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Lesson plan

Lesson 6: Picking Representatives

teaches Common Core State Standards MP4 http://corestandards.org/Math/Practice/MP4
teaches Common Core State Standards MP3 http://corestandards.org/Math/Practice/MP3
teaches Common Core State Standards 6.RP.A.2 http://corestandards.org/Math/Content/6/RP/A/2
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 Common Core State Standards 6.RP.A.3.c http://corestandards.org/Math/Content/6/RP/A/3/c
teaches Common Core State Standards 6.NS.B.3 http://corestandards.org/Math/Content/6/NS/B/3

Lesson 6: Picking Representatives

This lesson is optional. The five activities in this third lesson on the mathematics on voting return to the situation of an election with two choices. However, rather than directly choosing the result, voters elect representatives, each of whom then casts a single vote for all the people they represent. The activities explore ways to “share” the representatives fairly between groups of people. In the first activity, numbers have been designed so that representatives (or computers) can be shared exactly proportionally between several groups. In later activities, it’s impossible to share representatives fairly; students may use division with decimal quotients or with remainders to try to find the least unfair way. The final activity asks students to gerrymander several districts: to divide it into sections in two ways to influence the final voting result in opposite ways. The mathematics here involves geometric properties of shapes on maps: area and connectedness, as well as some proportional reasoning.

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 and decision making (MP3).

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

Lesson overview

  • 6.1 Activity: Computers for Kids (10 minutes)
  • 6.2 Activity: School Mascot (Part 1) (15 minutes)
  • 6.3 Activity: Advising the School Board (30 minutes)
  • 6.4 Activity: School Mascot (Part 2) (10 minutes)
  • 6.5 Activity: Fair and Unfair Districts (30 minutes)

Learning goals:

  • Compare and contrast different ways to distribute representatives, and recognize that changing the way the votes are grouped can affect the outcome.
  • Critique (orally and in writing) whether a method for distributing representatives is fair.
  • Suggest a method for distributing representatives and justify (orally) why is it fair.

Learning goals (student facing):

  • Let's think about fair representation.

Required materials:

  • four-function calculators


  • Access the complete Grade 6 glossary. 






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.

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