Module 19: Patterns & Generalizations

Investigate visual and numerical patterns, identify how they grow or repeat, and develop increasingly general ways to describe their structure.

Geometric Patterns - Explore patterns created with shapes and visual arrangements and describe how their structure changes from one stage to the next.

Number Patterns - Identify relationships within sequences of numbers and use those relationships to predict and extend patterns.

Finding Rules in Repetition - Analyze repeating patterns to identify the underlying rule that determines how the pattern continues.

Recursive vs. Explicit Patterns - Compare rules that describe a term using previous terms with rules that determine any term directly from its position.

Generalizing a Pattern with Variables - Use variables and expressions to describe a pattern in a way that applies to any stage or term.

Module 20: Introduction to Functions

Develop the idea of a function as a relationship between quantities and connect function rules to tables, graphs, and other representations.

Inputs, Outputs, & Rules - Understand functions as rules that connect allowable input values to corresponding output values.

Function Tables - Organize input-output relationships in tables and use patterns in the values to understand or identify a function rule.

Graphing Functions - Represent functions on coordinate graphs to visualize how one quantity changes in relation to another.

Multiple Representations of Functions - Connect verbal descriptions, rules, tables, graphs, and other representations of the same functional relationship.

Module 21: Linear & Nonlinear Relationships

Compare different types of functional relationships by examining patterns of change, graphical behavior, and the distinction between constant and changing rates.

Linear Functions - Explore relationships with a constant rate of change and connect their tables, graphs, equations, and real-world meanings.

Other Functions - Examine examples of nonlinear relationships and compare their behavior with familiar linear patterns.

Constant vs. Changing Rate of Change - Determine whether a relationship changes at a constant rate or whether its rate itself varies.

Comparing Linear & Nonlinear Patterns - Use tables, graphs, equations, and patterns to distinguish linear relationships from nonlinear ones.

Module 22: Mathematical Structure & Problem Solving

Strengthen mathematical problem solving by looking for structure, making conjectures, describing relationships precisely, and clearly explaining the reasoning behind a solution.

Geometric Problems - Apply geometric ideas and relationships to solve problems that require visualization, reasoning, and connecting multiple concepts.

Describing Geometry - Use precise mathematical language, properties, and relationships to communicate geometric reasoning clearly.

Looking for Structure - Identify useful patterns, properties, and relationships within a problem that can make unfamiliar mathematics easier to understand.

Making and Testing Conjectures - Form mathematical predictions from observed patterns and test them using examples, counterexamples, and logical reasoning.

Explaining Mathematical Reasoning - Communicate not only an answer but also the mathematical evidence and reasoning that show why the answer makes sense.