Introducing Graphs of Proportional Relationships

5 min

Teacher Prep
Setup
3 minutes quiet work time followed by a whole-class discussion.
Required Preparation
For the digital version of the activity, acquire devices that can run the applet.

Narrative

This Warm-up prepares students for graphing proportional relationships in the coordinate plane. They practice graphing coordinate points and notice that all points lie on a straight line.

In the digital version of the activity, students use an applet to plot points on the coordinate plane. The applet allows students to add, remove, adjust, and label points. The digital version may help students graph quickly and accurately so they can focus more on the mathematical analysis.

Launch

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

Student Task

  1. Plot the points (0,10),(1,8),(2,6),(3,4),(4,2)(0,10), (1,8), (2,6), (3,4), (4,2).

    Grid with Quadrant 1. Horizontal axis, labeled x, 0 to 7, by 1's. Vertical axis, labeled y, 0 to 11, by 1's.

  2. What do you notice about the graph?

Sample Response

  1. ​ 
    <p>Scatterplot. Trend linearly downward and right.</p>
  2. Sample responses:
    • The points line up so that they could all be connected with a single line.
    • The line goes down when reading left to right.
    • Every time the xx-coordinate goes up 1, the yy-coordinate goes down 2.
Activity Synthesis (Teacher Notes)

The goal of this discussion is to review how to graph ordered pairs, (x,y)(x, y), on the coordinate plane. Invite students to share their observations about the graph. Ask if other students agree. If some students do not agree that the points lie on a straight line, ask which points break the pattern and give students a chance to self-correct their work.

MLR8 Discussion Supports. Revoice student ideas to demonstrate and amplify mathematical language use. For example, revoice the student statement “The points are straight” as ”The points line up on the coordinate plane so that they could all be connected with a single line.”
Advances: Representing
Anticipated Misconceptions
Some students may reverse the xx- and yy-coordinates when plotting points, such as plotting (10,0)(10, 0) and (8,1)(8, 1) instead of (0,10)(0, 10) and (1,8)(1, 8). Direct their attention to the xx and yy labels in the image and clarify that an ordered pair is written (x,y)(x, y).
Standards
Building On
  • 5.G.A·Graph points on the coordinate plane to solve real-world and mathematical problems.
  • 5.G.A·Graph points on the coordinate plane to solve real-world and mathematical problems.
Building Toward
  • 7.RP.2.a·Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
  • 7.RP.A.2.a·Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

10 min

25 min