Lesson 5

More than Two Choices

Lesson Narrative

This lesson is optional. It is the second of three lessons that explores the mathematics of voting. The activities in this lesson build on each other and on the previous lesson. As with all lessons in this unit, all related standards have been addressed in prior units; this lesson provides an optional opportunity to go more deeply and make connections between domains.

The five activities in this lesson deal with elections in which there are more than two choices. For example, if there are three choices, then the top vote getter might be approved by only 34% of the voters. Students explore several different rules for determining the winner: plurality, runoff, and instant runoff, and discover that the rules can give different results from the same set of voter preferences. They think about which voting rule more fairly represents the opinions of the voters. The mathematics in these activities emphasizes quantitative reasoning in a real-world situation (MP2 and MP4).

Most of the activities use students’ skills from earlier units to reason about ratios and proportional relationships (MP2) in the context of real-world problems (MP4). While some of the activities do not involve much computation, they all require serious thinking.

Most importantly, this lesson addresses topics that are important for citizens in a democracy to understand. Teachers may wish to collaborate with a civics/government teacher to learn how the fictional middle-school situations in this lesson relate to real-world elections.

Learning Goals

Teacher Facing

  • Apply reasoning about ratios and percentages to analyze (orally and in writing) voting situations involving more than two choices.
  • Choose and justify (orally) which voting system seems the fairest for dealing with more than two choices.
  • Compare and contrast (orally and in writing) different voting systems for dealing with more than two choices, i.e., plurality, runoff, and instant runoff.

Student Facing

Let's explore different ways to determine a winner.

CCSS Standards

Building On