Rate of change is a fundamental concept when working with functions. Too often it is presented by writing y = mx + b on the board, with m—the rate of change—being defined as the slope. This lesson focuses students on function tables, looking for patterns and making observations. From there, we connect what students see to how the things they observe appear in function rules, and we introduce the vocabulary of “rate of change” and “starting amount,” which can later be referred to as “slope” and “y-intercept.” Before we talk about slope and y-intercept though, we want students to have a flexible understanding of how to identify rate of change and starting amount in tables, rules, and graphs, and to know how they can use these concepts in solving problems.

This unit offers detailed lesson plans, student handouts and supplemental materials for building a deep conceptual understanding of rate of change and starting amount in functions.

Unit Goals:

• Students will discover the relationship between rate of change, starting amount, and function rules.
• Students will use rate of change and starting amount to determine function rules from tables.
• Students will determine rate of change, starting amount, domain, range and function rules for contextualized problems.

Additional HSE-style problems for the concepts explored in this unit can be found here.