Standards

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.]

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: Domain and Range.]

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

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

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.]

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.]

Write a function that describes a relationship between two quantities. [See: Restating the Problem; Problem Decomposition; Collision Detection.]

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: Domain and Range.]

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. [See: Solving Word Problems; Simple Inequalities; Compound Inequalities.]

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

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

Reason abstractly and quantitatively [See: The Numbers Inside Video Games; Coordinates and Game Design; Order of Operations; Defining Values; Character Animation; The Distance Formula.]

Model with mathematics [See: Simple Inequalities.]

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.]