
 MA.HSA.SSE.A.2

Use the structure of an expression to identify ways to rewrite it. [See: Order of Operations.]
 MA.HSA.SSE.B

Write expressions in equivalent forms to solve problems. [See: Order of Operations.]
 MA.HSF.BF.A

Build a function that models a relationship between two quantities. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 MA.HSF.BF.A.1

Write a function that describes a relationship between two quantities. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 MA.HSF.BF.A.1.B

Combine standard function types using arithmetic operations. [See: Function Composition.]
 MA.HSF.BF.A.1.C

Compose functions. [See: Function Composition; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality.]
 MA.HSF.BF.B

Build new functions from existing functions. [See: Problem Decomposition; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality.]
 MA.HSF.IF.A

Understand the concept of a function and use function notation. [See: Functions Make Life Easier!; Function Notation.]
 MA.HSF.IF.A.1

Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). [See: Contracts; The Vertical Line Test.]
 MA.HSF.IF.A.2

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. [See: Contracts; Making Flags; Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 MA.HSF.IF.B

Interpret functions that arise in applications in terms of the context. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 MA.HSF.IF.B.5

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. [See: Functions Can Be Linear; Defining Linear Functions.]
 MA.HSF.IF.C

Analyze functions using different representations. [See: The Vertical Line Test; Functions: Contracts, Examples & Definitions; Functions Can Be Linear; Defining Linear Functions; Solving Word Problems with the Design Recipe.]
 MA.HSF.IF.C.9

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [See: Functions Can Be Linear; Defining Linear Functions; Problem Decomposition.]
 MA.HSN.Q.A

Reason quantitatively and use units to solve problems. [See: Making Flags.]
 MA.HSS.CP.A.1

Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ('or', 'and', 'not'). [See: Compound Inequalities: Solutions & NonSolutions.]
 MA.HSS.CP.B.9

Use permutations and combinations to compute probabilities of compound events and solve problems. [See: Permutations; Combinations.]
 MA.HSS.IC.A

Understand and evaluate random processes underlying statistical experiments. [See: Probability, Inference, and Sample Size.]
 MA.HSS.IC.A.1

Understand statistics as a process for making inferences about population parameters based on a random sample from that population. [See: Probability, Inference, and Sample Size.]
 MA.HSS.IC.B

Make inferences and justify conclusions from sample surveys, experiments, and observational studies. [See: Collecting Data.]
 MA.HSS.IC.B.3

Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. [See: Probability, Inference, and Sample Size; Collecting Data.]
 MA.HSS.IC.B.4

Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. [See: Collecting Data.]
 MA.HSS.IC.B.6

Evaluate reports based on data. [See: Threats to Validity.]
 MA.HSS.ID.A

Summarize, represent, and interpret data on a single count or measurement variable. [See: Bar and Pie Charts; Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 MA.HSS.ID.A.1

Represent data with plots on the real number line (dot plots, histograms, and box plots). [See: Histograms; Visualizing the “Shape” of Data; Box Plots; Standard Deviation.]
 MA.HSS.ID.A.2

Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. [See: Histograms; Measures of Center; Box Plots; Standard Deviation.]
 MA.HSS.ID.A.3

Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots; Standard Deviation.]
 MA.HSS.ID.B

Summarize, represent, and interpret data on two categorical and quantitative variables. [See: Scatter Plots; Correlations.]
 MA.HSS.ID.B.6

Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. [See: Scatter Plots; Correlations.]
 MA.HSS.ID.B.6.A

Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. [See: Linear Regression.]
 MA.HSS.ID.B.6.C

Fit a linear function for a scatter plot that suggests a linear association. [See: Linear Regression.]
 MA.HSS.ID.C

Interpret linear models. [See: Linear Regression.]
 MA.HSS.ID.C.7

Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. [See: Linear Regression.]
 MA.HSS.ID.C.8

Compute (using technology) and interpret the correlation coefficient of a linear fit. [See: Scatter Plots; Correlations; Linear Regression.]
 MA.HSS.ID.C.9

Distinguish between correlation and causation. [See: Correlations; Linear Regression.]
 MA.SL.910.1

Initiate and participate effectively in a range of collaborative discussions (oneonone, in groups, and teacherled) with diverse partners on grades 910 topics, texts, and issues, building on others' ideas and expressing their own clearly and persuasively. [See: Introduction to Data Science.]
Mississippi Standards
 MS.5.G.A.1

Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., xaxis and xcoordinate, yaxis and ycoordinate). [See: Coordinates and Game Design.]
 MS.5.OA.A

Write and interpret numerical expressions. [See: Order of Operations.]
 MS.5.OA.A.1

Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. [See: Order of Operations.]
 MS.6.EE.B

Reason about and solve onevariable equations and inequalities. [See: Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 MS.6.EE.B.6

Use variables to represent numbers and write expressions when solving a realworld or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. [See: Piecewise Functions and Conditionals; Function Composition; Defining Values; Functions Make Life Easier!; Functions: Contracts, Examples & Definitions; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Surface Area of a Rectangular Prism; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality; Defining Table Functions; Grouped Samples; Linear Regression.]
 MS.6.EE.B.8

Write an inequality of the form x > c or x < c to represent a constraint or condition in a realworld or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. [See: Simple Inequalities; Sam the Butterfly  Applying Inequalities.]
 MS.6.G.A

Solve realworld and mathematical problems involving area, surface area, and volume. [See: Surface Area of a Rectangular Prism.]
 MS.6.G.A.4

Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [See: Surface Area of a Rectangular Prism.]
 MS.6.RP.A

Understand ratio concepts and use ratio reasoning to solve problems. [See: Making Flags; Bar and Pie Charts.]
 MS.6.RP.A.1

Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. [See: Making Flags.]
 MS.6.RP.A.3.D

Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. [See: Making Flags.]
 MS.6.SP.A

Develop understanding of statistical variability. [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 MS.6.SP.A.1

Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. [See: Introduction to Data Science; The Data Cycle; Choosing Your Dataset.]
 MS.6.SP.A.2

Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots; Standard Deviation.]
 MS.6.SP.A.3

Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. [See: Box Plots; Standard Deviation.]
 MS.6.SP.B

Summarize and describe distributions. [See: Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 MS.6.SP.B.4

Display numerical data in plots on a number line, including dot plots, histograms, and box plots. [See: Histograms; Visualizing the “Shape” of Data; Box Plots; Standard Deviation.]
 MS.6.SP.B.5

Summarize numerical data sets in relation to their context. [See: Measures of Center; Box Plots; Standard Deviation.]
 MS.6.SP.B.5.C

Summarize numerical data sets in relation to their context by giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. [See: Measures of Center; Box Plots; Standard Deviation.]
 MS.6.SP.B.5.D

Summarize numerical data sets in relation to their context by relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. [See: Measures of Center.]
 MS.7.EE.A.2

Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. [See: Problem Decomposition.]
 MS.7.EE.B

Solve reallife and mathematical problems using numerical and algebraic expressions and equations. [See: Piecewise Functions and Conditionals; Solving Word Problems with the Design Recipe; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Player Animation; The Distance Formula.]
 MS.7.EE.B.4

Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. [See: Defining Values; Functions Make Life Easier!; Solving Word Problems with the Design Recipe; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 MS.7.G.B.4

Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. [See: Solving Word Problems with the Design Recipe.]
 MS.7.G.B.6

Solve realworld and mathematical problems involving area, volume and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [See: Solving Word Problems with the Design Recipe; Surface Area of a Rectangular Prism.]
 MS.7.RP.A

Analyze proportional relationships and use them to solve realworld and mathematical problems. [See: Making Flags; Making Game Images.]
 MS.7.RP.A.1

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. [See: Making Flags.]
 MS.7.RP.A.2.A

Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. [See: Functions Can Be Linear; Defining Linear Functions.]
 MS.7.RP.A.2.B

Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. [See: Functions Can Be Linear; Defining Linear Functions.]
 MS.7.SP.A

Use random sampling to draw inferences about a population. [See: Probability, Inference, and Sample Size.]
 MS.7.SP.A.1

Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. [See: Probability, Inference, and Sample Size.]
 MS.7.SP.A.2

Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. [See: Probability, Inference, and Sample Size.]
 MS.7.SP.B

Draw informal comparative inferences about two populations. [See: Bar and Pie Charts.]
 MS.8.EE.B

Understand the connections between proportional relationships, lines, and linear equations. [See: Functions Can Be Linear; Defining Linear Functions.]
 MS.8.EE.B.5

Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [See: Functions Can Be Linear; Defining Linear Functions.]
 MS.8.F.A.1

Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. [See: Contracts; The Vertical Line Test.]
 MS.8.F.A.2

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [See: Functions Can Be Linear; Defining Linear Functions.]
 MS.8.F.A.3

Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. [See: Functions Can Be Linear; Defining Linear Functions.]
 MS.8.F.B

Use functions to model relationships between quantities. [See: Functions Make Life Easier!; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition.]
 MS.8.F.B.4

Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. [See: Functions Can Be Linear; Defining Linear Functions.]
 MS.8.F.B.5

Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. [See: Functions Can Be Linear; Defining Linear Functions.]
 MS.8.G.A.1

Verify experimentally the properties of rotations, reflections, and translations. [See: Making Game Images.]
 MS.8.G.B

Understand and apply the Pythagorean Theorem. [See: The Distance Formula.]
 MS.8.G.B.7

Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions. [See: The Distance Formula.]
 MS.8.G.B.8

Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. [See: The Distance Formula.]
 MS.8.SP.A.1

Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. [See: Scatter Plots; Grouped Samples; Correlations; Linear Regression.]
 MS.8.SP.A.2

Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. [See: Scatter Plots; Correlations; Linear Regression.]
 MS.8.SP.A.3

Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. [See: Linear Regression.]
 MS.HSA.CED.A

Create equations that describe numbers or relationships. [See: Solving Word Problems with the Design Recipe; Surface Area of a Rectangular Prism; Problem Decomposition; Sam the Butterfly  Applying Inequalities.]
 MS.HSA.CED.A.1

Create equations and inequalities in one variable and use them to solve problems. [See: Sam the Butterfly  Applying Inequalities.]
 MS.HSA.CED.A.2

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [See: Sam the Butterfly  Applying Inequalities.]
 MS.HSA.CED.A.3

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. [See: Sam the Butterfly  Applying Inequalities.]
 MS.HSA.SSE.A.1

Interpret expressions that represent a quantity in terms of its context. [See: Defining Values; Functions Make Life Easier!; Solving Word Problems with the Design Recipe.]
 MS.HSA.SSE.A.1.A

Interpret parts of an expression, such as terms, factors, and coefficients. [See: Piecewise Functions and Conditionals; Player Animation.]
 MS.HSA.SSE.A.1.B

Interpret complicated expressions by viewing one or more of their parts as a single entity. [See: Piecewise Functions and Conditionals; Player Animation; Custom Scatter Plots.]
 MS.HSA.SSE.A.2

Use the structure of an expression to identify ways to rewrite it. [See: Order of Operations.]
 MS.HSA.SSE.B

Write expressions in equivalent forms to solve problems. [See: Order of Operations.]
 MS.HSF.BF.A

Build a function that models a relationship between two quantities. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 MS.HSF.BF.A.1

Write a function that describes a relationship between two quantities. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 MS.HSF.BF.A.1.B

Combine standard function types using arithmetic operations. [See: Function Composition.]
 MS.HSF.BF.A.1.C

Compose functions. [See: Function Composition; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality.]
 MS.HSF.BF.B

Build new functions from existing functions. [See: Problem Decomposition; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality.]
 MS.HSF.IF.A

Understand the concept of a function and use function notation. [See: Functions Make Life Easier!; Function Notation.]
 MS.HSF.IF.A.1

Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). [See: Contracts; The Vertical Line Test.]
 MS.HSF.IF.A.2

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. [See: Contracts; Making Flags; Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 MS.HSF.IF.B

Interpret functions that arise in applications in terms of the context. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 MS.HSF.IF.B.5

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. [See: Functions Can Be Linear; Defining Linear Functions.]
 MS.HSF.IF.C

Analyze functions using different representations. [See: The Vertical Line Test; Functions: Contracts, Examples & Definitions; Functions Can Be Linear; Defining Linear Functions; Solving Word Problems with the Design Recipe.]
 MS.HSF.IF.C.9

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [See: Functions Can Be Linear; Defining Linear Functions; Problem Decomposition.]
 MS.HSN.Q.A

Reason quantitatively and use units to solve problems. [See: Making Flags.]
 MS.HSS.CP.A.1

Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ('or', 'and', 'not'). [See: Compound Inequalities: Solutions & NonSolutions.]
 MS.HSS.CP.B.9

Use permutations and combinations to compute probabilities of compound events and solve problems. [See: Permutations; Combinations.]
 MS.HSS.IC.A

Understand and evaluate random processes underlying statistical experiments. [See: Probability, Inference, and Sample Size.]
 MS.HSS.IC.A.1

Understand statistics as a process for making inferences about population parameters based on a random sample from that population. [See: Probability, Inference, and Sample Size.]
 MS.HSS.IC.B

Make inferences and justify conclusions from sample surveys, experiments, and observational studies. [See: Collecting Data.]
 MS.HSS.IC.B.3

Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. [See: Probability, Inference, and Sample Size; Collecting Data.]
 MS.HSS.IC.B.4

Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. [See: Collecting Data.]
 MS.HSS.IC.B.6

Evaluate reports based on data. [See: Threats to Validity.]
 MS.HSS.ID.A

Summarize, represent, and interpret data on a single count or measurement variable. [See: Bar and Pie Charts; Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 MS.HSS.ID.A.1

Represent data with plots on the real number line (dot plots, histograms, and box plots). [See: Histograms; Visualizing the “Shape” of Data; Box Plots; Standard Deviation.]
 MS.HSS.ID.A.2

Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. [See: Histograms; Measures of Center; Box Plots; Standard Deviation.]
 MS.HSS.ID.A.3

Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots; Standard Deviation.]
 MS.HSS.ID.B

Summarize, represent, and interpret data on two categorical and quantitative variables. [See: Scatter Plots; Correlations.]
 MS.HSS.ID.B.6

Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. [See: Scatter Plots; Correlations.]
 MS.HSS.ID.B.6.A

Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. [See: Linear Regression.]
 MS.HSS.ID.B.6.C

Fit a linear function for a scatter plot that suggests a linear association. [See: Linear Regression.]
 MS.HSS.ID.C

Interpret linear models. [See: Linear Regression.]
 MS.HSS.ID.C.7

Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. [See: Linear Regression.]
 MS.HSS.ID.C.8

Compute (using technology) and interpret the correlation coefficient of a linear fit. [See: Scatter Plots; Correlations; Linear Regression.]
 MS.HSS.ID.C.9

Distinguish between correlation and causation. [See: Correlations; Linear Regression.]
 MS.SL.910.1

Initiate and participate effectively in a range of collaborative discussions (oneonone, in groups, and teacherled) with diverse partners on grades 910 topics, texts, and issues, building on others' ideas and expressing their own clearly and persuasively. [See: Introduction to Data Science.]
Missouri Standards
 MO.5.G.A.1

Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., xaxis and xcoordinate, yaxis and ycoordinate). [See: Coordinates and Game Design.]
 MO.5.OA.A

Write and interpret numerical expressions. [See: Order of Operations.]
 MO.5.OA.A.1

Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. [See: Order of Operations.]
 MO.6.EE.B

Reason about and solve onevariable equations and inequalities. [See: Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 MO.6.EE.B.6

Use variables to represent numbers and write expressions when solving a realworld or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. [See: Piecewise Functions and Conditionals; Function Composition; Defining Values; Functions Make Life Easier!; Functions: Contracts, Examples & Definitions; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Surface Area of a Rectangular Prism; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality; Defining Table Functions; Grouped Samples; Linear Regression.]
 MO.6.EE.B.8

Write an inequality of the form x > c or x < c to represent a constraint or condition in a realworld or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. [See: Simple Inequalities; Sam the Butterfly  Applying Inequalities.]
 MO.6.G.A

Solve realworld and mathematical problems involving area, surface area, and volume. [See: Surface Area of a Rectangular Prism.]
 MO.6.G.A.4

Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [See: Surface Area of a Rectangular Prism.]
 MO.6.RP.A

Understand ratio concepts and use ratio reasoning to solve problems. [See: Making Flags; Bar and Pie Charts.]
 MO.6.RP.A.1

Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. [See: Making Flags.]
 MO.6.RP.A.3.D

Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. [See: Making Flags.]
 MO.6.SP.A

Develop understanding of statistical variability. [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 MO.6.SP.A.1

Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. [See: Introduction to Data Science; The Data Cycle; Choosing Your Dataset.]
 MO.6.SP.A.2

Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots; Standard Deviation.]
 MO.6.SP.A.3

Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. [See: Box Plots; Standard Deviation.]
 MO.6.SP.B

Summarize and describe distributions. [See: Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 MO.6.SP.B.4

Display numerical data in plots on a number line, including dot plots, histograms, and box plots. [See: Histograms; Visualizing the “Shape” of Data; Box Plots; Standard Deviation.]
 MO.6.SP.B.5

Summarize numerical data sets in relation to their context. [See: Measures of Center; Box Plots; Standard Deviation.]
 MO.6.SP.B.5.C

Summarize numerical data sets in relation to their context by giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. [See: Measures of Center; Box Plots; Standard Deviation.]
 MO.6.SP.B.5.D

Summarize numerical data sets in relation to their context by relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. [See: Measures of Center.]
 MO.7.EE.A.2

Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. [See: Problem Decomposition.]
 MO.7.EE.B

Solve reallife and mathematical problems using numerical and algebraic expressions and equations. [See: Piecewise Functions and Conditionals; Solving Word Problems with the Design Recipe; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Player Animation; The Distance Formula.]
 MO.7.EE.B.4

Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. [See: Defining Values; Functions Make Life Easier!; Solving Word Problems with the Design Recipe; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 MO.7.G.B.4

Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. [See: Solving Word Problems with the Design Recipe.]
 MO.7.G.B.6

Solve realworld and mathematical problems involving area, volume and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [See: Solving Word Problems with the Design Recipe; Surface Area of a Rectangular Prism.]
 MO.7.RP.A

Analyze proportional relationships and use them to solve realworld and mathematical problems. [See: Making Flags; Making Game Images.]
 MO.7.RP.A.1

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. [See: Making Flags.]
 MO.7.RP.A.2.A

Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. [See: Functions Can Be Linear; Defining Linear Functions.]
 MO.7.RP.A.2.B

Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. [See: Functions Can Be Linear; Defining Linear Functions.]
 MO.7.SP.A

Use random sampling to draw inferences about a population. [See: Probability, Inference, and Sample Size.]
 MO.7.SP.A.1

Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. [See: Probability, Inference, and Sample Size.]
 MO.7.SP.A.2

Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. [See: Probability, Inference, and Sample Size.]
 MO.7.SP.B

Draw informal comparative inferences about two populations. [See: Bar and Pie Charts.]
 MO.8.EE.B

Understand the connections between proportional relationships, lines, and linear equations. [See: Functions Can Be Linear; Defining Linear Functions.]
 MO.8.EE.B.5

Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [See: Functions Can Be Linear; Defining Linear Functions.]
 MO.8.F.A.1

Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. [See: Contracts; The Vertical Line Test.]
 MO.8.F.A.2

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [See: Functions Can Be Linear; Defining Linear Functions.]
 MO.8.F.A.3

Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. [See: Functions Can Be Linear; Defining Linear Functions.]
 MO.8.F.B

Use functions to model relationships between quantities. [See: Functions Make Life Easier!; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition.]
 MO.8.F.B.4

Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. [See: Functions Can Be Linear; Defining Linear Functions.]
 MO.8.F.B.5

Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. [See: Functions Can Be Linear; Defining Linear Functions.]
 MO.8.G.A.1

Verify experimentally the properties of rotations, reflections, and translations. [See: Making Game Images.]
 MO.8.G.B

Understand and apply the Pythagorean Theorem. [See: The Distance Formula.]
 MO.8.G.B.7

Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions. [See: The Distance Formula.]
 MO.8.G.B.8

Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. [See: The Distance Formula.]
 MO.8.SP.A.1

Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. [See: Scatter Plots; Grouped Samples; Correlations; Linear Regression.]
 MO.8.SP.A.2

Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. [See: Scatter Plots; Correlations; Linear Regression.]
 MO.8.SP.A.3

Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. [See: Linear Regression.]
 MO.HSA.CED.A

Create equations that describe numbers or relationships. [See: Solving Word Problems with the Design Recipe; Surface Area of a Rectangular Prism; Problem Decomposition; Sam the Butterfly  Applying Inequalities.]
 MO.HSA.CED.A.1

Create equations and inequalities in one variable and use them to solve problems. [See: Sam the Butterfly  Applying Inequalities.]
 MO.HSA.CED.A.2

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [See: Sam the Butterfly  Applying Inequalities.]
 MO.HSA.CED.A.3

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. [See: Sam the Butterfly  Applying Inequalities.]
 MO.HSA.SSE.A.1

Interpret expressions that represent a quantity in terms of its context. [See: Defining Values; Functions Make Life Easier!; Solving Word Problems with the Design Recipe.]
 MO.HSA.SSE.A.1.A

Interpret parts of an expression, such as terms, factors, and coefficients. [See: Piecewise Functions and Conditionals; Player Animation.]
 MO.HSA.SSE.A.1.B

Interpret complicated expressions by viewing one or more of their parts as a single entity. [See: Piecewise Functions and Conditionals; Player Animation; Custom Scatter Plots.]
 MO.HSA.SSE.A.2

Use the structure of an expression to identify ways to rewrite it. [See: Order of Operations.]
 MO.HSA.SSE.B

Write expressions in equivalent forms to solve problems. [See: Order of Operations.]
 MO.HSF.BF.A

Build a function that models a relationship between two quantities. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 MO.HSF.BF.A.1

Write a function that describes a relationship between two quantities. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 MO.HSF.BF.A.1.B

Combine standard function types using arithmetic operations. [See: Function Composition.]
 MO.HSF.BF.A.1.C

Compose functions. [See: Function Composition; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality.]
 MO.HSF.BF.B

Build new functions from existing functions. [See: Problem Decomposition; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality.]
 MO.HSF.IF.A

Understand the concept of a function and use function notation. [See: Functions Make Life Easier!; Function Notation.]
 MO.HSF.IF.A.1

Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). [See: Contracts; The Vertical Line Test.]
 MO.HSF.IF.A.2

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. [See: Contracts; Making Flags; Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 MO.HSF.IF.B

Interpret functions that arise in applications in terms of the context. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 MO.HSF.IF.B.5

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. [See: Functions Can Be Linear; Defining Linear Functions.]
 MO.HSF.IF.C

Analyze functions using different representations. [See: The Vertical Line Test; Functions: Contracts, Examples & Definitions; Functions Can Be Linear; Defining Linear Functions; Solving Word Problems with the Design Recipe.]
 MO.HSF.IF.C.9

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [See: Functions Can Be Linear; Defining Linear Functions; Problem Decomposition.]
 MO.HSN.Q.A

Reason quantitatively and use units to solve problems. [See: Making Flags.]
 MO.HSS.CP.A.1

Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ('or', 'and', 'not'). [See: Compound Inequalities: Solutions & NonSolutions.]
 MO.HSS.CP.B.9

Use permutations and combinations to compute probabilities of compound events and solve problems. [See: Permutations; Combinations.]
 MO.HSS.IC.A

Understand and evaluate random processes underlying statistical experiments. [See: Probability, Inference, and Sample Size.]
 MO.HSS.IC.A.1

Understand statistics as a process for making inferences about population parameters based on a random sample from that population. [See: Probability, Inference, and Sample Size.]
 MO.HSS.IC.B

Make inferences and justify conclusions from sample surveys, experiments, and observational studies. [See: Collecting Data.]
 MO.HSS.IC.B.3

Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. [See: Probability, Inference, and Sample Size; Collecting Data.]
 MO.HSS.IC.B.4

Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. [See: Collecting Data.]
 MO.HSS.IC.B.6

Evaluate reports based on data. [See: Threats to Validity.]
 MO.HSS.ID.A

Summarize, represent, and interpret data on a single count or measurement variable. [See: Bar and Pie Charts; Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 MO.HSS.ID.A.1

Represent data with plots on the real number line (dot plots, histograms, and box plots). [See: Histograms; Visualizing the “Shape” of Data; Box Plots; Standard Deviation.]
 MO.HSS.ID.A.2

Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. [See: Histograms; Measures of Center; Box Plots; Standard Deviation.]
 MO.HSS.ID.A.3

Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots; Standard Deviation.]
 MO.HSS.ID.B

Summarize, represent, and interpret data on two categorical and quantitative variables. [See: Scatter Plots; Correlations.]
 MO.HSS.ID.B.6

Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. [See: Scatter Plots; Correlations.]
 MO.HSS.ID.B.6.A

Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. [See: Linear Regression.]
 MO.HSS.ID.B.6.C

Fit a linear function for a scatter plot that suggests a linear association. [See: Linear Regression.]
 MO.HSS.ID.C

Interpret linear models. [See: Linear Regression.]
 MO.HSS.ID.C.7

Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. [See: Linear Regression.]
 MO.HSS.ID.C.8

Compute (using technology) and interpret the correlation coefficient of a linear fit. [See: Scatter Plots; Correlations; Linear Regression.]
 MO.HSS.ID.C.9

Distinguish between correlation and causation. [See: Correlations; Linear Regression.]
 MO.SL.910.1

Initiate and participate effectively in a range of collaborative discussions (oneonone, in groups, and teacherled) with diverse partners on grades 910 topics, texts, and issues, building on others' ideas and expressing their own clearly and persuasively. [See: Introduction to Data Science.]
Montana Standards
 MT.5.G.A.1

Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., xaxis and xcoordinate, yaxis and ycoordinate). [See: Coordinates and Game Design.]
 MT.5.OA.A

Write and interpret numerical expressions. [See: Order of Operations.]
 MT.5.OA.A.1

Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. [See: Order of Operations.]
 MT.6.EE.B

Reason about and solve onevariable equations and inequalities. [See: Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 MT.6.EE.B.6

Use variables to represent numbers and write expressions when solving a realworld or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. [See: Piecewise Functions and Conditionals; Function Composition; Defining Values; Functions Make Life Easier!; Functions: Contracts, Examples & Definitions; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Surface Area of a Rectangular Prism; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality; Defining Table Functions; Grouped Samples; Linear Regression.]
 MT.6.EE.B.8

Write an inequality of the form x > c or x < c to represent a constraint or condition in a realworld or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. [See: Simple Inequalities; Sam the Butterfly  Applying Inequalities.]
 MT.6.G.A

Solve realworld and mathematical problems involving area, surface area, and volume. [See: Surface Area of a Rectangular Prism.]
 MT.6.G.A.4

Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [See: Surface Area of a Rectangular Prism.]
 MT.6.RP.A

Understand ratio concepts and use ratio reasoning to solve problems. [See: Making Flags; Bar and Pie Charts.]
 MT.6.RP.A.1

Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. [See: Making Flags.]
 MT.6.RP.A.3.D

Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. [See: Making Flags.]
 MT.6.SP.A

Develop understanding of statistical variability. [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 MT.6.SP.A.1

Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. [See: Introduction to Data Science; The Data Cycle; Choosing Your Dataset.]
 MT.6.SP.A.2

Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots; Standard Deviation.]
 MT.6.SP.A.3

Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. [See: Box Plots; Standard Deviation.]
 MT.6.SP.B

Summarize and describe distributions. [See: Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 MT.6.SP.B.4

Display numerical data in plots on a number line, including dot plots, histograms, and box plots. [See: Histograms; Visualizing the “Shape” of Data; Box Plots; Standard Deviation.]
 MT.6.SP.B.5

Summarize numerical data sets in relation to their context. [See: Measures of Center; Box Plots; Standard Deviation.]
 MT.6.SP.B.5.C

Summarize numerical data sets in relation to their context by giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. [See: Measures of Center; Box Plots; Standard Deviation.]
 MT.6.SP.B.5.D

Summarize numerical data sets in relation to their context by relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. [See: Measures of Center.]
 MT.7.EE.A.2

Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. [See: Problem Decomposition.]
 MT.7.EE.B

Solve reallife and mathematical problems using numerical and algebraic expressions and equations. [See: Piecewise Functions and Conditionals; Solving Word Problems with the Design Recipe; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Player Animation; The Distance Formula.]
 MT.7.EE.B.4

Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. [See: Defining Values; Functions Make Life Easier!; Solving Word Problems with the Design Recipe; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 MT.7.G.B.4

Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. [See: Solving Word Problems with the Design Recipe.]
 MT.7.G.B.6

Solve realworld and mathematical problems involving area, volume and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [See: Solving Word Problems with the Design Recipe; Surface Area of a Rectangular Prism.]
 MT.7.RP.A

Analyze proportional relationships and use them to solve realworld and mathematical problems. [See: Making Flags; Making Game Images.]
 MT.7.RP.A.1

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. [See: Making Flags.]
 MT.7.RP.A.2.A

Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. [See: Functions Can Be Linear; Defining Linear Functions.]
 MT.7.RP.A.2.B

Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. [See: Functions Can Be Linear; Defining Linear Functions.]
 MT.7.SP.A

Use random sampling to draw inferences about a population. [See: Probability, Inference, and Sample Size.]
 MT.7.SP.A.1

Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. [See: Probability, Inference, and Sample Size.]
 MT.7.SP.A.2

Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. [See: Probability, Inference, and Sample Size.]
 MT.7.SP.B

Draw informal comparative inferences about two populations. [See: Bar and Pie Charts.]
 MT.8.EE.B

Understand the connections between proportional relationships, lines, and linear equations. [See: Functions Can Be Linear; Defining Linear Functions.]
 MT.8.EE.B.5

Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [See: Functions Can Be Linear; Defining Linear Functions.]
 MT.8.F.A.1

Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. [See: Contracts; The Vertical Line Test.]
 MT.8.F.A.2

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [See: Functions Can Be Linear; Defining Linear Functions.]
 MT.8.F.A.3

Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. [See: Functions Can Be Linear; Defining Linear Functions.]
 MT.8.F.B

Use functions to model relationships between quantities. [See: Functions Make Life Easier!; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition.]
 MT.8.F.B.4

Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. [See: Functions Can Be Linear; Defining Linear Functions.]
 MT.8.F.B.5

Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. [See: Functions Can Be Linear; Defining Linear Functions.]
 MT.8.G.A.1

Verify experimentally the properties of rotations, reflections, and translations. [See: Making Game Images.]
 MT.8.G.B

Understand and apply the Pythagorean Theorem. [See: The Distance Formula.]
 MT.8.G.B.7

Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions. [See: The Distance Formula.]
 MT.8.G.B.8

Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. [See: The Distance Formula.]
 MT.8.SP.A.1

Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. [See: Scatter Plots; Grouped Samples; Correlations; Linear Regression.]
 MT.8.SP.A.2

Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. [See: Scatter Plots; Correlations; Linear Regression.]
 MT.8.SP.A.3

Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. [See: Linear Regression.]
 MT.HSA.CED.A

Create equations that describe numbers or relationships. [See: Solving Word Problems with the Design Recipe; Surface Area of a Rectangular Prism; Problem Decomposition; Sam the Butterfly  Applying Inequalities.]
 MT.HSA.CED.A.1

Create equations and inequalities in one variable and use them to solve problems. [See: Sam the Butterfly  Applying Inequalities.]
 MT.HSA.CED.A.2

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [See: Sam the Butterfly  Applying Inequalities.]
 MT.HSA.CED.A.3

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. [See: Sam the Butterfly  Applying Inequalities.]
 MT.HSA.SSE.A.1

Interpret expressions that represent a quantity in terms of its context. [See: Defining Values; Functions Make Life Easier!; Solving Word Problems with the Design Recipe.]
 MT.HSA.SSE.A.1.A

Interpret parts of an expression, such as terms, factors, and coefficients. [See: Piecewise Functions and Conditionals; Player Animation.]
 MT.HSA.SSE.A.1.B

Interpret complicated expressions by viewing one or more of their parts as a single entity. [See: Piecewise Functions and Conditionals; Player Animation; Custom Scatter Plots.]
 MT.HSA.SSE.A.2

Use the structure of an expression to identify ways to rewrite it. [See: Order of Operations.]
 MT.HSA.SSE.B

Write expressions in equivalent forms to solve problems. [See: Order of Operations.]
 MT.HSF.BF.A

Build a function that models a relationship between two quantities. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 MT.HSF.BF.A.1

Write a function that describes a relationship between two quantities. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 MT.HSF.BF.A.1.B

Combine standard function types using arithmetic operations. [See: Function Composition.]
 MT.HSF.BF.A.1.C

Compose functions. [See: Function Composition; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality.]
 MT.HSF.BF.B

Build new functions from existing functions. [See: Problem Decomposition; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality.]
 MT.HSF.IF.A

Understand the concept of a function and use function notation. [See: Functions Make Life Easier!; Function Notation.]
 MT.HSF.IF.A.1

Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). [See: Contracts; The Vertical Line Test.]
 MT.HSF.IF.A.2

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. [See: Contracts; Making Flags; Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 MT.HSF.IF.B

Interpret functions that arise in applications in terms of the context. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 MT.HSF.IF.B.5

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. [See: Functions Can Be Linear; Defining Linear Functions.]
 MT.HSF.IF.C

Analyze functions using different representations. [See: The Vertical Line Test; Functions: Contracts, Examples & Definitions; Functions Can Be Linear; Defining Linear Functions; Solving Word Problems with the Design Recipe.]
 MT.HSF.IF.C.9

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [See: Functions Can Be Linear; Defining Linear Functions; Problem Decomposition.]
 MT.HSN.Q.A

Reason quantitatively and use units to solve problems. [See: Making Flags.]
 MT.HSS.CP.A.1

Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ('or', 'and', 'not'). [See: Compound Inequalities: Solutions & NonSolutions.]
 MT.HSS.CP.B.9

Use permutations and combinations to compute probabilities of compound events and solve problems. [See: Permutations; Combinations.]
 MT.HSS.IC.A

Understand and evaluate random processes underlying statistical experiments. [See: Probability, Inference, and Sample Size.]
 MT.HSS.IC.A.1

Understand statistics as a process for making inferences about population parameters based on a random sample from that population. [See: Probability, Inference, and Sample Size.]
 MT.HSS.IC.B

Make inferences and justify conclusions from sample surveys, experiments, and observational studies. [See: Collecting Data.]
 MT.HSS.IC.B.3

Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. [See: Probability, Inference, and Sample Size; Collecting Data.]
 MT.HSS.IC.B.4

Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. [See: Collecting Data.]
 MT.HSS.IC.B.6

Evaluate reports based on data. [See: Threats to Validity.]
 MT.HSS.ID.A

Summarize, represent, and interpret data on a single count or measurement variable. [See: Bar and Pie Charts; Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 MT.HSS.ID.A.1

Represent data with plots on the real number line (dot plots, histograms, and box plots). [See: Histograms; Visualizing the “Shape” of Data; Box Plots; Standard Deviation.]
 MT.HSS.ID.A.2

Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. [See: Histograms; Measures of Center; Box Plots; Standard Deviation.]
 MT.HSS.ID.A.3

Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots; Standard Deviation.]
 MT.HSS.ID.B

Summarize, represent, and interpret data on two categorical and quantitative variables. [See: Scatter Plots; Correlations.]
 MT.HSS.ID.B.6

Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. [See: Scatter Plots; Correlations.]
 MT.HSS.ID.B.6.A

Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. [See: Linear Regression.]
 MT.HSS.ID.B.6.C

Fit a linear function for a scatter plot that suggests a linear association. [See: Linear Regression.]
 MT.HSS.ID.C

Interpret linear models. [See: Linear Regression.]
 MT.HSS.ID.C.7

Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. [See: Linear Regression.]
 MT.HSS.ID.C.8

Compute (using technology) and interpret the correlation coefficient of a linear fit. [See: Scatter Plots; Correlations; Linear Regression.]
 MT.HSS.ID.C.9

Distinguish between correlation and causation. [See: Correlations; Linear Regression.]
 MT.SL.910.1

Initiate and participate effectively in a range of collaborative discussions (oneonone, in groups, and teacherled) with diverse partners on grades 910 topics, texts, and issues, building on others' ideas and expressing their own clearly and persuasively. [See: Introduction to Data Science.]
New Hampshire Standards
 NH.5.G.A.1

Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., xaxis and xcoordinate, yaxis and ycoordinate). [See: Coordinates and Game Design.]
 NH.5.OA.A

Write and interpret numerical expressions. [See: Order of Operations.]
 NH.5.OA.A.1

Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. [See: Order of Operations.]
 NH.6.EE.B

Reason about and solve onevariable equations and inequalities. [See: Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 NH.6.EE.B.6

Use variables to represent numbers and write expressions when solving a realworld or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. [See: Piecewise Functions and Conditionals; Function Composition; Defining Values; Functions Make Life Easier!; Functions: Contracts, Examples & Definitions; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Surface Area of a Rectangular Prism; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality; Defining Table Functions; Grouped Samples; Linear Regression.]
 NH.6.EE.B.8

Write an inequality of the form x > c or x < c to represent a constraint or condition in a realworld or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. [See: Simple Inequalities; Sam the Butterfly  Applying Inequalities.]
 NH.6.G.A

Solve realworld and mathematical problems involving area, surface area, and volume. [See: Surface Area of a Rectangular Prism.]
 NH.6.G.A.4

Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [See: Surface Area of a Rectangular Prism.]
 NH.6.RP.A

Understand ratio concepts and use ratio reasoning to solve problems. [See: Making Flags; Bar and Pie Charts.]
 NH.6.RP.A.1

Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. [See: Making Flags.]
 NH.6.RP.A.3.D

Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. [See: Making Flags.]
 NH.6.SP.A

Develop understanding of statistical variability. [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 NH.6.SP.A.1

Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. [See: Introduction to Data Science; The Data Cycle; Choosing Your Dataset.]
 NH.6.SP.A.2

Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots; Standard Deviation.]
 NH.6.SP.A.3

Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. [See: Box Plots; Standard Deviation.]
 NH.6.SP.B

Summarize and describe distributions. [See: Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 NH.6.SP.B.4

Display numerical data in plots on a number line, including dot plots, histograms, and box plots. [See: Histograms; Visualizing the “Shape” of Data; Box Plots; Standard Deviation.]
 NH.6.SP.B.5

Summarize numerical data sets in relation to their context. [See: Measures of Center; Box Plots; Standard Deviation.]
 NH.6.SP.B.5.C

Summarize numerical data sets in relation to their context by giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. [See: Measures of Center; Box Plots; Standard Deviation.]
 NH.6.SP.B.5.D

Summarize numerical data sets in relation to their context by relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. [See: Measures of Center.]
 NH.7.EE.A.2

Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. [See: Problem Decomposition.]
 NH.7.EE.B

Solve reallife and mathematical problems using numerical and algebraic expressions and equations. [See: Piecewise Functions and Conditionals; Solving Word Problems with the Design Recipe; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Player Animation; The Distance Formula.]
 NH.7.EE.B.4

Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. [See: Defining Values; Functions Make Life Easier!; Solving Word Problems with the Design Recipe; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 NH.7.G.B.4

Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. [See: Solving Word Problems with the Design Recipe.]
 NH.7.G.B.6

Solve realworld and mathematical problems involving area, volume and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [See: Solving Word Problems with the Design Recipe; Surface Area of a Rectangular Prism.]
 NH.7.RP.A

Analyze proportional relationships and use them to solve realworld and mathematical problems. [See: Making Flags; Making Game Images.]
 NH.7.RP.A.1

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. [See: Making Flags.]
 NH.7.RP.A.2.A

Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. [See: Functions Can Be Linear; Defining Linear Functions.]
 NH.7.RP.A.2.B

Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. [See: Functions Can Be Linear; Defining Linear Functions.]
 NH.7.SP.A

Use random sampling to draw inferences about a population. [See: Probability, Inference, and Sample Size.]
 NH.7.SP.A.1

Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. [See: Probability, Inference, and Sample Size.]
 NH.7.SP.A.2

Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. [See: Probability, Inference, and Sample Size.]
 NH.7.SP.B

Draw informal comparative inferences about two populations. [See: Bar and Pie Charts.]
 NH.8.EE.B

Understand the connections between proportional relationships, lines, and linear equations. [See: Functions Can Be Linear; Defining Linear Functions.]
 NH.8.EE.B.5

Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [See: Functions Can Be Linear; Defining Linear Functions.]
 NH.8.F.A.1

Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. [See: Contracts; The Vertical Line Test.]
 NH.8.F.A.2

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [See: Functions Can Be Linear; Defining Linear Functions.]
 NH.8.F.A.3

Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. [See: Functions Can Be Linear; Defining Linear Functions.]
 NH.8.F.B

Use functions to model relationships between quantities. [See: Functions Make Life Easier!; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition.]
 NH.8.F.B.4

Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. [See: Functions Can Be Linear; Defining Linear Functions.]
 NH.8.F.B.5

Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. [See: Functions Can Be Linear; Defining Linear Functions.]
 NH.8.G.A.1

Verify experimentally the properties of rotations, reflections, and translations. [See: Making Game Images.]
 NH.8.G.B

Understand and apply the Pythagorean Theorem. [See: The Distance Formula.]
 NH.8.G.B.7

Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions. [See: The Distance Formula.]
 NH.8.G.B.8

Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. [See: The Distance Formula.]
 NH.8.SP.A.1

Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. [See: Scatter Plots; Grouped Samples; Correlations; Linear Regression.]
 NH.8.SP.A.2

Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. [See: Scatter Plots; Correlations; Linear Regression.]
 NH.8.SP.A.3

Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. [See: Linear Regression.]
 NH.HSA.CED.A

Create equations that describe numbers or relationships. [See: Solving Word Problems with the Design Recipe; Surface Area of a Rectangular Prism; Problem Decomposition; Sam the Butterfly  Applying Inequalities.]
 NH.HSA.CED.A.1

Create equations and inequalities in one variable and use them to solve problems. [See: Sam the Butterfly  Applying Inequalities.]
 NH.HSA.CED.A.2

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [See: Sam the Butterfly  Applying Inequalities.]
 NH.HSA.CED.A.3

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. [See: Sam the Butterfly  Applying Inequalities.]
 NH.HSA.SSE.A.1

Interpret expressions that represent a quantity in terms of its context. [See: Defining Values; Functions Make Life Easier!; Solving Word Problems with the Design Recipe.]
 NH.HSA.SSE.A.1.A

Interpret parts of an expression, such as terms, factors, and coefficients. [See: Piecewise Functions and Conditionals; Player Animation.]
 NH.HSA.SSE.A.1.B

Interpret complicated expressions by viewing one or more of their parts as a single entity. [See: Piecewise Functions and Conditionals; Player Animation; Custom Scatter Plots.]
 NH.HSA.SSE.A.2

Use the structure of an expression to identify ways to rewrite it. [See: Order of Operations.]
 NH.HSA.SSE.B

Write expressions in equivalent forms to solve problems. [See: Order of Operations.]
 NH.HSF.BF.A

Build a function that models a relationship between two quantities. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 NH.HSF.BF.A.1

Write a function that describes a relationship between two quantities. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 NH.HSF.BF.A.1.B

Combine standard function types using arithmetic operations. [See: Function Composition.]
 NH.HSF.BF.A.1.C

Compose functions. [See: Function Composition; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality.]
 NH.HSF.BF.B

Build new functions from existing functions. [See: Problem Decomposition; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality.]
 NH.HSF.IF.A

Understand the concept of a function and use function notation. [See: Functions Make Life Easier!; Function Notation.]
 NH.HSF.IF.A.1

Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). [See: Contracts; The Vertical Line Test.]
 NH.HSF.IF.A.2

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. [See: Contracts; Making Flags; Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 NH.HSF.IF.B

Interpret functions that arise in applications in terms of the context. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 NH.HSF.IF.B.5

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. [See: Functions Can Be Linear; Defining Linear Functions.]
 NH.HSF.IF.C

Analyze functions using different representations. [See: The Vertical Line Test; Functions: Contracts, Examples & Definitions; Functions Can Be Linear; Defining Linear Functions; Solving Word Problems with the Design Recipe.]
 NH.HSF.IF.C.9

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [See: Functions Can Be Linear; Defining Linear Functions; Problem Decomposition.]
 NH.HSN.Q.A

Reason quantitatively and use units to solve problems. [See: Making Flags.]
 NH.HSS.CP.A.1

Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ('or', 'and', 'not'). [See: Compound Inequalities: Solutions & NonSolutions.]
 NH.HSS.CP.B.9

Use permutations and combinations to compute probabilities of compound events and solve problems. [See: Permutations; Combinations.]
 NH.HSS.IC.A

Understand and evaluate random processes underlying statistical experiments. [See: Probability, Inference, and Sample Size.]
 NH.HSS.IC.A.1

Understand statistics as a process for making inferences about population parameters based on a random sample from that population. [See: Probability, Inference, and Sample Size.]
 NH.HSS.IC.B

Make inferences and justify conclusions from sample surveys, experiments, and observational studies. [See: Collecting Data.]
 NH.HSS.IC.B.3

Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. [See: Probability, Inference, and Sample Size; Collecting Data.]
 NH.HSS.IC.B.4

Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. [See: Collecting Data.]
 NH.HSS.IC.B.6

Evaluate reports based on data. [See: Threats to Validity.]
 NH.HSS.ID.A

Summarize, represent, and interpret data on a single count or measurement variable. [See: Bar and Pie Charts; Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 NH.HSS.ID.A.1

Represent data with plots on the real number line (dot plots, histograms, and box plots). [See: Histograms; Visualizing the “Shape” of Data; Box Plots; Standard Deviation.]
 NH.HSS.ID.A.2

Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. [See: Histograms; Measures of Center; Box Plots; Standard Deviation.]
 NH.HSS.ID.A.3

Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots; Standard Deviation.]
 NH.HSS.ID.B

Summarize, represent, and interpret data on two categorical and quantitative variables. [See: Scatter Plots; Correlations.]
 NH.HSS.ID.B.6

Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. [See: Scatter Plots; Correlations.]
 NH.HSS.ID.B.6.A

Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. [See: Linear Regression.]
 NH.HSS.ID.B.6.C

Fit a linear function for a scatter plot that suggests a linear association. [See: Linear Regression.]
 NH.HSS.ID.C

Interpret linear models. [See: Linear Regression.]
 NH.HSS.ID.C.7

Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. [See: Linear Regression.]
 NH.HSS.ID.C.8

Compute (using technology) and interpret the correlation coefficient of a linear fit. [See: Scatter Plots; Correlations; Linear Regression.]
 NH.HSS.ID.C.9

Distinguish between correlation and causation. [See: Correlations; Linear Regression.]
 NH.SL.910.1

Initiate and participate effectively in a range of collaborative discussions (oneonone, in groups, and teacherled) with diverse partners on grades 910 topics, texts, and issues, building on others' ideas and expressing their own clearly and persuasively. [See: Introduction to Data Science.]
Nevada Standards
 NV.5.G.A.1

Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., xaxis and xcoordinate, yaxis and ycoordinate). [See: Coordinates and Game Design.]
 NV.5.OA.A

Write and interpret numerical expressions. [See: Order of Operations.]
 NV.5.OA.A.1

Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. [See: Order of Operations.]
 NV.6.EE.B

Reason about and solve onevariable equations and inequalities. [See: Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 NV.6.EE.B.6

Use variables to represent numbers and write expressions when solving a realworld or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. [See: Piecewise Functions and Conditionals; Function Composition; Defining Values; Functions Make Life Easier!; Functions: Contracts, Examples & Definitions; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Surface Area of a Rectangular Prism; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality; Defining Table Functions; Grouped Samples; Linear Regression.]
 NV.6.EE.B.8

Write an inequality of the form x > c or x < c to represent a constraint or condition in a realworld or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. [See: Simple Inequalities; Sam the Butterfly  Applying Inequalities.]
 NV.6.G.A

Solve realworld and mathematical problems involving area, surface area, and volume. [See: Surface Area of a Rectangular Prism.]
 NV.6.G.A.4

Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [See: Surface Area of a Rectangular Prism.]
 NV.6.RP.A

Understand ratio concepts and use ratio reasoning to solve problems. [See: Making Flags; Bar and Pie Charts.]
 NV.6.RP.A.1

Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. [See: Making Flags.]
 NV.6.RP.A.3.D

Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. [See: Making Flags.]
 NV.6.SP.A

Develop understanding of statistical variability. [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 NV.6.SP.A.1

Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. [See: Introduction to Data Science; The Data Cycle; Choosing Your Dataset.]
 NV.6.SP.A.2

Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots; Standard Deviation.]
 NV.6.SP.A.3

Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. [See: Box Plots; Standard Deviation.]
 NV.6.SP.B

Summarize and describe distributions. [See: Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 NV.6.SP.B.4

Display numerical data in plots on a number line, including dot plots, histograms, and box plots. [See: Histograms; Visualizing the “Shape” of Data; Box Plots; Standard Deviation.]
 NV.6.SP.B.5

Summarize numerical data sets in relation to their context. [See: Measures of Center; Box Plots; Standard Deviation.]
 NV.6.SP.B.5.C

Summarize numerical data sets in relation to their context by giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. [See: Measures of Center; Box Plots; Standard Deviation.]
 NV.6.SP.B.5.D

Summarize numerical data sets in relation to their context by relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. [See: Measures of Center.]
 NV.7.EE.A.2

Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. [See: Problem Decomposition.]
 NV.7.EE.B

Solve reallife and mathematical problems using numerical and algebraic expressions and equations. [See: Piecewise Functions and Conditionals; Solving Word Problems with the Design Recipe; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Player Animation; The Distance Formula.]
 NV.7.EE.B.4

Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. [See: Defining Values; Functions Make Life Easier!; Solving Word Problems with the Design Recipe; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 NV.7.G.B.4

Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. [See: Solving Word Problems with the Design Recipe.]
 NV.7.G.B.6

Solve realworld and mathematical problems involving area, volume and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [See: Solving Word Problems with the Design Recipe; Surface Area of a Rectangular Prism.]
 NV.7.RP.A

Analyze proportional relationships and use them to solve realworld and mathematical problems. [See: Making Flags; Making Game Images.]
 NV.7.RP.A.1

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. [See: Making Flags.]
 NV.7.RP.A.2.A

Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. [See: Functions Can Be Linear; Defining Linear Functions.]
 NV.7.RP.A.2.B

Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. [See: Functions Can Be Linear; Defining Linear Functions.]
 NV.7.SP.A

Use random sampling to draw inferences about a population. [See: Probability, Inference, and Sample Size.]
 NV.7.SP.A.1

Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. [See: Probability, Inference, and Sample Size.]
 NV.7.SP.A.2

Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. [See: Probability, Inference, and Sample Size.]
 NV.7.SP.B

Draw informal comparative inferences about two populations. [See: Bar and Pie Charts.]
 NV.8.EE.B

Understand the connections between proportional relationships, lines, and linear equations. [See: Functions Can Be Linear; Defining Linear Functions.]
 NV.8.EE.B.5

Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [See: Functions Can Be Linear; Defining Linear Functions.]
 NV.8.F.A.1

Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. [See: Contracts; The Vertical Line Test.]
 NV.8.F.A.2

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [See: Functions Can Be Linear; Defining Linear Functions.]
 NV.8.F.A.3

Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. [See: Functions Can Be Linear; Defining Linear Functions.]
 NV.8.F.B

Use functions to model relationships between quantities. [See: Functions Make Life Easier!; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition.]
 NV.8.F.B.4

Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. [See: Functions Can Be Linear; Defining Linear Functions.]
 NV.8.F.B.5

Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. [See: Functions Can Be Linear; Defining Linear Functions.]
 NV.8.G.A.1

Verify experimentally the properties of rotations, reflections, and translations. [See: Making Game Images.]
 NV.8.G.B

Understand and apply the Pythagorean Theorem. [See: The Distance Formula.]
 NV.8.G.B.7

Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions. [See: The Distance Formula.]
 NV.8.G.B.8

Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. [See: The Distance Formula.]
 NV.8.SP.A.1

Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. [See: Scatter Plots; Grouped Samples; Correlations; Linear Regression.]
 NV.8.SP.A.2

Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. [See: Scatter Plots; Correlations; Linear Regression.]
 NV.8.SP.A.3

Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. [See: Linear Regression.]
 NV.HSA.CED.A

Create equations that describe numbers or relationships. [See: Solving Word Problems with the Design Recipe; Surface Area of a Rectangular Prism; Problem Decomposition; Sam the Butterfly  Applying Inequalities.]
 NV.HSA.CED.A.1

Create equations and inequalities in one variable and use them to solve problems. [See: Sam the Butterfly  Applying Inequalities.]
 NV.HSA.CED.A.2

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [See: Sam the Butterfly  Applying Inequalities.]
 NV.HSA.CED.A.3

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. [See: Sam the Butterfly  Applying Inequalities.]
 NV.HSA.SSE.A.1

Interpret expressions that represent a quantity in terms of its context. [See: Defining Values; Functions Make Life Easier!; Solving Word Problems with the Design Recipe.]
 NV.HSA.SSE.A.1.A

Interpret parts of an expression, such as terms, factors, and coefficients. [See: Piecewise Functions and Conditionals; Player Animation.]
 NV.HSA.SSE.A.1.B

Interpret complicated expressions by viewing one or more of their parts as a single entity. [See: Piecewise Functions and Conditionals; Player Animation; Custom Scatter Plots.]
 NV.HSA.SSE.A.2

Use the structure of an expression to identify ways to rewrite it. [See: Order of Operations.]
 NV.HSA.SSE.B

Write expressions in equivalent forms to solve problems. [See: Order of Operations.]
 NV.HSF.BF.A

Build a function that models a relationship between two quantities. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 NV.HSF.BF.A.1

Write a function that describes a relationship between two quantities. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 NV.HSF.BF.A.1.B

Combine standard function types using arithmetic operations. [See: Function Composition.]
 NV.HSF.BF.A.1.C

Compose functions. [See: Function Composition; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality.]
 NV.HSF.BF.B

Build new functions from existing functions. [See: Problem Decomposition; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality.]
 NV.HSF.IF.A

Understand the concept of a function and use function notation. [See: Functions Make Life Easier!; Function Notation.]
 NV.HSF.IF.A.1

Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). [See: Contracts; The Vertical Line Test.]
 NV.HSF.IF.A.2

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. [See: Contracts; Making Flags; Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 NV.HSF.IF.B

Interpret functions that arise in applications in terms of the context. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 NV.HSF.IF.B.5

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. [See: Functions Can Be Linear; Defining Linear Functions.]
 NV.HSF.IF.C

Analyze functions using different representations. [See: The Vertical Line Test; Functions: Contracts, Examples & Definitions; Functions Can Be Linear; Defining Linear Functions; Solving Word Problems with the Design Recipe.]
 NV.HSF.IF.C.9

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [See: Functions Can Be Linear; Defining Linear Functions; Problem Decomposition.]
 NV.HSN.Q.A

Reason quantitatively and use units to solve problems. [See: Making Flags.]
 NV.HSS.CP.A.1

Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ('or', 'and', 'not'). [See: Compound Inequalities: Solutions & NonSolutions.]
 NV.HSS.CP.B.9

Use permutations and combinations to compute probabilities of compound events and solve problems. [See: Permutations; Combinations.]
 NV.HSS.IC.A

Understand and evaluate random processes underlying statistical experiments. [See: Probability, Inference, and Sample Size.]
 NV.HSS.IC.A.1

Understand statistics as a process for making inferences about population parameters based on a random sample from that population. [See: Probability, Inference, and Sample Size.]
 NV.HSS.IC.B

Make inferences and justify conclusions from sample surveys, experiments, and observational studies. [See: Collecting Data.]
 NV.HSS.IC.B.3

Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. [See: Probability, Inference, and Sample Size; Collecting Data.]
 NV.HSS.IC.B.4

Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. [See: Collecting Data.]
 NV.HSS.IC.B.6

Evaluate reports based on data. [See: Threats to Validity.]
 NV.HSS.ID.A

Summarize, represent, and interpret data on a single count or measurement variable. [See: Bar and Pie Charts; Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 NV.HSS.ID.A.1

Represent data with plots on the real number line (dot plots, histograms, and box plots). [See: Histograms; Visualizing the “Shape” of Data; Box Plots; Standard Deviation.]
 NV.HSS.ID.A.2

Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. [See: Histograms; Measures of Center; Box Plots; Standard Deviation.]
 NV.HSS.ID.A.3

Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots; Standard Deviation.]
 NV.HSS.ID.B

Summarize, represent, and interpret data on two categorical and quantitative variables. [See: Scatter Plots; Correlations.]
 NV.HSS.ID.B.6

Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. [See: Scatter Plots; Correlations.]
 NV.HSS.ID.B.6.A

Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. [See: Linear Regression.]
 NV.HSS.ID.B.6.C

Fit a linear function for a scatter plot that suggests a linear association. [See: Linear Regression.]
 NV.HSS.ID.C

Interpret linear models. [See: Linear Regression.]
 NV.HSS.ID.C.7

Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. [See: Linear Regression.]
 NV.HSS.ID.C.8

Compute (using technology) and interpret the correlation coefficient of a linear fit. [See: Scatter Plots; Correlations; Linear Regression.]
 NV.HSS.ID.C.9

Distinguish between correlation and causation. [See: Correlations; Linear Regression.]
 NV.SL.910.1

Initiate and participate effectively in a range of collaborative discussions (oneonone, in groups, and teacherled) with diverse partners on grades 910 topics, texts, and issues, building on others' ideas and expressing their own clearly and persuasively. [See: Introduction to Data Science.]
New Jersey Standards
 NJ.5.G.A.1

Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., xaxis and xcoordinate, yaxis and ycoordinate). [See: Coordinates and Game Design.]
 NJ.5.OA.A

Write and interpret numerical expressions. [See: Order of Operations.]
 NJ.5.OA.A.1

Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. [See: Order of Operations.]
 NJ.6.EE.B

Reason about and solve onevariable equations and inequalities. [See: Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 NJ.6.EE.B.6

Use variables to represent numbers and write expressions when solving a realworld or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. [See: Piecewise Functions and Conditionals; Function Composition; Defining Values; Functions Make Life Easier!; Functions: Contracts, Examples & Definitions; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Surface Area of a Rectangular Prism; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality; Defining Table Functions; Grouped Samples; Linear Regression.]
 NJ.6.EE.B.8

Write an inequality of the form x > c or x < c to represent a constraint or condition in a realworld or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. [See: Simple Inequalities; Sam the Butterfly  Applying Inequalities.]
 NJ.6.G.A

Solve realworld and mathematical problems involving area, surface area, and volume. [See: Surface Area of a Rectangular Prism.]
 NJ.6.G.A.4

Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [See: Surface Area of a Rectangular Prism.]
 NJ.6.RP.A

Understand ratio concepts and use ratio reasoning to solve problems. [See: Making Flags; Bar and Pie Charts.]
 NJ.6.RP.A.1

Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. [See: Making Flags.]
 NJ.6.RP.A.3.D

Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. [See: Making Flags.]
 NJ.6.SP.A

Develop understanding of statistical variability. [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 NJ.6.SP.A.1

Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. [See: Introduction to Data Science; The Data Cycle; Choosing Your Dataset.]
 NJ.6.SP.A.2

Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots; Standard Deviation.]
 NJ.6.SP.A.3

Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. [See: Box Plots; Standard Deviation.]
 NJ.6.SP.B

Summarize and describe distributions. [See: Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 NJ.6.SP.B.4

Display numerical data in plots on a number line, including dot plots, histograms, and box plots. [See: Histograms; Visualizing the “Shape” of Data; Box Plots; Standard Deviation.]
 NJ.6.SP.B.5

Summarize numerical data sets in relation to their context. [See: Measures of Center; Box Plots; Standard Deviation.]
 NJ.6.SP.B.5.C

Summarize numerical data sets in relation to their context by giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. [See: Measures of Center; Box Plots; Standard Deviation.]
 NJ.6.SP.B.5.D

Summarize numerical data sets in relation to their context by relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. [See: Measures of Center.]
 NJ.7.EE.A.2

Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. [See: Problem Decomposition.]
 NJ.7.EE.B

Solve reallife and mathematical problems using numerical and algebraic expressions and equations. [See: Piecewise Functions and Conditionals; Solving Word Problems with the Design Recipe; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Player Animation; The Distance Formula.]
 NJ.7.EE.B.4

Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. [See: Defining Values; Functions Make Life Easier!; Solving Word Problems with the Design Recipe; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 NJ.7.G.B.4

Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. [See: Solving Word Problems with the Design Recipe.]
 NJ.7.G.B.6

Solve realworld and mathematical problems involving area, volume and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [See: Solving Word Problems with the Design Recipe; Surface Area of a Rectangular Prism.]
 NJ.7.RP.A

Analyze proportional relationships and use them to solve realworld and mathematical problems. [See: Making Flags; Making Game Images.]
 NJ.7.RP.A.1

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. [See: Making Flags.]
 NJ.7.RP.A.2.A

Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. [See: Functions Can Be Linear; Defining Linear Functions.]
 NJ.7.RP.A.2.B

Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. [See: Functions Can Be Linear; Defining Linear Functions.]
 NJ.7.SP.A

Use random sampling to draw inferences about a population. [See: Probability, Inference, and Sample Size.]
 NJ.7.SP.A.1

Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. [See: Probability, Inference, and Sample Size.]
 NJ.7.SP.A.2

Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. [See: Probability, Inference, and Sample Size.]
 NJ.7.SP.B

Draw informal comparative inferences about two populations. [See: Bar and Pie Charts.]
 NJ.8.EE.B

Understand the connections between proportional relationships, lines, and linear equations. [See: Functions Can Be Linear; Defining Linear Functions.]
 NJ.8.EE.B.5

Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [See: Functions Can Be Linear; Defining Linear Functions.]
 NJ.8.F.A.1

Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. [See: Contracts; The Vertical Line Test.]
 NJ.8.F.A.2

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [See: Functions Can Be Linear; Defining Linear Functions.]
 NJ.8.F.A.3

Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. [See: Functions Can Be Linear; Defining Linear Functions.]
 NJ.8.F.B

Use functions to model relationships between quantities. [See: Functions Make Life Easier!; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition.]
 NJ.8.F.B.4

Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. [See: Functions Can Be Linear; Defining Linear Functions.]
 NJ.8.F.B.5

Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. [See: Functions Can Be Linear; Defining Linear Functions.]
 NJ.8.G.A.1

Verify experimentally the properties of rotations, reflections, and translations. [See: Making Game Images.]
 NJ.8.G.B

Understand and apply the Pythagorean Theorem. [See: The Distance Formula.]
 NJ.8.G.B.7

Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions. [See: The Distance Formula.]
 NJ.8.G.B.8

Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. [See: The Distance Formula.]
 NJ.8.SP.A.1

Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. [See: Scatter Plots; Grouped Samples; Correlations; Linear Regression.]
 NJ.8.SP.A.2

Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. [See: Scatter Plots; Correlations; Linear Regression.]
 NJ.8.SP.A.3

Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. [See: Linear Regression.]
 NJ.HSA.CED.A

Create equations that describe numbers or relationships. [See: Solving Word Problems with the Design Recipe; Surface Area of a Rectangular Prism; Problem Decomposition; Sam the Butterfly  Applying Inequalities.]
 NJ.HSA.CED.A.1

Create equations and inequalities in one variable and use them to solve problems. [See: Sam the Butterfly  Applying Inequalities.]
 NJ.HSA.CED.A.2

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [See: Sam the Butterfly  Applying Inequalities.]
 NJ.HSA.CED.A.3

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. [See: Sam the Butterfly  Applying Inequalities.]
 NJ.HSA.SSE.A.1

Interpret expressions that represent a quantity in terms of its context. [See: Defining Values; Functions Make Life Easier!; Solving Word Problems with the Design Recipe.]
 NJ.HSA.SSE.A.1.A

Interpret parts of an expression, such as terms, factors, and coefficients. [See: Piecewise Functions and Conditionals; Player Animation.]
 NJ.HSA.SSE.A.1.B

Interpret complicated expressions by viewing one or more of their parts as a single entity. [See: Piecewise Functions and Conditionals; Player Animation; Custom Scatter Plots.]
 NJ.HSA.SSE.A.2

Use the structure of an expression to identify ways to rewrite it. [See: Order of Operations.]
 NJ.HSA.SSE.B

Write expressions in equivalent forms to solve problems. [See: Order of Operations.]
 NJ.HSF.BF.A

Build a function that models a relationship between two quantities. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 NJ.HSF.BF.A.1

Write a function that describes a relationship between two quantities. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 NJ.HSF.BF.A.1.B

Combine standard function types using arithmetic operations. [See: Function Composition.]
 NJ.HSF.BF.A.1.C

Compose functions. [See: Function Composition; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality.]
 NJ.HSF.BF.B

Build new functions from existing functions. [See: Problem Decomposition; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality.]
 NJ.HSF.IF.A

Understand the concept of a function and use function notation. [See: Functions Make Life Easier!; Function Notation.]
 NJ.HSF.IF.A.1

Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). [See: Contracts; The Vertical Line Test.]
 NJ.HSF.IF.A.2

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. [See: Contracts; Making Flags; Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 NJ.HSF.IF.B

Interpret functions that arise in applications in terms of the context. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 NJ.HSF.IF.B.5

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. [See: Functions Can Be Linear; Defining Linear Functions.]
 NJ.HSF.IF.C

Analyze functions using different representations. [See: The Vertical Line Test; Functions: Contracts, Examples & Definitions; Functions Can Be Linear; Defining Linear Functions; Solving Word Problems with the Design Recipe.]
 NJ.HSF.IF.C.9

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [See: Functions Can Be Linear; Defining Linear Functions; Problem Decomposition.]
 NJ.HSN.Q.A

Reason quantitatively and use units to solve problems. [See: Making Flags.]
 NJ.HSS.CP.A.1

Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ('or', 'and', 'not'). [See: Compound Inequalities: Solutions & NonSolutions.]
 NJ.HSS.CP.B.9

Use permutations and combinations to compute probabilities of compound events and solve problems. [See: Permutations; Combinations.]
 NJ.HSS.IC.A

Understand and evaluate random processes underlying statistical experiments. [See: Probability, Inference, and Sample Size.]
 NJ.HSS.IC.A.1

Understand statistics as a process for making inferences about population parameters based on a random sample from that population. [See: Probability, Inference, and Sample Size.]
 NJ.HSS.IC.B

Make inferences and justify conclusions from sample surveys, experiments, and observational studies. [See: Collecting Data.]
 NJ.HSS.IC.B.3

Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. [See: Probability, Inference, and Sample Size; Collecting Data.]
 NJ.HSS.IC.B.4

Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. [See: Collecting Data.]
 NJ.HSS.IC.B.6

Evaluate reports based on data. [See: Threats to Validity.]
 NJ.HSS.ID.A

Summarize, represent, and interpret data on a single count or measurement variable. [See: Bar and Pie Charts; Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 NJ.HSS.ID.A.1

Represent data with plots on the real number line (dot plots, histograms, and box plots). [See: Histograms; Visualizing the “Shape” of Data; Box Plots; Standard Deviation.]
 NJ.HSS.ID.A.2

Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. [See: Histograms; Measures of Center; Box Plots; Standard Deviation.]
 NJ.HSS.ID.A.3

Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots; Standard Deviation.]
 NJ.HSS.ID.B

Summarize, represent, and interpret data on two categorical and quantitative variables. [See: Scatter Plots; Correlations.]
 NJ.HSS.ID.B.6

Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. [See: Scatter Plots; Correlations.]
 NJ.HSS.ID.B.6.A

Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. [See: Linear Regression.]
 NJ.HSS.ID.B.6.C

Fit a linear function for a scatter plot that suggests a linear association. [See: Linear Regression.]
 NJ.HSS.ID.C

Interpret linear models. [See: Linear Regression.]
 NJ.HSS.ID.C.7

Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. [See: Linear Regression.]
 NJ.HSS.ID.C.8

Compute (using technology) and interpret the correlation coefficient of a linear fit. [See: Scatter Plots; Correlations; Linear Regression.]
 NJ.HSS.ID.C.9

Distinguish between correlation and causation. [See: Correlations; Linear Regression.]
 NJ.SL.910.1

Initiate and participate effectively in a range of collaborative discussions (oneonone, in groups, and teacherled) with diverse partners on grades 910 topics, texts, and issues, building on others' ideas and expressing their own clearly and persuasively. [See: Introduction to Data Science.]
New Mexico Standards
 NM.5.G.A.1

Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., xaxis and xcoordinate, yaxis and ycoordinate). [See: Coordinates and Game Design.]
 NM.5.OA.A

Write and interpret numerical expressions. [See: Order of Operations.]
 NM.5.OA.A.1

Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. [See: Order of Operations.]
 NM.6.EE.B

Reason about and solve onevariable equations and inequalities. [See: Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 NM.6.EE.B.6

Use variables to represent numbers and write expressions when solving a realworld or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. [See: Piecewise Functions and Conditionals; Function Composition; Defining Values; Functions Make Life Easier!; Functions: Contracts, Examples & Definitions; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Surface Area of a Rectangular Prism; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality; Defining Table Functions; Grouped Samples; Linear Regression.]
 NM.6.EE.B.8

Write an inequality of the form x > c or x < c to represent a constraint or condition in a realworld or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. [See: Simple Inequalities; Sam the Butterfly  Applying Inequalities.]
 NM.6.G.A

Solve realworld and mathematical problems involving area, surface area, and volume. [See: Surface Area of a Rectangular Prism.]
 NM.6.G.A.4

Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [See: Surface Area of a Rectangular Prism.]
 NM.6.RP.A

Understand ratio concepts and use ratio reasoning to solve problems. [See: Making Flags; Bar and Pie Charts.]
 NM.6.RP.A.1

Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. [See: Making Flags.]
 NM.6.RP.A.3.D

Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. [See: Making Flags.]
 NM.6.SP.A

Develop understanding of statistical variability. [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 NM.6.SP.A.1

Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. [See: Introduction to Data Science; The Data Cycle; Choosing Your Dataset.]
 NM.6.SP.A.2

Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots; Standard Deviation.]
 NM.6.SP.A.3

Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. [See: Box Plots; Standard Deviation.]
 NM.6.SP.B

Summarize and describe distributions. [See: Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 NM.6.SP.B.4

Display numerical data in plots on a number line, including dot plots, histograms, and box plots. [See: Histograms; Visualizing the “Shape” of Data; Box Plots; Standard Deviation.]
 NM.6.SP.B.5

Summarize numerical data sets in relation to their context. [See: Measures of Center; Box Plots; Standard Deviation.]
 NM.6.SP.B.5.C

Summarize numerical data sets in relation to their context by giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. [See: Measures of Center; Box Plots; Standard Deviation.]
 NM.6.SP.B.5.D

Summarize numerical data sets in relation to their context by relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. [See: Measures of Center.]
 NM.7.EE.A.2

Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. [See: Problem Decomposition.]
 NM.7.EE.B

Solve reallife and mathematical problems using numerical and algebraic expressions and equations. [See: Piecewise Functions and Conditionals; Solving Word Problems with the Design Recipe; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Player Animation; The Distance Formula.]
 NM.7.EE.B.4

Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. [See: Defining Values; Functions Make Life Easier!; Solving Word Problems with the Design Recipe; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 NM.7.G.B.4

Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. [See: Solving Word Problems with the Design Recipe.]
 NM.7.G.B.6

Solve realworld and mathematical problems involving area, volume and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [See: Solving Word Problems with the Design Recipe; Surface Area of a Rectangular Prism.]
 NM.7.RP.A

Analyze proportional relationships and use them to solve realworld and mathematical problems. [See: Making Flags; Making Game Images.]
 NM.7.RP.A.1

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. [See: Making Flags.]
 NM.7.RP.A.2.A

Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. [See: Functions Can Be Linear; Defining Linear Functions.]
 NM.7.RP.A.2.B

Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. [See: Functions Can Be Linear; Defining Linear Functions.]
 NM.7.SP.A

Use random sampling to draw inferences about a population. [See: Probability, Inference, and Sample Size.]
 NM.7.SP.A.1

Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. [See: Probability, Inference, and Sample Size.]
 NM.7.SP.A.2

Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. [See: Probability, Inference, and Sample Size.]
 NM.7.SP.B

Draw informal comparative inferences about two populations. [See: Bar and Pie Charts.]
 NM.8.EE.B

Understand the connections between proportional relationships, lines, and linear equations. [See: Functions Can Be Linear; Defining Linear Functions.]
 NM.8.EE.B.5

Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [See: Functions Can Be Linear; Defining Linear Functions.]
 NM.8.F.A.1

Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. [See: Contracts; The Vertical Line Test.]
 NM.8.F.A.2

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [See: Functions Can Be Linear; Defining Linear Functions.]
 NM.8.F.A.3

Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. [See: Functions Can Be Linear; Defining Linear Functions.]
 NM.8.F.B

Use functions to model relationships between quantities. [See: Functions Make Life Easier!; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition.]
 NM.8.F.B.4

Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. [See: Functions Can Be Linear; Defining Linear Functions.]
 NM.8.F.B.5

Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. [See: Functions Can Be Linear; Defining Linear Functions.]
 NM.8.G.A.1

Verify experimentally the properties of rotations, reflections, and translations. [See: Making Game Images.]
 NM.8.G.B

Understand and apply the Pythagorean Theorem. [See: The Distance Formula.]
 NM.8.G.B.7

Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions. [See: The Distance Formula.]
 NM.8.G.B.8

Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. [See: The Distance Formula.]
 NM.8.SP.A.1

Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. [See: Scatter Plots; Grouped Samples; Correlations; Linear Regression.]
 NM.8.SP.A.2

Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. [See: Scatter Plots; Correlations; Linear Regression.]
 NM.8.SP.A.3

Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. [See: Linear Regression.]
 NM.HSA.CED.A

Create equations that describe numbers or relationships. [See: Solving Word Problems with the Design Recipe; Surface Area of a Rectangular Prism; Problem Decomposition; Sam the Butterfly  Applying Inequalities.]
 NM.HSA.CED.A.1

Create equations and inequalities in one variable and use them to solve problems. [See: Sam the Butterfly  Applying Inequalities.]
 NM.HSA.CED.A.2

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [See: Sam the Butterfly  Applying Inequalities.]
 NM.HSA.CED.A.3

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. [See: Sam the Butterfly  Applying Inequalities.]
 NM.HSA.SSE.A.1

Interpret expressions that represent a quantity in terms of its context. [See: Defining Values; Functions Make Life Easier!; Solving Word Problems with the Design Recipe.]
 NM.HSA.SSE.A.1.A

Interpret parts of an expression, such as terms, factors, and coefficients. [See: Piecewise Functions and Conditionals; Player Animation.]
 NM.HSA.SSE.A.1.B

Interpret complicated expressions by viewing one or more of their parts as a single entity. [See: Piecewise Functions and Conditionals; Player Animation; Custom Scatter Plots.]
 NM.HSA.SSE.A.2

Use the structure of an expression to identify ways to rewrite it. [See: Order of Operations.]
 NM.HSA.SSE.B

Write expressions in equivalent forms to solve problems. [See: Order of Operations.]
 NM.HSF.BF.A

Build a function that models a relationship between two quantities. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 NM.HSF.BF.A.1

Write a function that describes a relationship between two quantities. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 NM.HSF.BF.A.1.B

Combine standard function types using arithmetic operations. [See: Function Composition.]
 NM.HSF.BF.A.1.C

Compose functions. [See: Function Composition; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality.]
 NM.HSF.BF.B

Build new functions from existing functions. [See: Problem Decomposition; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality.]
 NM.HSF.IF.A

Understand the concept of a function and use function notation. [See: Functions Make Life Easier!; Function Notation.]
 NM.HSF.IF.A.1

Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). [See: Contracts; The Vertical Line Test.]
 NM.HSF.IF.A.2

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. [See: Contracts; Making Flags; Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 NM.HSF.IF.B

Interpret functions that arise in applications in terms of the context. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 NM.HSF.IF.B.5

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. [See: Functions Can Be Linear; Defining Linear Functions.]
 NM.HSF.IF.C

Analyze functions using different representations. [See: The Vertical Line Test; Functions: Contracts, Examples & Definitions; Functions Can Be Linear; Defining Linear Functions; Solving Word Problems with the Design Recipe.]
 NM.HSF.IF.C.9

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [See: Functions Can Be Linear; Defining Linear Functions; Problem Decomposition.]
 NM.HSN.Q.A

Reason quantitatively and use units to solve problems. [See: Making Flags.]
 NM.HSS.CP.A.1

Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ('or', 'and', 'not'). [See: Compound Inequalities: Solutions & NonSolutions.]
 NM.HSS.CP.B.9

Use permutations and combinations to compute probabilities of compound events and solve problems. [See: Permutations; Combinations.]
 NM.HSS.IC.A

Understand and evaluate random processes underlying statistical experiments. [See: Probability, Inference, and Sample Size.]
 NM.HSS.IC.A.1

Understand statistics as a process for making inferences about population parameters based on a random sample from that population. [See: Probability, Inference, and Sample Size.]
 NM.HSS.IC.B

Make inferences and justify conclusions from sample surveys, experiments, and observational studies. [See: Collecting Data.]
 NM.HSS.IC.B.3

Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. [See: Probability, Inference, and Sample Size; Collecting Data.]
 NM.HSS.IC.B.4

Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. [See: Collecting Data.]
 NM.HSS.IC.B.6

Evaluate reports based on data. [See: Threats to Validity.]
 NM.HSS.ID.A

Summarize, represent, and interpret data on a single count or measurement variable. [See: Bar and Pie Charts; Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 NM.HSS.ID.A.1

Represent data with plots on the real number line (dot plots, histograms, and box plots). [See: Histograms; Visualizing the “Shape” of Data; Box Plots; Standard Deviation.]
 NM.HSS.ID.A.2

Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. [See: Histograms; Measures of Center; Box Plots; Standard Deviation.]
 NM.HSS.ID.A.3

Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots; Standard Deviation.]
 NM.HSS.ID.B

Summarize, represent, and interpret data on two categorical and quantitative variables. [See: Scatter Plots; Correlations.]
 NM.HSS.ID.B.6

Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. [See: Scatter Plots; Correlations.]
 NM.HSS.ID.B.6.A

Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. [See: Linear Regression.]
 NM.HSS.ID.B.6.C

Fit a linear function for a scatter plot that suggests a linear association. [See: Linear Regression.]
 NM.HSS.ID.C

Interpret linear models. [See: Linear Regression.]
 NM.HSS.ID.C.7

Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. [See: Linear Regression.]
 NM.HSS.ID.C.8

Compute (using technology) and interpret the correlation coefficient of a linear fit. [See: Scatter Plots; Correlations; Linear Regression.]
 NM.HSS.ID.C.9

Distinguish between correlation and causation. [See: Correlations; Linear Regression.]
 NM.SL.910.1

Initiate and participate effectively in a range of collaborative discussions (oneonone, in groups, and teacherled) with diverse partners on grades 910 topics, texts, and issues, building on others' ideas and expressing their own clearly and persuasively. [See: Introduction to Data Science.]
North Carolina Standards
 NC.5.G.A.1

Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., xaxis and xcoordinate, yaxis and ycoordinate). [See: Coordinates and Game Design.]
 NC.5.OA.A

Write and interpret numerical expressions. [See: Order of Operations.]
 NC.5.OA.A.1

Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. [See: Order of Operations.]
 NC.6.EE.B

Reason about and solve onevariable equations and inequalities. [See: Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 NC.6.EE.B.6

Use variables to represent numbers and write expressions when solving a realworld or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. [See: Piecewise Functions and Conditionals; Function Composition; Defining Values; Functions Make Life Easier!; Functions: Contracts, Examples & Definitions; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Surface Area of a Rectangular Prism; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality; Defining Table Functions; Grouped Samples; Linear Regression.]
 NC.6.EE.B.8

Write an inequality of the form x > c or x < c to represent a constraint or condition in a realworld or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. [See: Simple Inequalities; Sam the Butterfly  Applying Inequalities.]
 NC.6.G.A

Solve realworld and mathematical problems involving area, surface area, and volume. [See: Surface Area of a Rectangular Prism.]
 NC.6.G.A.4

Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [See: Surface Area of a Rectangular Prism.]
 NC.6.RP.A

Understand ratio concepts and use ratio reasoning to solve problems. [See: Making Flags; Bar and Pie Charts.]
 NC.6.RP.A.1

Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. [See: Making Flags.]
 NC.6.RP.A.3.D

Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. [See: Making Flags.]
 NC.6.SP.A

Develop understanding of statistical variability. [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 NC.6.SP.A.1

Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. [See: Introduction to Data Science; The Data Cycle; Choosing Your Dataset.]
 NC.6.SP.A.2

Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots; Standard Deviation.]
 NC.6.SP.A.3

Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. [See: Box Plots; Standard Deviation.]
 NC.6.SP.B

Summarize and describe distributions. [See: Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 NC.6.SP.B.4

Display numerical data in plots on a number line, including dot plots, histograms, and box plots. [See: Histograms; Visualizing the “Shape” of Data; Box Plots; Standard Deviation.]
 NC.6.SP.B.5

Summarize numerical data sets in relation to their context. [See: Measures of Center; Box Plots; Standard Deviation.]
 NC.6.SP.B.5.C

Summarize numerical data sets in relation to their context by giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. [See: Measures of Center; Box Plots; Standard Deviation.]
 NC.6.SP.B.5.D

Summarize numerical data sets in relation to their context by relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. [See: Measures of Center.]
 NC.7.EE.A.2

Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. [See: Problem Decomposition.]
 NC.7.EE.B

Solve reallife and mathematical problems using numerical and algebraic expressions and equations. [See: Piecewise Functions and Conditionals; Solving Word Problems with the Design Recipe; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Player Animation; The Distance Formula.]
 NC.7.EE.B.4

Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. [See: Defining Values; Functions Make Life Easier!; Solving Word Problems with the Design Recipe; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 NC.7.G.B.4

Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. [See: Solving Word Problems with the Design Recipe.]
 NC.7.G.B.6

Solve realworld and mathematical problems involving area, volume and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [See: Solving Word Problems with the Design Recipe; Surface Area of a Rectangular Prism.]
 NC.7.RP.A

Analyze proportional relationships and use them to solve realworld and mathematical problems. [See: Making Flags; Making Game Images.]
 NC.7.RP.A.1

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. [See: Making Flags.]
 NC.7.RP.A.2.A

Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. [See: Functions Can Be Linear; Defining Linear Functions.]
 NC.7.RP.A.2.B

Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. [See: Functions Can Be Linear; Defining Linear Functions.]
 NC.7.SP.A

Use random sampling to draw inferences about a population. [See: Probability, Inference, and Sample Size.]
 NC.7.SP.A.1

Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. [See: Probability, Inference, and Sample Size.]
 NC.7.SP.A.2

Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. [See: Probability, Inference, and Sample Size.]
 NC.7.SP.B

Draw informal comparative inferences about two populations. [See: Bar and Pie Charts.]
 NC.8.EE.B

Understand the connections between proportional relationships, lines, and linear equations. [See: Functions Can Be Linear; Defining Linear Functions.]
 NC.8.EE.B.5

Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [See: Functions Can Be Linear; Defining Linear Functions.]
 NC.8.F.A.1

Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. [See: Contracts; The Vertical Line Test.]
 NC.8.F.A.2

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [See: Functions Can Be Linear; Defining Linear Functions.]
 NC.8.F.A.3

Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. [See: Functions Can Be Linear; Defining Linear Functions.]
 NC.8.F.B

Use functions to model relationships between quantities. [See: Functions Make Life Easier!; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition.]
 NC.8.F.B.4

Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. [See: Functions Can Be Linear; Defining Linear Functions.]
 NC.8.F.B.5

Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. [See: Functions Can Be Linear; Defining Linear Functions.]
 NC.8.G.A.1

Verify experimentally the properties of rotations, reflections, and translations. [See: Making Game Images.]
 NC.8.G.B

Understand and apply the Pythagorean Theorem. [See: The Distance Formula.]
 NC.8.G.B.7

Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions. [See: The Distance Formula.]
 NC.8.G.B.8

Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. [See: The Distance Formula.]
 NC.8.SP.A.1

Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. [See: Scatter Plots; Grouped Samples; Correlations; Linear Regression.]
 NC.8.SP.A.2

Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. [See: Scatter Plots; Correlations; Linear Regression.]
 NC.8.SP.A.3

Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. [See: Linear Regression.]
 NC.HSA.CED.A

Create equations that describe numbers or relationships. [See: Solving Word Problems with the Design Recipe; Surface Area of a Rectangular Prism; Problem Decomposition; Sam the Butterfly  Applying Inequalities.]
 NC.HSA.CED.A.1

Create equations and inequalities in one variable and use them to solve problems. [See: Sam the Butterfly  Applying Inequalities.]
 NC.HSA.CED.A.2

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [See: Sam the Butterfly  Applying Inequalities.]
 NC.HSA.CED.A.3

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. [See: Sam the Butterfly  Applying Inequalities.]
 NC.HSA.SSE.A.1

Interpret expressions that represent a quantity in terms of its context. [See: Defining Values; Functions Make Life Easier!; Solving Word Problems with the Design Recipe.]
 NC.HSA.SSE.A.1.A

Interpret parts of an expression, such as terms, factors, and coefficients. [See: Piecewise Functions and Conditionals; Player Animation.]
 NC.HSA.SSE.A.1.B

Interpret complicated expressions by viewing one or more of their parts as a single entity. [See: Piecewise Functions and Conditionals; Player Animation; Custom Scatter Plots.]
 NC.HSA.SSE.A.2

Use the structure of an expression to identify ways to rewrite it. [See: Order of Operations.]
 NC.HSA.SSE.B

Write expressions in equivalent forms to solve problems. [See: Order of Operations.]
 NC.HSF.BF.A

Build a function that models a relationship between two quantities. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 NC.HSF.BF.A.1

Write a function that describes a relationship between two quantities. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 NC.HSF.BF.A.1.B

Combine standard function types using arithmetic operations. [See: Function Composition.]
 NC.HSF.BF.A.1.C

Compose functions. [See: Function Composition; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality.]
 NC.HSF.BF.B

Build new functions from existing functions. [See: Problem Decomposition; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality.]
 NC.HSF.IF.A

Understand the concept of a function and use function notation. [See: Functions Make Life Easier!; Function Notation.]
 NC.HSF.IF.A.1

Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). [See: Contracts; The Vertical Line Test.]
 NC.HSF.IF.A.2

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. [See: Contracts; Making Flags; Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 NC.HSF.IF.B

Interpret functions that arise in applications in terms of the context. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 NC.HSF.IF.B.5

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. [See: Functions Can Be Linear; Defining Linear Functions.]
 NC.HSF.IF.C

Analyze functions using different representations. [See: The Vertical Line Test; Functions: Contracts, Examples & Definitions; Functions Can Be Linear; Defining Linear Functions; Solving Word Problems with the Design Recipe.]
 NC.HSF.IF.C.9

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [See: Functions Can Be Linear; Defining Linear Functions; Problem Decomposition.]
 NC.HSN.Q.A

Reason quantitatively and use units to solve problems. [See: Making Flags.]
 NC.HSS.CP.A.1

Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ('or', 'and', 'not'). [See: Compound Inequalities: Solutions & NonSolutions.]
 NC.HSS.CP.B.9

Use permutations and combinations to compute probabilities of compound events and solve problems. [See: Permutations; Combinations.]
 NC.HSS.IC.A

Understand and evaluate random processes underlying statistical experiments. [See: Probability, Inference, and Sample Size.]
 NC.HSS.IC.A.1

Understand statistics as a process for making inferences about population parameters based on a random sample from that population. [See: Probability, Inference, and Sample Size.]
 NC.HSS.IC.B

Make inferences and justify conclusions from sample surveys, experiments, and observational studies. [See: Collecting Data.]
 NC.HSS.IC.B.3

Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. [See: Probability, Inference, and Sample Size; Collecting Data.]
 NC.HSS.IC.B.4

Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. [See: Collecting Data.]
 NC.HSS.IC.B.6

Evaluate reports based on data. [See: Threats to Validity.]
 NC.HSS.ID.A

Summarize, represent, and interpret data on a single count or measurement variable. [See: Bar and Pie Charts; Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 NC.HSS.ID.A.1

Represent data with plots on the real number line (dot plots, histograms, and box plots). [See: Histograms; Visualizing the “Shape” of Data; Box Plots; Standard Deviation.]
 NC.HSS.ID.A.2

Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. [See: Histograms; Measures of Center; Box Plots; Standard Deviation.]
 NC.HSS.ID.A.3

Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots; Standard Deviation.]
 NC.HSS.ID.B

Summarize, represent, and interpret data on two categorical and quantitative variables. [See: Scatter Plots; Correlations.]
 NC.HSS.ID.B.6

Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. [See: Scatter Plots; Correlations.]
 NC.HSS.ID.B.6.A

Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models. [See: Linear Regression.]
 NC.HSS.ID.B.6.C

Fit a linear function for a scatter plot that suggests a linear association. [See: Linear Regression.]
 NC.HSS.ID.C

Interpret linear models. [See: Linear Regression.]
 NC.HSS.ID.C.7

Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. [See: Linear Regression.]
 NC.HSS.ID.C.8

Compute (using technology) and interpret the correlation coefficient of a linear fit. [See: Scatter Plots; Correlations; Linear Regression.]
 NC.HSS.ID.C.9

Distinguish between correlation and causation. [See: Correlations; Linear Regression.]
 NC.SL.910.1

Initiate and participate effectively in a range of collaborative discussions (oneonone, in groups, and teacherled) with diverse partners on grades 910 topics, texts, and issues, building on others' ideas and expressing their own clearly and persuasively. [See: Introduction to Data Science.]
North Dakota Standards
 ND.5.G.A.1

Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., xaxis and xcoordinate, yaxis and ycoordinate). [See: Coordinates and Game Design.]
 ND.5.OA.A

Write and interpret numerical expressions. [See: Order of Operations.]
 ND.5.OA.A.1

Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. [See: Order of Operations.]
 ND.6.EE.B

Reason about and solve onevariable equations and inequalities. [See: Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 ND.6.EE.B.6

Use variables to represent numbers and write expressions when solving a realworld or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. [See: Piecewise Functions and Conditionals; Function Composition; Defining Values; Functions Make Life Easier!; Functions: Contracts, Examples & Definitions; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Surface Area of a Rectangular Prism; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality; Defining Table Functions; Grouped Samples; Linear Regression.]
 ND.6.EE.B.8

Write an inequality of the form x > c or x < c to represent a constraint or condition in a realworld or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. [See: Simple Inequalities; Sam the Butterfly  Applying Inequalities.]
 ND.6.G.A

Solve realworld and mathematical problems involving area, surface area, and volume. [See: Surface Area of a Rectangular Prism.]
 ND.6.G.A.4

Represent threedimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving realworld and mathematical problems. [See: Surface Area of a Rectangular Prism.]
 ND.6.RP.A

Understand ratio concepts and use ratio reasoning to solve problems. [See: Making Flags; Bar and Pie Charts.]
 ND.6.RP.A.1

Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. [See: Making Flags.]
 ND.6.RP.A.3.D

Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. [See: Making Flags.]
 ND.6.SP.A

Develop understanding of statistical variability. [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 ND.6.SP.A.1

Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. [See: Introduction to Data Science; The Data Cycle; Choosing Your Dataset.]
 ND.6.SP.A.2

Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. [See: Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots; Standard Deviation.]
 ND.6.SP.A.3

Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. [See: Box Plots; Standard Deviation.]
 ND.6.SP.B

Summarize and describe distributions. [See: Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 ND.6.SP.B.4

Display numerical data in plots on a number line, including dot plots, histograms, and box plots. [See: Histograms; Visualizing the “Shape” of Data; Box Plots; Standard Deviation.]
 ND.6.SP.B.5

Summarize numerical data sets in relation to their context. [See: Measures of Center; Box Plots; Standard Deviation.]
 ND.6.SP.B.5.C

Summarize numerical data sets in relation to their context by giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. [See: Measures of Center; Box Plots; Standard Deviation.]
 ND.6.SP.B.5.D

Summarize numerical data sets in relation to their context by relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. [See: Measures of Center.]
 ND.7.EE.A.2

Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. [See: Problem Decomposition.]
 ND.7.EE.B

Solve reallife and mathematical problems using numerical and algebraic expressions and equations. [See: Piecewise Functions and Conditionals; Solving Word Problems with the Design Recipe; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Player Animation; The Distance Formula.]
 ND.7.EE.B.4

Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. [See: Defining Values; Functions Make Life Easier!; Solving Word Problems with the Design Recipe; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 ND.7.G.B.4

Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle. [See: Solving Word Problems with the Design Recipe.]
 ND.7.G.B.6

Solve realworld and mathematical problems involving area, volume and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [See: Solving Word Problems with the Design Recipe; Surface Area of a Rectangular Prism.]
 ND.7.RP.A

Analyze proportional relationships and use them to solve realworld and mathematical problems. [See: Making Flags; Making Game Images.]
 ND.7.RP.A.1

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. [See: Making Flags.]
 ND.7.RP.A.2.A

Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. [See: Functions Can Be Linear; Defining Linear Functions.]
 ND.7.RP.A.2.B

Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. [See: Functions Can Be Linear; Defining Linear Functions.]
 ND.7.SP.A

Use random sampling to draw inferences about a population. [See: Probability, Inference, and Sample Size.]
 ND.7.SP.A.1

Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. [See: Probability, Inference, and Sample Size.]
 ND.7.SP.A.2

Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. [See: Probability, Inference, and Sample Size.]
 ND.7.SP.B

Draw informal comparative inferences about two populations. [See: Bar and Pie Charts.]
 ND.8.EE.B

Understand the connections between proportional relationships, lines, and linear equations. [See: Functions Can Be Linear; Defining Linear Functions.]
 ND.8.EE.B.5

Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. [See: Functions Can Be Linear; Defining Linear Functions.]
 ND.8.F.A.1

Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. [See: Contracts; The Vertical Line Test.]
 ND.8.F.A.2

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [See: Functions Can Be Linear; Defining Linear Functions.]
 ND.8.F.A.3

Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. [See: Functions Can Be Linear; Defining Linear Functions.]
 ND.8.F.B

Use functions to model relationships between quantities. [See: Functions Make Life Easier!; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition.]
 ND.8.F.B.4

Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. [See: Functions Can Be Linear; Defining Linear Functions.]
 ND.8.F.B.5

Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. [See: Functions Can Be Linear; Defining Linear Functions.]
 ND.8.G.A.1

Verify experimentally the properties of rotations, reflections, and translations. [See: Making Game Images.]
 ND.8.G.B

Understand and apply the Pythagorean Theorem. [See: The Distance Formula.]
 ND.8.G.B.7

Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions. [See: The Distance Formula.]
 ND.8.G.B.8

Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. [See: The Distance Formula.]
 ND.8.SP.A.1

Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. [See: Scatter Plots; Grouped Samples; Correlations; Linear Regression.]
 ND.8.SP.A.2

Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. [See: Scatter Plots; Correlations; Linear Regression.]
 ND.8.SP.A.3

Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. [See: Linear Regression.]
 ND.HSA.CED.A

Create equations that describe numbers or relationships. [See: Solving Word Problems with the Design Recipe; Surface Area of a Rectangular Prism; Problem Decomposition; Sam the Butterfly  Applying Inequalities.]
 ND.HSA.CED.A.1

Create equations and inequalities in one variable and use them to solve problems. [See: Sam the Butterfly  Applying Inequalities.]
 ND.HSA.CED.A.2

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. [See: Sam the Butterfly  Applying Inequalities.]
 ND.HSA.CED.A.3

Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. [See: Sam the Butterfly  Applying Inequalities.]
 ND.HSA.SSE.A.1

Interpret expressions that represent a quantity in terms of its context. [See: Defining Values; Functions Make Life Easier!; Solving Word Problems with the Design Recipe.]
 ND.HSA.SSE.A.1.A

Interpret parts of an expression, such as terms, factors, and coefficients. [See: Piecewise Functions and Conditionals; Player Animation.]
 ND.HSA.SSE.A.1.B

Interpret complicated expressions by viewing one or more of their parts as a single entity. [See: Piecewise Functions and Conditionals; Player Animation; Custom Scatter Plots.]
 ND.HSA.SSE.A.2

Use the structure of an expression to identify ways to rewrite it. [See: Order of Operations.]
 ND.HSA.SSE.B

Write expressions in equivalent forms to solve problems. [See: Order of Operations.]
 ND.HSF.BF.A

Build a function that models a relationship between two quantities. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 ND.HSF.BF.A.1

Write a function that describes a relationship between two quantities. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 ND.HSF.BF.A.1.B

Combine standard function types using arithmetic operations. [See: Function Composition.]
 ND.HSF.BF.A.1.C

Compose functions. [See: Function Composition; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality.]
 ND.HSF.BF.B

Build new functions from existing functions. [See: Problem Decomposition; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality.]
 ND.HSF.IF.A

Understand the concept of a function and use function notation. [See: Functions Make Life Easier!; Function Notation.]
 ND.HSF.IF.A.1

Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). [See: Contracts; The Vertical Line Test.]
 ND.HSF.IF.A.2

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. [See: Contracts; Making Flags; Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 ND.HSF.IF.B

Interpret functions that arise in applications in terms of the context. [See: Function Notation; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Defining Table Functions.]
 ND.HSF.IF.B.5

Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. [See: Functions Can Be Linear; Defining Linear Functions.]
 ND.HSF.IF.C

Analyze functions using different representations. [See: The Vertical Line Test; Functions: Contracts, Examples & Definitions; Functions Can Be Linear; Defining Linear Functions; Solving Word Problems with the Design Recipe.]
 ND.HSF.IF.C.9

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). [See: Functions Can Be Linear; Defining Linear Functions; Problem Decomposition.]
 ND.HSN.Q.A

Reason quantitatively and use units to solve problems. [See: Making Flags.]
 ND.HSS.CP.A.1

Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ('or', 'and', 'not'). [See: Compound Inequalities: Solutions & NonSolutions.]
 ND.HSS.CP.B.9

Use permutations and combinations to compute probabilities of compound events and solve problems. [See: Permutations; Combinations.]
 ND.HSS.IC.A

Understand and evaluate random processes underlying statistical experiments. [See: Probability, Inference, and Sample Size.]
 ND.HSS.IC.A.1

Understand statistics as a process for making inferences about population parameters based on a random sample from that population. [See: Probability, Inference, and Sample Size.]
 ND.HSS.IC.B

Make inferences and justify conclusions from sample surveys, experiments, and observational studies. [See: Collecting Data.]
 ND.HSS.IC.B.3

Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. [See: Probability, Inference, and Sample Size; Collecting Data.]
 ND.HSS.IC.B.4

Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. [See: Collecting Data.]
 ND.HSS.IC.B.6

Evaluate reports based on data. [See: Threats to Validity.]
 ND.HSS.ID.A

Summarize, represent, and interpret data on a single count or measurement variable. [See: Bar and Pie Charts; Histograms; Visualizing the “Shape” of Data; Measures of Center; Box Plots.]
 ND.HSS.ID.A.1

Represent data with plots on the real number line (dot plots, histograms, and box plots). [See: Histograms; Visualizing the “Shape” of Data; Box Plots; Standard Deviation.]
 ND.HSS.ID.A.2

Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. [See: Histograms; Measures of Center; Box Plots; Standard Deviation.]
 ND.HSS.ID.A.3

Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). [See: Histograms;