*The materials on this page are two lessons that we developed as part of our design work. These lessons were part of a sequence of 10 lessons focused on developing the idea of slope as a rate of change, and culminating in generalizations to writing a linear equation to model motion. The lesson “Measuring Fastness” was from the start of the unit. The lesson “Emma’s Average Rate” was from the end of the unit. For background on our design principles click here*.

## Measuring Fastness

This is an introductory lesson. The main goal is to get students to focus on the relevant quantities that are used to measure “fastness.” Since this is an introductory lesson, the CCSSM alignment is in 6th grade. Nonetheless, this lesson is worth doing even in 9th grade because many students struggle with focusing on the relevant quantities when modeling situations involving speed. By the end of the lesson the goal is that students will focus on both distance and time when talking about speed.

## Emma’s Average Rate

The main goal with this lesson is for students to develop understanding of average rate of change using a distance-time piecewise linear graph to motivate the calculation. The Desmos activity shows two characters, Emma who walks at a non-constant rate and “Average Emma” who always starts and ends in the same place and time as Emma, but who moves at a constant rate.