# Lesson 14

Four Representations

### Lesson Narrative

In this lesson, students examine tables, equations, and graphs of proportional relationships, and use them to reason about relationships that are proportional as well as relationships that are not proportional.

This lesson requires students to use everything they have learned since the beginning of the unit. This unit is meant to help students understand:

• What is a proportional relationship?
• What kinds of situations can be represented by proportional relationships?
• What form does an equation of a proportional relationship have?
• What do graphs of proportional relationships look like?

The next lesson in this unit is intended as a bridge to Unit 7.4 which is about applications of proportional relationships. It gives an example of how proportional relationships, and the derived units they give rise to, help to solve problems about the real world.

### Learning Goals

Teacher Facing

• Calculate the constant of proportionality for a proportional relationship in an unfamiliar context, and express it (in writing) using the correct units.
• Critique (orally and in writing) presentations of proportional and nonproportional relationships.
• Invent and describe (in writing and using other representations) a proportional relationship and a nonproportional relationship.

### Student Facing

Let’s contrast relationships that are and are not proportional in four different ways.

### Required Preparation

Students are asked to make displays of their work in groups of 2. Prepare materials for creating a visual display in this way such as markers, chart paper, board space, etc.

### Student Facing

• I can make connections between the graphs, tables, and equations of a proportional relationship.
• I can use units to help me understand information about proportional relationships.

Building On