# Lesson 10

Rate of Change

These materials, when encountered before Algebra 1, Unit 5, Lesson 10 support success in that lesson.

### Lesson Narrative

The purpose of this lesson is to review finding the constant rate of change of a linear relationship represented with a graph. It connects to concepts learned in grade 8, such as rate of change and slope. The work is scaffolded and additionally gives students an opportunity to revisit interpreting function notation. In the associated Algebra 1 lesson, students apply the idea of average rate of change to exponential functions. In each activity, students are asked to interpret function notation and graphs in terms of the context they represent, giving them an opportunity to reason abstractly and quantitatively (MP2). When students interpret \(\dfrac{b(7)-b(4)}{7-4}\) and see \(b(7)-b(4)\) as an object that has a value, they have an opportunity to notice and make use of structure (MP7).

### Learning Goals

Teacher Facing

- Calculate the rate of change of a linear function given its graph.
- Interpret the meaning of statements written using function notation when a function is represented by a graph.
- Recognize that the rate of change of the linear relationship is the same value as the slope of the graph of the relationship.

### Student Facing

- Let’s calculate the rate of change of some relationships.