Alignments

Describe the difference between digital artifacts that are open or free and those that are protected by copyright. [See: Making Game Images.]

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., x-axis and x-coordinate, y-axis and y-coordinate). [See: Coordinates and Game Design.]

Write and interpret numerical expressions. [See: Order of Operations.]

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

Explain how copyright law and licensing protect the owner of intellectual property. [See: Making Game Images.]

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 & Non-Solutions; Sam the Butterfly - Applying Inequalities.]

Design solutions that use repetition and conditionals. [See: Piecewise Functions and Conditionals; Player Animation.]

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 & Non-Solutions; Sam the Butterfly - Applying Inequalities.]

Individually and collaboratively decompose a problem and create a sub-solution for each of its parts (e.g., video game, robot obstacle course, making dinner). [See: Problem Decomposition; Collision Detection - Distance and Inequality.]

Recognize that boundaries need to be taken into account for an algorithm to produce correct results. [See: Sam the Butterfly - Applying Inequalities.]

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 & Non-Solutions; Sam the Butterfly - Applying Inequalities.]

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.]

Trace programs step-by-step 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 & Non-Solutions; Sam the Butterfly - Applying Inequalities.]

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.]

Reason about and solve one-variable equations and inequalities. [See: Simple Inequalities; Compound Inequalities: Solutions & Non-Solutions.]

Use variables to represent numbers and write expressions when solving a real-world 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; 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.]

Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world 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.]

Solve real-world and mathematical problems involving area, surface area, and volume. [See: Surface Area of a Rectangular Prism.]

Represent three-dimensional 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 real-world and mathematical problems. [See: Surface Area of a Rectangular Prism.]

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

Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. [See: Making Flags.]

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

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.]

Solve real-life 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.]

Use variables to represent quantities in a real-world 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 & Non-Solutions.]

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.]

Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. [See: Solving Word Problems with the Design Recipe; Surface Area of a Rectangular Prism.]

Analyze proportional relationships and use them to solve real-world and mathematical problems. [See: Making Flags; Making Game Images.]

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.]

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.]

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

Understand the connections between proportional relationships, lines, and linear equations. [See: Functions Can Be Linear.]

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.]

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.]

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.]

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.]

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

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.]

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.]

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

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

Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. [See: The Distance Formula.]

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

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.]

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 & Non-Solutions; Sam the Butterfly - Applying Inequalities.]

Use an iterative design process, including learning from making mistakes, to gain a better understanding of the problem domain. [See: Making Flags.]

Demonstrate how to document a program so that others can understand its design and implementation. [See: Solving Word Problems with the Design Recipe.]

Use appropriate conditional structures in programs (e.g., IF-THEN, IF-THEN-ELSE, SWITCH). [See: Piecewise Functions and Conditionals; Player Animation.]

Use a programming language or tool feature correctly to enforce operator precedence. [See: Order of Operations.]

Use global and local scope appropriately in program design (e.g., for variables). [See: Making Flags.]

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.]

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

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.]

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.]

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.]

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

Interpret complicated expressions by viewing one or more of their parts as a single entity. [See: Piecewise Functions and Conditionals; Player Animation.]

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

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

Build a function that models a relationship between two quantities. [See: Function Notation; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & Non-Solutions.]

Write a function that describes a relationship between two quantities. [See: Function Notation; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & Non-Solutions.]

Combine standard function types using arithmetic operations. [See: Function Composition.]

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

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

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

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.]

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; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & Non-Solutions.]

Interpret functions that arise in applications in terms of the context. [See: Function Notation; Solving Word Problems with the Design Recipe; Functions for Character Animation; Problem Decomposition; Simple Inequalities; Compound Inequalities: Solutions & Non-Solutions.]

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

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

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; Problem Decomposition.]

Reason quantitatively and use units to solve problems. [See: Making Flags.]

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 & Non-Solutions.]