Common Core Math Standards
 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.]
 5.OA.A

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

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

Reason about and solve onevariable equations and inequalities. [See: Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 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: 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; Piecewise Functions and Conditionals; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality.]
 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.]
 6.G.A

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

Understand ratio concepts and use ratio reasoning to solve problems. [See: Making Flags.]
 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.]
 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.]
 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.]
 7.EE.B

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

Analyze proportional relationships and use them to solve realworld and mathematical problems. [See: Making Flags; Making Game Images.]
 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.]
 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.]
 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.]
 8.EE.B

Understand the connections between proportional relationships, lines, and linear equations. [See: Functions Can Be Linear; Defining Linear Functions.]
 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.]
 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.]
 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.]
 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.]
 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.]
 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.]
 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.]
 8.G.A.1

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

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

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

Create equations and inequalities in one variable and use them to solve problems. [See: Sam the Butterfly  Applying Inequalities.]
 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.]
 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.]
 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.]
 HSA.SSE.A.1.A

Interpret parts of an expression, such as terms, factors, and coefficients. [See: Piecewise Functions and Conditionals; Player Animation.]
 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.]
 HSA.SSE.A.2

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

Write expressions in equivalent forms to solve problems. [See: Order of Operations.]
 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.]
 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.]
 HSF.BF.A.1.B

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

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

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

Understand the concept of a function and use function notation. [See: Functions Make Life Easier!; Function Notation.]
 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.]
 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.]
 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.]
 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.]
 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.]
 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.]
 HSN.Q.A

Reason quantitatively and use units to solve problems. [See: Making Flags.]
 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.]
CSTA Standards
 1BAP09

Create programs that use variables to store and modify data. [See: Defining Values.]
 1BAP10

Create programs that include sequences, events, loops, and conditionals. [See: Functions for Character Animation; Piecewise Functions and Conditionals; Player Animation.]
 1BAP11

Decompose (break down) problems into smaller, manageable subproblems to facilitate the program development process. [See: Problem Decomposition.]
 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: Making Game Images; Piecewise Functions and Conditionals; Player Animation.]
 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!.]
 1BIC21

Use public domain or creative commons media, and refrain from copying or using material created by others without permission. [See: Making Game Images.]
 2AP11

Create clearly named variables that represent different data types and perform operations on their values. [See: Simple Data Types; Function Composition; Defining Values; Functions Make Life Easier!; Functions for Character Animation; Surface Area of a Rectangular Prism; Problem Decomposition; Piecewise Functions and Conditionals; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality.]
 2AP13

Decompose problems and subproblems into parts to facilitate the design, implementation, and review of programs [See: Problem Decomposition.]
 2AP14

Create procedures with parameters to organize code and make it easier to reuse. [See: Functions Make Life Easier!.]
 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: Function Composition; Functions Make Life Easier!; Functions for Character Animation; Surface Area of a Rectangular Prism; Problem Decomposition; Piecewise Functions and Conditionals; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality.]
 2AP19

Document programs in order to make them easier to follow, test, and debug. [See: Function Composition; Functions Make Life Easier!; Functions for Character Animation; Surface Area of a Rectangular Prism; Problem Decomposition; Piecewise Functions and Conditionals; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality.]
 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.]
 3AAP17

Decompose problems into smaller components through systematic analysis, using constructs such as procedures, modules, and/or objects. [See: Problem Decomposition.]
 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.]
 3AAP20

Evaluate licenses that limit or restrict use of computational artifacts when using resources such as libraries [See: Making Game Images.]
 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.]
 3BAP14

Construct solutions to problems using studentcreated components, such as procedures, modules and/or objects. [See: Functions Make Life Easier!; Functions for Character Animation; Problem Decomposition; Piecewise Functions and Conditionals; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality.]
 3BAP21

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

Modify an existing program to add additional functionality and discuss intended and unintended implications (e.g., breaking other functionality). [See: Player Animation.]
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.]
 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.]
 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.]
 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.]
 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!.]
 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: 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; Piecewise Functions and Conditionals; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality.]
 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.]
 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.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: Solving Word Problems with the Design Recipe; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Piecewise Functions and Conditionals; 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.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.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.]
 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.]
 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.]
 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.]
 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.]
 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.]
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: 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; Piecewise Functions and Conditionals; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality.]
 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.]
 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.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: Solving Word Problems with the Design Recipe; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Piecewise Functions and Conditionals; 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.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.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.]
 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.]
 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.]
 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.]
 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.]
 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.]
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: 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; Piecewise Functions and Conditionals; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality.]
 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.]
 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.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: Solving Word Problems with the Design Recipe; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Piecewise Functions and Conditionals; 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.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.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.]
 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.]
 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.]
 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.]
 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.]
 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.]
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: 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; Piecewise Functions and Conditionals; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality.]
 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.]
 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.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: Solving Word Problems with the Design Recipe; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Piecewise Functions and Conditionals; 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.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.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.]
 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.]
 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.]
 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.]
 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.]
 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.]
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: 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; Piecewise Functions and Conditionals; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality.]
 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.]
 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.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: Solving Word Problems with the Design Recipe; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Piecewise Functions and Conditionals; 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.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.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.]
 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.]
 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.]
 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.]
 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.]
 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.]
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: 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; Piecewise Functions and Conditionals; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality.]
 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.]
 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.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: Solving Word Problems with the Design Recipe; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Piecewise Functions and Conditionals; 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.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.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.]
 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.]
 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.]
 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.]
 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.]
 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.]
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: 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; Piecewise Functions and Conditionals; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality.]
 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.]
 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.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: Solving Word Problems with the Design Recipe; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Piecewise Functions and Conditionals; 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.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.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.]
 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.]
 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.]
 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.]
 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.]
 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.]
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: 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; Piecewise Functions and Conditionals; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality.]
 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.]
 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.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: Solving Word Problems with the Design Recipe; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Piecewise Functions and Conditionals; 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.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.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.]
 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.]
 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.]
 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.]
 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.]
 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.]
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: 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; Piecewise Functions and Conditionals; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality.]
 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.]
 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.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: Solving Word Problems with the Design Recipe; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Piecewise Functions and Conditionals; 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.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.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.]
 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.]
 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.]
 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.]
 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.]
 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.]
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: 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; Piecewise Functions and Conditionals; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality.]
 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.]
 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.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: Solving Word Problems with the Design Recipe; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Piecewise Functions and Conditionals; 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.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.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.]
 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.]
 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.]
 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.]
 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.]
 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.]
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: 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; Piecewise Functions and Conditionals; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality.]
 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.]
 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.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: Solving Word Problems with the Design Recipe; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Piecewise Functions and Conditionals; 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.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.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.]
 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.]
 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.]
 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.]
 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.]
 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.]
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: 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; Piecewise Functions and Conditionals; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality.]
 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.]
 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.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: Solving Word Problems with the Design Recipe; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Piecewise Functions and Conditionals; 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.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.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.]
 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.]
 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.]
 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.]
 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.]
 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.]
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: 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; Piecewise Functions and Conditionals; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality.]
 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.]
 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.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: Solving Word Problems with the Design Recipe; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Piecewise Functions and Conditionals; 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.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.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.]
 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.]
 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.]
 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.]
 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.]
 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.]
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: 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; Piecewise Functions and Conditionals; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality.]
 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.]
 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.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: Solving Word Problems with the Design Recipe; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Piecewise Functions and Conditionals; 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.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.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.]
 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.]
 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.]
 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.]
 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.]
 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.]
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: 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; Piecewise Functions and Conditionals; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality.]
 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.]
 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.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: Solving Word Problems with the Design Recipe; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Piecewise Functions and Conditionals; 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.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.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.]
 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.]
 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.]
 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.]
 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.]
 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.]
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: 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; Piecewise Functions and Conditionals; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality.]
 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.]
 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.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: Solving Word Problems with the Design Recipe; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Piecewise Functions and Conditionals; 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.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.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.]
 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.]
 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.]
 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.]
 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.]
 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.]
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: 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; Piecewise Functions and Conditionals; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality.]
 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.]
 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.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: Solving Word Problems with the Design Recipe; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Piecewise Functions and Conditionals; 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.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.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.]
 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.]
 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.]
 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.]
 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.]
 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.]
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.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.]
 MA.68.CT.b.1

Design solutions that use repetition and conditionals. [See: Piecewise Functions and Conditionals; Player Animation.]
 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.]
 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.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.]
 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.]
 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.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: 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; Piecewise Functions and Conditionals; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality.]
 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.]
 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.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: Solving Word Problems with the Design Recipe; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Piecewise Functions and Conditionals; 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.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.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.]
 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.]
 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.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.6

Use appropriate conditional structures in programs (e.g., IFTHEN, IFTHENELSE, SWITCH). [See: Piecewise Functions and Conditionals; Player Animation.]
 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.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.]
 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.]
 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.]
 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.]
 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.]
 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.]
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: 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; Piecewise Functions and Conditionals; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality.]
 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.]
 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.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: Solving Word Problems with the Design Recipe; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Piecewise Functions and Conditionals; 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.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.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.]
 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.]
 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.]
 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.]
 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.]
 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.]
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: 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; Piecewise Functions and Conditionals; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality.]
 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.]
 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.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: Solving Word Problems with the Design Recipe; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Piecewise Functions and Conditionals; 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.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.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.]
 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.]
 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.]
 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.]
 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.]
 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.]
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: 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; Piecewise Functions and Conditionals; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality.]
 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.]
 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.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: Solving Word Problems with the Design Recipe; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Piecewise Functions and Conditionals; 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.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.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.]
 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.]
 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.]
 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.]
 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.]
 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.]
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: 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; Piecewise Functions and Conditionals; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality.]
 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.]
 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.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: Solving Word Problems with the Design Recipe; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Piecewise Functions and Conditionals; 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.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.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.]
 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.]
 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.]
 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.]
 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.]
 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.]
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: 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; Piecewise Functions and Conditionals; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality.]
 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.]
 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.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: Solving Word Problems with the Design Recipe; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Piecewise Functions and Conditionals; 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.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.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.]
 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.]
 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.]
 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.]
 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.]
 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.]
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: 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; Piecewise Functions and Conditionals; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality.]
 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.]
 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.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: Solving Word Problems with the Design Recipe; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Piecewise Functions and Conditionals; 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.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.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.]
 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.]
 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.]
 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.]
 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.]
 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.]
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: 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; Piecewise Functions and Conditionals; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality.]
 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.]
 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.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: Solving Word Problems with the Design Recipe; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Piecewise Functions and Conditionals; 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.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.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.]
 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.]
 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.]
 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.]
 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.]
 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.]
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: 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; Piecewise Functions and Conditionals; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality.]
 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.]
 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.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: Solving Word Problems with the Design Recipe; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Piecewise Functions and Conditionals; 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.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.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.]
 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.]
 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.]
 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.]
 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.]
 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.]
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: 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; Piecewise Functions and Conditionals; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality.]
 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.]
 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.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: Solving Word Problems with the Design Recipe; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Piecewise Functions and Conditionals; 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.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.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.]
 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.]
 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.]
 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.]
 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.]
 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.]
New York Standards
 NY.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.]
 NY.5.OA.A

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

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

Reason about and solve onevariable equations and inequalities. [See: Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 NY.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: 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; Piecewise Functions and Conditionals; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality.]
 NY.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.]
 NY.6.G.A

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

Understand ratio concepts and use ratio reasoning to solve problems. [See: Making Flags.]
 NY.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.]
 NY.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.]
 NY.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.]
 NY.7.EE.B

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

Analyze proportional relationships and use them to solve realworld and mathematical problems. [See: Making Flags; Making Game Images.]
 NY.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.]
 NY.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.]
 NY.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.]
 NY.8.EE.B

Understand the connections between proportional relationships, lines, and linear equations. [See: Functions Can Be Linear; Defining Linear Functions.]
 NY.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.]
 NY.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.]
 NY.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.]
 NY.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.]
 NY.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.]
 NY.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.]
 NY.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.]
 NY.8.G.A.1

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

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

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

Create equations and inequalities in one variable and use them to solve problems. [See: Sam the Butterfly  Applying Inequalities.]
 NY.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.]
 NY.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.]
 NY.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.]
 NY.HSA.SSE.A.1.A

Interpret parts of an expression, such as terms, factors, and coefficients. [See: Piecewise Functions and Conditionals; Player Animation.]
 NY.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.]
 NY.HSA.SSE.A.2

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

Write expressions in equivalent forms to solve problems. [See: Order of Operations.]
 NY.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.]
 NY.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.]
 NY.HSF.BF.A.1.B

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

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

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

Understand the concept of a function and use function notation. [See: Functions Make Life Easier!; Function Notation.]
 NY.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.]
 NY.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.]
 NY.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.]
 NY.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.]
 NY.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.]
 NY.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.]
 NY.HSN.Q.A

Reason quantitatively and use units to solve problems. [See: Making Flags.]
 NY.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.]
Oklahoma Standards
 OK.3.A.V.01

Create programs that use variables to store and modify grade level appropriate data. [See: Defining Values.]
 OK.3.AP.A.01

Compare multiple algorithms for the same task. [See: Making Flags.]
 OK.3.AP.M.01

Decompose the steps needed to solve a problem into a precise sequence of instructions. [See: Making Flags.]
 OK.3.AP.M.02

With grade appropriate complexity, modify, remix, or incorporate portions of an existing program into one’s own work, to develop something new or add more advanced features. [See: Making Game Images; Functions for Character Animation; Player Animation.]
 OK.3.AP.PD.01

Use an iterative process to plan the development of a program while solving simple problems. [See: Functions Make Life Easier!; Solving Word Problems with the Design Recipe.]
 OK.3.AP.PD.02

Observe intellectual property rights and give appropriate credit when creating or remixing programs. [See: Making Game Images.]
 OK.3.AP.PD.03

Analyze and debug a program that includes sequencing, repetition and variables in a programming language. [See: Making Flags.]
 OK.3.AP.PD.04

Communicate and explain your program development using comments, presentations and demonstrations. [See: Solving Word Problems with the Design Recipe.]
 OK.4.AP.A.01

Compare and refine multiple algorithms for the same task. [See: Making Flags.]
 OK.4.AP.C.01

Create programs using a programming language that utilize sequencing, repetition, conditionals and variables using math operations manipulate values to solve a problem or express ideas both independently and collaboratively. [See: Making Flags.]
 OK.4.AP.M.01

Decompose large problems into smaller, manageable subproblems to facilitate the program development process. [See: Problem Decomposition.]
 OK.4.AP.M.02

With grade appropriate complexity, modify, remix, or incorporate portions of an existing program into one’s own work, to develop something new or add more advanced features. [See: Making Game Images; Functions for Character Animation; Player Animation.]
 OK.4.AP.PD.04

Communicate and explain your program development using comments, presentations and demonstrations. [See: Solving Word Problems with the Design Recipe.]
 OK.4.AP.V.01

Create programs that use variables to store and modify grade level appropriate data. [See: Defining Values.]
 OK.5.AP.A.01

Compare and refine multiple algorithms for the same task and determine which is the most efficient. [See: Function Composition; Making Flags.]
 OK.5.AP.M.01

Decompose large problems into smaller, manageable subproblems and then into a precise sequence of instructions. [See: Problem Decomposition.]
 OK.5.AP.M.02

With grade appropriate complexity, modify, remix, or incorporate portions of an existing program into one’s own work, to develop something new or add more advanced features. [See: Making Game Images; Functions for Character Animation; Player Animation.]
 OK.5.AP.PD.02

Observe intellectual property rights and give appropriate credit when creating or remixing programs. [See: Making Game Images.]
 OK.5.AP.PD.04

Communicate and explain your program development using comments, presentations and demonstrations. [See: Solving Word Problems with the Design Recipe.]
 OK.5.AP.V.01

Create programs that use variables to store and modify grade level appropriate data. [See: Defining Values.]
 OK.5.GM.1.1

Describe, classify and construct triangles, including equilateral, right, scalene, and isosceles triangles. Recognize triangles in various contexts. [See: Contracts.]
 OK.6.A.1.1

Plot integer and rationalvalued (limited to halves and fourths) orderedpairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs. [See: Coordinates and Game Design; Making Flags.]
 OK.6.A.1.3

Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false. [See: Simple Data Types.]
 OK.6.A.3.1

Represent realworld or mathematical situations using expressions, equations and inequalities involving variables and rational numbers. [See: Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 OK.6.AP.A.01

Use an existing algorithm in natural language or pseudocode to solve complex problems. [See: Solving Word Problems with the Design Recipe.]
 OK.6.AP.C.01

Develop programs that utilize combinations of repetition, conditionals, and the manipulation of variables representing different data types. [See: Sam the Butterfly  Applying Inequalities.]
 OK.6.AP.M.01

Decompose problems into parts to facilitate the design, implementation, and review of programs. [See: Making Flags; Problem Decomposition; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality.]
 OK.6.AP.PD.01

Seek and incorporate feedback from team members to refine a solution to a problem. [See: Making Flags; Making Game Images; Functions for Character Animation; Player Animation; Collision Detection  Distance and Inequality.]
 OK.6.AP.PD.02

Incorporate existing code, media, and libraries into original programs and give attribution. [See: Making Game Images.]
 OK.6.AP.PD.05

Document textbased programs in order to make them easier to follow, test, and debug. [See: Solving Word Problems with the Design Recipe.]
 OK.6.GM.2.2

Develop and use the fact that the sum of the interior angles of a triangle is 180Â° to determine missing angle measures in a triangle. [See: Contracts.]
 OK.6.IC.C.01

Explain how computing impacts people’s everyday activities. [See: Computing Needs All Voices.]
 OK.7.A.3.3

Represent realworld or mathematical situations using equations and inequalities involving variables and rational numbers. [See: Defining Values; Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Sam the Butterfly  Applying Inequalities.]
 OK.7.A.4.2

Apply understanding of order of operations and grouping symbols when using calculators and other technologies [See: Order of Operations.]
 OK.7.AP.A.01

Select and modify an existing algorithm in natural language or pseudocode to solve complex problems. [See: Simple Data Types; Solving Word Problems with the Design Recipe; Surface Area of a Rectangular Prism.]
 OK.7.AP.M.01

Decompose problems into parts to facilitate the design, implementation, and review of increasingly complex programs. [See: Problem Decomposition; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality.]
 OK.7.AP.PD.01

Seek and incorporate feedback from team members and users to refine a solution to a problem. [See: Making Game Images; Functions for Character Animation; Player Animation; Collision Detection  Distance and Inequality.]
 OK.7.AP.PD.02

Incorporate existing code, media, and libraries into original programs of increasing complexity and give attribution. [See: Making Game Images.]
 OK.7.AP.PD.05

Document textbased programs of increasing complexity in order to make them easier to follow, test, and debug. [See: Solving Word Problems with the Design Recipe.]
 OK.7.CS.T.01

Identify and fix increasingly complex software and hardware problems with computing devices and their components. [See: Problem Decomposition.]
 OK.7.GM.1.1

Using a variety of tools and strategies, develop the concept that surface area of a rectangular prism with rationalvalued edge lengths can be found by wrapping the figure with samesized square units without gaps or overlap. Use appropriate measurements such as cm^2 [See: Surface Area of a Rectangular Prism.]
 OK.7.GM.4.1

Describe the properties of similarity, compare geometric figures for similarity, and determine scale factors resulting from dilations. [See: Making Flags; Making Game Images.]
 OK.7.GM.4.2

Apply proportions, ratios, and scale factors to solve problems involving scale drawings and determine side lengths and areas of similar triangles and rectangles. [See: Making Flags; Making Game Images.]
 OK.7.N.1.1

Know that every rational number can be written as the ratio of two integers or as a terminating or repeating decimal. [See: Simple Data Types.]
 OK.7.N.1.2

Compare and order rational numbers expressed in various forms using the symbols <, >, and =. [See: Simple Data Types.]
 OK.7.N.1.3

Recognize and generate equivalent representations of rational numbers, including equivalent fractions. [See: Simple Data Types.]
 OK.8.AP.A.01

Design algorithms in natural language, flow and control diagrams, comments within code, and/or pseudocode to solve complex problems. [See: Making Flags; Making Game Images; Solving Word Problems with the Design Recipe; Functions for Character Animation.]
 OK.8.AP.C.01

Develop programs that utilize combinations of nested repetition, compound conditionals, procedures without parameters, and the manipulation of variables representing different data types. [See: Simple Data Types.]
 OK.8.AP.M.01

Decompose problems and subproblems into parts to facilitate the design, implementation, and review of complex programs. [See: Problem Decomposition; Sam the Butterfly  Applying Inequalities; Collision Detection  Distance and Inequality.]
 OK.8.AP.PD.02

Incorporate existing code, media, and libraries into original programs of increasing complexity and give attribution. [See: Functions Make Life Easier!.]
 OK.8.AP.PD.04

Explain how effective communication between participants is required for successful collaboration when developing computational artifacts. [See: Solving Word Problems with the Design Recipe.]
 OK.8.AP.PD.05

Document textbased programs of increasing complexity in order to make them easier to follow, test, and debug. [See: Solving Word Problems with the Design Recipe.]
 OK.8.CS.T.01

Systematically identify, fix, and document increasingly complex software and hardware problems with computing devices and their components. [See: Problem Decomposition.]
 OK.A1.A.1.1

Use knowledge of solving equations with rational values to represent and solve mathematical and realworld problems (e.g., angle measures, geometric formulas, science, or statistics) and interpret the solutions in the original context. [See: Functions Make Life Easier!.]
 OK.A1.A.2

Represent and solve realworld and mathematical problems using linear inequalities, compound inequalities and systems of linear inequalities; interpret solutions in the original context. [See: Sam the Butterfly  Applying Inequalities.]
 OK.A1.A.2.2

Represent relationships in various contexts with compound and absolute value inequalities and solve the resulting inequalities by graphing and interpreting the solutions on a number line. [See: Compound Inequalities: Solutions & NonSolutions; Sam the Butterfly  Applying Inequalities.]
 OK.A1.A.3

Generate equivalent algebraic expressions and use algebraic properties to evaluate expressions and arithmetic and geometric sequences. [See: Order of Operations.]
 OK.A1.A.3.1

Solve equations involving several variables for one variable in terms of the others. [See: Problem Decomposition.]
 OK.A1.A.4

Analyze mathematical change involving linear equations in realworld and mathematical problems. [See: Defining Linear Functions.]
 OK.A1.A.4.1

Calculate and interpret slope and the x and yintercepts of a line using a graph, an equation, two points, or a set of data points to solve realworld and mathematical problems. [See: Defining Linear Functions.]
 OK.A1.D.2.2

Describe the concepts of intersections, unions, and complements using Venn diagrams to evaluate probabilities. Understand the relationships between these concepts and the words AND, OR, and NOT. [See: Compound Inequalities: Solutions & NonSolutions.]
 OK.A1.F.1.2

Identify the dependent and independent variables as well as the domain and range given a function, equation, or graph. Identify restrictions on the domain and range in realworld contexts. [See: Contracts.]
 OK.A1.F.1.3

Write linear functions, using function notation, to model realworld and mathematical situations. [See: Contracts; Function Composition; Functions Make Life Easier!.]
 OK.A1.F.1.4

Given a graph modeling a realworld situation, read and interpret the linear piecewise function (excluding step functions). [See: Contracts.]
 OK.A1.F.2.1

Distinguish between linear and nonlinear (including exponential) functions arising from realworld and mathematical situations that are represented in tables, graphs, and equations. Understand that linear functions grow by equal intervals and that exponential functions grow by equal factors over equal intervals. [See: Functions Can Be Linear; Defining Linear Functions.]
 OK.A1.F.3

Represent functions in multiple ways and use the representation to interpret realworld and mathematical problems. [See: Function Composition; Defining Values; Defining Linear Functions.]
 OK.A1.F.3.1

Identify and generate equivalent representations of linear equations, graphs, tables, and realworld situations. [See: Defining Values; Defining Linear Functions.]
 OK.A1.F.3.2

Use function notation; evaluate a function, including nonlinear, at a given point in its domain algebraically and graphically. Interpret the results in terms of realworld and mathematical problems. [See: Function Composition.]
 OK.A1.F.3.3

Add, subtract, and multiply functions using function notation. [See: Function Composition.]
 OK.G.2D.1.5

Use coordinate geometry to represent and analyze line segments and polygons, including determining lengths, midpoints, and slopes of line segments. [See: The Distance Formula; Collision Detection  Distance and Inequality.]
 OK.G.2D.1.8

Construct logical arguments to prove triangle congruence (SSS, SAS, ASA, AAS and HL) and triangle similarity (AA, SSS, SAS). [See: Contracts.]
 OK.G.3D.1.1

Solve realworld and mathematical problems using the surface area and volume of prisms, cylinders, pyramids, cones, spheres, and composites of these figures. Use nets, measuring devices, or formulas as appropriate. [See: Surface Area of a Rectangular Prism.]
 OK.G.RT.1.1

Apply the distance formula and the Pythagorean Theorem and its converse to solve realworld and mathematical problems, as approximate and exact values, using algebraic and logical reasoning (include Pythagorean Triples). [See: The Distance Formula; Collision Detection  Distance and Inequality.]
 OK.L1.AP.A.01

Create a prototype that uses algorithms (e.g., searching, sorting, finding shortest distance) to provide a possible solution for a realworld problem. [See: Surface Area of a Rectangular Prism; Sam the Butterfly  Applying Inequalities.]
 OK.L1.AP.M.01

Break down a solution into procedures using systematic analysis and design. [See: Problem Decomposition; Piecewise Functions and Conditionals.]
 OK.L1.AP.M.02

Create computational artifacts by systematically organizing, manipulating and/or processing data. [See: Piecewise Functions and Conditionals.]
 OK.L1.CS.D.01

Explain how abstractions hide the underlying implementation details of computing systems embedded in everyday objects. [See: Coordinates and Game Design.]
 OK.L2.AP.M.03

Create programming solutions by reusing existing code (e.g., libraries, Application Programming Interface (APIs), code repositories). [See: Sam the Butterfly  Applying Inequalities.]
 OK.L2.AP.PD.03

Develop programs for multiple computing platforms. [See: Functions Make Life Easier!.]
 OK.L2.AP.PD.05

Develop and use a series of test cases to verify that a program performs according to its design specifications. [See: Solving Word Problems with the Design Recipe.]
 OK.L2.AP.PD.07

Modify an existing program to add additional functionality and discuss intended and unintended implications (e.g., breaking other functionality). [See: Player Animation.]
 OK.MAP.1

Develop a deep and flexible conceptual understanding. [See: Making Flags.]
 OK.MAP.2

Develop accurate and appropriate procedural fluency. [See: Order of Operations.]
 OK.MAP.3

Develop strategies for problem solving. [See: Functions for Character Animation.]
 OK.MAP.4

Develop mathematical reasoning. [See: Making Flags.]
 OK.MAP.5

Develop a productive mathematical disposition. [See: Functions Make Life Easier!.]
 OK.MAP.6

Develop the ability to make conjectures, model, and generalize. [See: Functions Make Life Easier!.]
 OK.MAP.7

Develop the ability to communicate mathematically. [See: Solving Word Problems with the Design Recipe.]
 OK.PA.A.1.1

Recognize that a function is a relationship between an independent variable and a dependent variable in which the value of the independent variable determines the value of the dependent variable. [See: Contracts; Functions Make Life Easier!; Piecewise Functions and Conditionals; Player Animation.]
 OK.PA.A.1.2

Use linear functions to represent and explain realworld and mathematical situations. [See: Functions Make Life Easier!; Solving Word Problems with the Design Recipe; Functions for Character Animation.]
 OK.PA.A.1.3

Identify a function as linear if it can be expressed in the form y = mx + b or if its graph is a straight line. [See: Solving Word Problems with the Design Recipe.]
 OK.PA.A.2

Recognize linear functions in realworld and mathematical situations; represent linear functions and other functions with tables, verbal descriptions, symbols, and graphs; solve problems involving linear functions and interpret results in the original context. [See: Solving Word Problems with the Design Recipe; Functions for Character Animation.]
 OK.PA.A.2.1

Represent linear functions with tables, verbal descriptions, symbols, and graphs; translate from one representation to another. [See: Functions Can Be Linear; Defining Linear Functions; Solving Word Problems with the Design Recipe; Functions for Character Animation.]
 OK.PA.A.2.2

Identify, describe, and analyze linear relationships between two variables. [See: Functions Can Be Linear; Defining Linear Functions.]
 OK.PA.A.2.3

Identify graphical properties of linear functions including slope and intercepts. Know that the slope equals the rate of change, and that the yintercept is zero when the function represents a proportional relationship. [See: Defining Linear Functions.]
 OK.PA.A.2.4

Predict the effect on the graph of a linear function when the slope or yintercept changes. Use appropriate tools to examine these effects. [See: Functions Can Be Linear; Defining Linear Functions.]
 OK.PA.A.3

Generate equivalent numerical and algebraic expressions and use algebraic properties to evaluate expressions. [See: Order of Operations.]
 OK.PA.A.3.1

Use substitution to simplify and evaluate algebraic expressions. [See: Function Composition; Defining Values.]
 OK.PA.A.4

Represent realworld and mathematical problems using equations and inequalities involving linear expressions. Solve and graph equations and inequalities symbolically and graphically. Interpret solutions in the original context. [See: Making Flags.]
 OK.PA.A.4.3

Represent realworld situations using equations and inequalities involving one variable. [See: Simple Inequalities; Compound Inequalities: Solutions & NonSolutions; Sam the Butterfly  Applying Inequalities.]
 OK.PA.GM.1

Solve problems involving right triangles using the Pythagorean Theorem. [See: The Distance Formula.]
 OK.PA.GM.1.1

Informally justify the Pythagorean Theorem using measurements, diagrams, or dynamic software and use the Pythagorean Theorem to solve problems in two and three dimensions involving right triangles. [See: The Distance Formula.]
 OK.PA.GM.1.2

Use the Pythagorean Theorem to find the distance between any two points in a coordinate plane. [See: The Distance Formula; Collision Detection  Distance and Inequality.]
 OK.PA.GM.2

Calculate surface area and volume of threedimensional figures. [See: Surface Area of a Rectangular Prism.]
 OK.PA.GM.2.1

Calculate the surface area of a rectangular prism using decomposition or nets. Use appropriate units of measure, such as square centimeters. [See: Surface Area of a Rectangular Prism.]
 OK.PA.GM.2.2

Calculate the surface area of a cylinder, in terms of pi and using approximations for pi, using decomposition or nets. Use appropriate units of measure, such as square centimeters. [See: Surface Area of a Rectangular Prism.]
Ohio Standards
 OH.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.]
 OH.5.OA.A

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

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

Reason about and solve onevariable equations and inequalities. [See: Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 OH.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: 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; Piecewise Functions and Conditionals; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality.]
 OH.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.]
 OH.6.G.A

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

Understand ratio concepts and use ratio reasoning to solve problems. [See: Making Flags.]
 OH.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.]
 OH.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.]
 OH.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.]
 OH.7.EE.B

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

Analyze proportional relationships and use them to solve realworld and mathematical problems. [See: Making Flags; Making Game Images.]
 OH.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.]
 OH.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.]
 OH.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.]
 OH.8.EE.B

Understand the connections between proportional relationships, lines, and linear equations. [See: Functions Can Be Linear; Defining Linear Functions.]
 OH.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.]
 OH.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.]
 OH.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.]
 OH.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.]
 OH.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.]
 OH.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.]
 OH.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.]
 OH.8.G.A.1

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

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

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

Create equations and inequalities in one variable and use them to solve problems. [See: Sam the Butterfly  Applying Inequalities.]
 OH.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.]
 OH.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.]
 OH.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.]
 OH.HSA.SSE.A.1.A

Interpret parts of an expression, such as terms, factors, and coefficients. [See: Piecewise Functions and Conditionals; Player Animation.]
 OH.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.]
 OH.HSA.SSE.A.2

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

Write expressions in equivalent forms to solve problems. [See: Order of Operations.]
 OH.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.]
 OH.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.]
 OH.HSF.BF.A.1.B

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

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

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

Understand the concept of a function and use function notation. [See: Functions Make Life Easier!; Function Notation.]
 OH.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.]
 OH.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.]
 OH.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.]
 OH.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.]
 OH.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.]
 OH.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.]
 OH.HSN.Q.A

Reason quantitatively and use units to solve problems. [See: Making Flags.]
 OH.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.]
Oregon Standards
 OR.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.]
 OR.5.OA.A

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

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

Reason about and solve onevariable equations and inequalities. [See: Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 OR.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: 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; Piecewise Functions and Conditionals; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality.]
 OR.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.]
 OR.6.G.A

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

Understand ratio concepts and use ratio reasoning to solve problems. [See: Making Flags.]
 OR.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.]
 OR.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.]
 OR.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.]
 OR.7.EE.B

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

Analyze proportional relationships and use them to solve realworld and mathematical problems. [See: Making Flags; Making Game Images.]
 OR.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.]
 OR.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.]
 OR.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.]
 OR.8.EE.B

Understand the connections between proportional relationships, lines, and linear equations. [See: Functions Can Be Linear; Defining Linear Functions.]
 OR.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.]
 OR.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.]
 OR.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.]
 OR.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.]
 OR.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.]
 OR.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.]
 OR.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.]
 OR.8.G.A.1

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

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

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

Create equations and inequalities in one variable and use them to solve problems. [See: Sam the Butterfly  Applying Inequalities.]
 OR.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.]
 OR.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.]
 OR.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.]
 OR.HSA.SSE.A.1.A

Interpret parts of an expression, such as terms, factors, and coefficients. [See: Piecewise Functions and Conditionals; Player Animation.]
 OR.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.]
 OR.HSA.SSE.A.2

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

Write expressions in equivalent forms to solve problems. [See: Order of Operations.]
 OR.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.]
 OR.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.]
 OR.HSF.BF.A.1.B

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

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

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

Understand the concept of a function and use function notation. [See: Functions Make Life Easier!; Function Notation.]
 OR.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.]
 OR.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.]
 OR.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.]
 OR.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.]
 OR.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.]
 OR.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.]
 OR.HSN.Q.A

Reason quantitatively and use units to solve problems. [See: Making Flags.]
 OR.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.]
Pennsylvania Standards
 PA.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.]
 PA.5.OA.A

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

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

Reason about and solve onevariable equations and inequalities. [See: Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 PA.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: 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; Piecewise Functions and Conditionals; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality.]
 PA.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.]
 PA.6.G.A

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

Understand ratio concepts and use ratio reasoning to solve problems. [See: Making Flags.]
 PA.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.]
 PA.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.]
 PA.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.]
 PA.7.EE.B

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

Analyze proportional relationships and use them to solve realworld and mathematical problems. [See: Making Flags; Making Game Images.]
 PA.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.]
 PA.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.]
 PA.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.]
 PA.8.EE.B

Understand the connections between proportional relationships, lines, and linear equations. [See: Functions Can Be Linear; Defining Linear Functions.]
 PA.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.]
 PA.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.]
 PA.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.]
 PA.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.]
 PA.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.]
 PA.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.]
 PA.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.]
 PA.8.G.A.1

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

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

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

Create equations and inequalities in one variable and use them to solve problems. [See: Sam the Butterfly  Applying Inequalities.]
 PA.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.]
 PA.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.]
 PA.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.]
 PA.HSA.SSE.A.1.A

Interpret parts of an expression, such as terms, factors, and coefficients. [See: Piecewise Functions and Conditionals; Player Animation.]
 PA.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.]
 PA.HSA.SSE.A.2

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

Write expressions in equivalent forms to solve problems. [See: Order of Operations.]
 PA.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.]
 PA.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.]
 PA.HSF.BF.A.1.B

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

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

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

Understand the concept of a function and use function notation. [See: Functions Make Life Easier!; Function Notation.]
 PA.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.]
 PA.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.]
 PA.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.]
 PA.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.]
 PA.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.]
 PA.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.]
 PA.HSN.Q.A

Reason quantitatively and use units to solve problems. [See: Making Flags.]
 PA.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.]
Rhode Island Standards
 RI.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.]
 RI.5.OA.A

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

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

Reason about and solve onevariable equations and inequalities. [See: Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 RI.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: 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; Piecewise Functions and Conditionals; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality.]
 RI.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.]
 RI.6.G.A

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

Understand ratio concepts and use ratio reasoning to solve problems. [See: Making Flags.]
 RI.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.]
 RI.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.]
 RI.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.]
 RI.7.EE.B

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

Analyze proportional relationships and use them to solve realworld and mathematical problems. [See: Making Flags; Making Game Images.]
 RI.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.]
 RI.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.]
 RI.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.]
 RI.8.EE.B

Understand the connections between proportional relationships, lines, and linear equations. [See: Functions Can Be Linear; Defining Linear Functions.]
 RI.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.]
 RI.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.]
 RI.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.]
 RI.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.]
 RI.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.]
 RI.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.]
 RI.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.]
 RI.8.G.A.1

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

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

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

Create equations and inequalities in one variable and use them to solve problems. [See: Sam the Butterfly  Applying Inequalities.]
 RI.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.]
 RI.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.]
 RI.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.]
 RI.HSA.SSE.A.1.A

Interpret parts of an expression, such as terms, factors, and coefficients. [See: Piecewise Functions and Conditionals; Player Animation.]
 RI.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.]
 RI.HSA.SSE.A.2

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

Write expressions in equivalent forms to solve problems. [See: Order of Operations.]
 RI.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.]
 RI.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.]
 RI.HSF.BF.A.1.B

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

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

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

Understand the concept of a function and use function notation. [See: Functions Make Life Easier!; Function Notation.]
 RI.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.]
 RI.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.]
 RI.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.]
 RI.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.]
 RI.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.]
 RI.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.]
 RI.HSN.Q.A

Reason quantitatively and use units to solve problems. [See: Making Flags.]
 RI.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.]
South Dakota Standards
 SD.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.]
 SD.5.OA.A

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

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

Reason about and solve onevariable equations and inequalities. [See: Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 SD.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: 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; Piecewise Functions and Conditionals; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality.]
 SD.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.]
 SD.6.G.A

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

Understand ratio concepts and use ratio reasoning to solve problems. [See: Making Flags.]
 SD.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.]
 SD.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.]
 SD.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.]
 SD.7.EE.B

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

Analyze proportional relationships and use them to solve realworld and mathematical problems. [See: Making Flags; Making Game Images.]
 SD.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.]
 SD.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.]
 SD.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.]
 SD.8.EE.B

Understand the connections between proportional relationships, lines, and linear equations. [See: Functions Can Be Linear; Defining Linear Functions.]
 SD.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.]
 SD.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.]
 SD.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.]
 SD.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.]
 SD.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.]
 SD.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.]
 SD.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.]
 SD.8.G.A.1

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

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

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

Create equations and inequalities in one variable and use them to solve problems. [See: Sam the Butterfly  Applying Inequalities.]
 SD.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.]
 SD.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.]
 SD.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.]
 SD.HSA.SSE.A.1.A

Interpret parts of an expression, such as terms, factors, and coefficients. [See: Piecewise Functions and Conditionals; Player Animation.]
 SD.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.]
 SD.HSA.SSE.A.2

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

Write expressions in equivalent forms to solve problems. [See: Order of Operations.]
 SD.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.]
 SD.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.]
 SD.HSF.BF.A.1.B

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

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

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

Understand the concept of a function and use function notation. [See: Functions Make Life Easier!; Function Notation.]
 SD.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.]
 SD.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.]
 SD.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.]
 SD.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.]
 SD.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.]
 SD.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.]
 SD.HSN.Q.A

Reason quantitatively and use units to solve problems. [See: Making Flags.]
 SD.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.]
Tennessee Standards
 TN.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.]
 TN.5.OA.A

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

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

Reason about and solve onevariable equations and inequalities. [See: Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 TN.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: 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; Piecewise Functions and Conditionals; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality.]
 TN.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.]
 TN.6.G.A

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

Understand ratio concepts and use ratio reasoning to solve problems. [See: Making Flags.]
 TN.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.]
 TN.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.]
 TN.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.]
 TN.7.EE.B

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

Analyze proportional relationships and use them to solve realworld and mathematical problems. [See: Making Flags; Making Game Images.]
 TN.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.]
 TN.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.]
 TN.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.]
 TN.8.EE.B

Understand the connections between proportional relationships, lines, and linear equations. [See: Functions Can Be Linear; Defining Linear Functions.]
 TN.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.]
 TN.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.]
 TN.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.]
 TN.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.]
 TN.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.]
 TN.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.]
 TN.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.]
 TN.8.G.A.1

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

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

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

Create equations and inequalities in one variable and use them to solve problems. [See: Sam the Butterfly  Applying Inequalities.]
 TN.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.]
 TN.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.]
 TN.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.]
 TN.HSA.SSE.A.1.A

Interpret parts of an expression, such as terms, factors, and coefficients. [See: Piecewise Functions and Conditionals; Player Animation.]
 TN.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.]
 TN.HSA.SSE.A.2

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

Write expressions in equivalent forms to solve problems. [See: Order of Operations.]
 TN.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.]
 TN.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.]
 TN.HSF.BF.A.1.B

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

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

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

Understand the concept of a function and use function notation. [See: Functions Make Life Easier!; Function Notation.]
 TN.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.]
 TN.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.]
 TN.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.]
 TN.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.]
 TN.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.]
 TN.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.]
 TN.HSN.Q.A

Reason quantitatively and use units to solve problems. [See: Making Flags.]
 TN.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.]
Utah Standards
 UT.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.]
 UT.5.OA.A

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

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

Reason about and solve onevariable equations and inequalities. [See: Simple Inequalities; Compound Inequalities: Solutions & NonSolutions.]
 UT.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: 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; Piecewise Functions and Conditionals; Player Animation; The Distance Formula; Collision Detection  Distance and Inequality.]
 UT.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.]
 UT.6.G.A

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

Understand ratio concepts and use ratio reasoning to solve problems. [See: Making Flags.]
 UT.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.]
 UT.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.]
 UT.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.]
 UT.7.EE.B

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

Analyze proportional relationships and use them to solve realworld and mathematical problems. [See: Making Flags; Making Game Images.]
 UT.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.]
 UT.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.]
 UT.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.]
 UT.8.EE.B

Understand the connections between proportional relationships, lines, and linear equations. [See: Functions Can Be Linear; Defining Linear Functions.]
 UT.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.]
 UT.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.]
 UT.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.]
 UT.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.]
 UT.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.]
 UT.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.]
 UT.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.]
 UT.8.G.A.1

Verify experimentally the properties of rotations, reflections, and translations. [See: