Ch 8: The Mathematics of Apportionment Lesson Plans

About This Chapter

The Mathematics of Apportionment chapter of this course is designed to help you plan and teach various methods for solving apportionment problems in your classroom. The video lessons, quizzes and transcripts can easily be adapted to provide your lesson plans with engaging and dynamic educational content. Make planning your course easier by using our syllabus as a guide.

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

9 Lessons in Chapter 8: The Mathematics of Apportionment Lesson Plans
Test your knowledge with a 30-question chapter practice test
The Problem of Apportionment in Politics

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.

Hamilton's Method of Apportionment in Politics

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.

The Quota Rule in Apportionment in Politics

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.

The Alabama, New States & Population Paradoxes

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.

Jefferson's Method of Apportionment in Politics

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.

Adams' Method of Apportionment in Politics

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.

Webster's Method of Apportionment in Politics

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.

Huntington-Hill Method of Apportionment in Politics

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.

Balinski & Young's Impossibility Theorem & Political Apportionment

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.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
Not Taken
Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken

Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

Support