Lesson plan

Lesson 5: More than Two Choices

teaches Common Core State Standards MP4 http://corestandards.org/Math/Practice/MP4
teaches Common Core State Standards 6.RP.A.3 http://corestandards.org/Math/Content/6/RP/A/3
teaches Common Core State Standards MP2 http://corestandards.org/Math/Practice/MP2
teaches New York State Standards NY-6.RP.3.

Lesson 5: More than Two Choices

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.

Lesson overview

  • 5.1 Optional Activity: Field Day (5 minutes)
  • 5.2 Optional Activity: School Lunches (Part 1) (30 minutes)
  • 5.3 Optional Activity: School Lunch (Part 2) (20 minutes)
  • 5.4 Optional Activity: Just Vote Once (30 minutes)
    • Includes "Are you Ready for More?" extension problem
  • 5.5 Optional Activity: Weekend Choices (10 minutes)

Learning goals:

  • 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.

Learning goals (student facing):

  • Let's explore different ways to determine a winner.


  • Access the complete Grade 6 glossary. 


  • This lesson builds on the standard:CCSS.6.RP.A.3MS.6.RP.3






IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 2017-2019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/math-curriculum/.

Adaptations and updates to IM 6–8 Math are copyright 2019 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

Adaptations to add additional English language learner supports are copyright 2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

The Illustrative Mathematics name and logo are not subject to the Creative Commons license and may not be used without the prior and express written consent of Illustrative Mathematics.

This site includes public domain images or openly licensed images that are copyrighted by their respective owners. Openly licensed images remain under the terms of their respective licenses.