More than Two Choices

5 min

Teacher Prep
Setup
Quiet work time followed by whole-class discussion.

Narrative

This is the first of 6 activities about elections in which there are more than two choices. This introductory activity gets students thinking about the fairness of a voting rule. If the choice with the most votes wins, it’s possible that the winning choice was preferred by only a small percentage of the voters.

Launch

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

Student Task

Students in a sixth-grade class were asked, “What activity would you most like to do for field day?” The results are shown in the table.

activity number of votes
softball game 16
scavenger hunt 10
dancing talent show 8
marshmallow throw 4
no preference 2
  1. What percentage of the class voted for softball?

  2. What percentage did not vote for softball as their first choice?

Sample Response

  1. 40% voted for softball since 1640=25=40%\frac{16}{40}=\frac25=40\%.
  2. 60% did not vote for softball as their first choice.
Activity Synthesis (Teacher Notes)

The goal of this discussion is to show that in elections with more than two options sometimes the winning choice is not the majority’s choice. Here are some questions for discussion:

  • Which activity has the most votes? (softball)
  • Does softball have a majority of the votes? (No, a majority would be more than 50%, but softball only has 40%.)
  • If the class can do only one activity for field day, explain why they should or should not do softball. (They should do softball because more people voted for it than any other activity. They should not do softball because most people did not pick softball.)

Tell students that this system of voting, where everyone gets one vote and the option with the most votes wins, is called plurality voting. Explain that, while 60% of the people did not vote for softball, that does not mean those people were against softball, just that they liked a different option more. In the upcoming activities, students will see other ways of voting, including some that can take this situation into account.

Standards
Addressing
  • 6.RP.3·Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
  • 6.RP.A.3·Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

20 min

20 min