Standards

Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. [See: Simple Inequalities.]

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 Functions; Solving Word Problems; Functions for Character Animation; Surface Area of a Rectangular Prism; Problem Decomposition; Sam the Butterfly - Applying Inequalities; Piecewise Functions; 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.]

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.]

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; Problem Decomposition; Sam the Butterfly - Applying Inequalities; Piecewise Functions; 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; Defining Functions; Solving Word Problems; Simple Inequalities; Compound Inequalities: Solutions & Non-Solutions.]

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: Surface Area of a Rectangular Prism.]

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. [See: Making Game Images.]

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.]

Use functions to model relationships between quantities. [See: Defining Functions; Solving Word Problems; Restating the Problem; Functions for Character Animation.]

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.]

Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. [See: Defining Functions.]

Create equations and inequalities in one variable and use them to solve problems. [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; Defining Functions.]

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

Interpret complicated expressions by viewing one or more of their parts as a single entity. [See: Piecewise Functions; 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 Composition; Problem Decomposition.]

Write a function that describes a relationship between two quantities. [See: Defining Functions; Restating the Problem; Problem Decomposition; Collision Detection - Distance and Inequality.]

Compose functions. [See: Function Composition; Problem Decomposition; Sam the Butterfly - Applying Inequalities.]

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: Defining Functions.]

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.]

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; Defining Functions; Solving Word Problems; Simple Inequalities; Compound Inequalities: Solutions & Non-Solutions.]

Interpret functions that arise in applications in terms of the context. [See: Making Flags; Defining Functions.]

Analyze functions using different representations. [See: Defining Functions.]

Interpret expressions for functions in terms of the situation they model. [See: Functions for Character Animation.]

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 ( [See: Compound Inequalities: Solutions & Non-Solutions.]

Make sense of problems and persevere in solving them [See: Order of Operations; Function Composition; Restating the Problem; Problem Decomposition; Simple Inequalities.]

Reason abstractly and quantitatively [See: Coordinates and Game Design; Order of Operations; Defining Values; Functions for Character Animation; The Distance Formula.]

Construct viable arguments and critique the reasoning of others [See: Order of Operations; Problem Decomposition; The Distance Formula; Collision Detection - Distance and Inequality.]

Model with mathematics [See: Order of Operations; Defining Functions; Solving Word Problems; Functions for Character Animation; Surface Area of a Rectangular Prism; Problem Decomposition; Simple Inequalities; Sam the Butterfly - Applying Inequalities; Player Animation.]

Use appropriate tools strategically [See: Function Composition.]

Attend to precision [See: Making Game Images; Problem Decomposition.]

Look for and make use of structure [See: Defining Values; Restating the Problem.]

Look for and express regularity in repeated reasoning [See: Piecewise Functions.]