#### Consortium for Mathematics and its Applications

Product ID: 5608
Supplementary Print
High School

# The Apportionment Problem: The Search for the Perfect Democracy (HiMAP)

### Author: Sandi Bennett; Duane DeTemple; Michael Dirks; Bob Newell; Jack M. Robertson; Bob Tyus

A look at the apportionment of the House of Representatives, and how many representatives from each state are sent to Congress. HiMAP Module 8.

HiMAP library now available on CD-ROM product no. 7593

PART I: THE HAMILTON METHOD OF APPORTIONMENT

Introduction
Apportioning the Student Council (Activity)
The Goal of Apportionment
Quota
Finding Quota (Activity)
Hamilton Method of Apportionment
Finding Hamilton Apportionments (Activity)
An Unexpected Problem!
Another Problem! (Activity)
Yet Another Problem! (Activity)
The Hamilton Method - Summary
Exercises

PART II: DIVISOR METHODS OF APPORTIONMENT
Rounding Off Fractional Parts of Quota
Rounding Off Quota (Activity)
Webster Method of Apportionment
Visualizing Webster's Method
A Webster Apportionment (Activity)
Another Webster Apportionment and Another Flaw (Activity)
Satisfying Quota
Other Divisor Methods
A Jefferson Apportionment (Activity)
The Hill Method of Apportionment
A Hill Apportionment (Activity)
Divisor Methods - Summary
The Apportionment Impossibility Theorem
Exercises

HiMAP
73 pages

#### Mathematics Topics:

• Discrete & Finite Mathematics

#### Application Areas:

• Social Studies ,
• Political Science, Voting Theory

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COMAP develops curriculum resources, professional development programs, and contest opportunities that are multidisciplinary, academically rigorous, and fun for educators and students. COMAP's educational philosophy is centered around mathematical modeling: using mathematical tools to explore real-world problems.

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