# Lesson 2

Graphs of Proportional Relationships

### Lesson Narrative

The purpose of this lesson is for students to understand that there are many successful ways to set up and scale axes in order to graph a proportional relationship. Sometimes, however, we choose specific ranges for the axes in order to see specific information.

In the first activity, students sort graphs on cards based on what proportional relationship they represent. Each graph has a different scale, and some scales are purposefully quite different so students cannot use “looks like” as a way to tell the difference between the relationships. This activity presses the need for paying attention to scale and relying on mathematical definitions of steepness and not just visual ones.

In the second activity, students graph a proportional relationship representing water filling a tank on two differently scaled axes. Then they compare their graph to a graph of a non-proportional relationship and answer questions about the situation. By looking at the same two relationships graphed at different scales, students see how much effect the scale of the axes has on the information we can figure out.

### Learning Goals

Teacher Facing

• Compare graphs that represent the same proportional relationship using differently scaled axes.
• Create graphs representing the same proportional relationship using differently scaled axes, and identify which graph to use to answer specific questions.

### Required Preparation

For Card Sort: Proportional Relationships, prepare 1 copy of the blackline master for every 2 students and cut them up ahead of time. Provide access to straightedges.

### Student Facing

• I can graph a proportional relationship from an equation.
• I can tell when two graphs are of the same proportional relationship even if the scales are different.

Building On