Comparing Proportional Relationships

10 min

Teacher Prep
Setup
Groups of 2. Give 2–3 minutes of quiet work time followed by a whole-class discussion.

Narrative

The purpose of this Warm-up is for students to describe a situation presented by an equation using other representations. Students decide on a context and then create a table and a graph, scaling the axes appropriately to the situation (MP2). Moving between representations of a proportional relationship here will be useful in a following activity where students compare proportional relationships represented in different ways.

Launch

Arrange students in groups of 2. Give them 2–3 minutes of quiet work time followed by a whole-class discussion.

Student Task

The equation y=4.2xy=4.2x could represent a variety of different situations.

  1. Describe a situation that can be represented by this equation. What do the quantities xx and yy represent in your situation?
  2. Create a table and a graph that represent the situation.

    Blank quadrant 1

Sample Response

  1. Sample response: A frog jumps 16.8 feet in 4 seconds, where xx represents the time in seconds and yy represents how far the frog jumps in feet.

  2. Sample response:

    Table:

    xx yy
    3 12.60
    4 16.80

    Graph:

    <p>Graph of line in quadrant 1</p>

Activity Synthesis (Teacher Notes)

Invite several students to share their situations and display their graphs for all to see. Ask:

  • “What does the rate of change represent in this situation?”
  • “How did you decide on the scale for your axes?”
Standards
Addressing
  • 8.EE.B·Understand the connections between proportional relationships, lines, and linear equations.
  • 8.EE.B·Understand the connections between proportional relationships, lines, and linear equations.

25 min