Ch 8: The Mathematics of Apportionment Lesson Plans
About This Chapter
Weekly Syllabus
Below is a sample breakdown of the Mathematics of Apportionment chapter into a 5-day school week. Based on the pace of your course, you may need to adapt the lesson plan to fit your needs.
| Day | Topics | Key Terms and Concepts Covered |
|---|---|---|
| Monday | The apportionment problem and quota rule | Apportionment problem in politics, population, seats, standard divisor and quota, quota rule and upper and lower quota |
| Tuesday | Hamilton's apportionment method and the related paradoxes | Hamilton method of apportionment, population Paradox, New State Paradox and Alabama Paradox |
| Wednesday | Jefferson's and Adams' apportionment methods | Steps in Jefferson's and Adams' method of apportionment, modified divisor, modified quota and modified lower quota |
| Thursday | The Webster and Huntington-Hill apportionment methods | Using Webster's apportionment method to solve problems, steps in the Huntington-Hill apportionment approach and geometric mean |
| Friday | Balinski and Young's impossibility theorem | The impossibility theorem from Young and Balinski and the principal apportionment fairness measures |
1. The Problem of Apportionment in Politics
This lesson discusses the problem of apportionment. It deals with how to fairly give each state its portion of representation in the government. Terms will be defined and an example will be used to illustrate the problem.
2. Hamilton's Method of Apportionment in Politics
There are many different methods used to assign House of Representative voting seats to each state. In this lesson, we will explore Hamilton's Method of Apportionment.
3. The Quota Rule in Apportionment in Politics
The quota rule refers to the strict use of calculated quotas in apportionment. If a method of apportionment allows a state to have more (or fewer) seats than its quotas determine, then the method is said to be in violation of the quota rule.
4. The Alabama, New States & Population Paradoxes
A paradox is a logical procedure that results in illogical outcomes. This lesson will review three paradoxes that are associated with population-based apportionment.
5. Jefferson's Method of Apportionment in Politics
The Jefferson Method of Apportionment is just one of many different methods of apportionment. In this lesson, we will review the Jefferson Method using examples to solidify the concepts.
6. Adams' Method of Apportionment in Politics
In the 1830s, John Quincy Adams believed that the method of apportionment being used by Congress was biased. In this lesson, we review his method of apportionment.
7. Webster's Method of Apportionment in Politics
Daniel Webster proposed his method of apportionment in the 1830s. It was adopted and used by the House of Representatives for many years. This lesson reviews his method.
8. Huntington-Hill Method of Apportionment in Politics
The Huntington-Hill Method of Apportionment is the currently used method to assign each state its number of representative voting seats in the House of Representatives. This lesson reviews how to calculate this method.
9. Balinski & Young's Impossibility Theorem & Political Apportionment
The Balinski & Young Impossibility Theorem points out that there is no apportionment method that allows for the Quota Rule and does not allow any paradoxes to occur. This lesson investigates that statement.
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Other Chapters
Other chapters within the Contemporary Math Syllabus Resource & Lesson Plans course
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- Probability Overview Lesson Plans
- Discrete Probability Distributions Lesson Plans
- Continuous Probability Distributions Lesson Plans
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