# Lesson 5

Connections between Representations

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

### Lesson Narrative

The mathematical purpose of this lesson is for students to recall how verbal descriptions, tables, graphs, and equations are different representations of the same relationship. They connect an equation to a graph or table of values in the context of linear relationships. They interpret a graph to answer questions about a context. They focus on the meaning of the numbers \(m\) and \(b\) in a linear equation of the form \(y=b+mx\). Then, to preview the work in the Algebra 1 lesson, they encounter a model characterized by exponential decay. This lesson parallels the work in the associated Algebra 1 lesson, except students are revisiting linear relationships here, and will encounter exponential relationships there. When students explain how a graph or expression representing a model relates to the situation it represents, they are contextualizing the representation (MP2).

### Learning Goals

Teacher Facing

- Interpret equations and graphs that represent linear relationships

### Student Facing

- Let’s look at the relationship of verbal descriptions, equations, tables, and graphs.