Ch 8: The Mathematics of Apportionment: Help and Review

About This Chapter

The Mathematics of Apportionment chapter of this Contemporary Math: Help & Review course is the simplest way to master the math of apportionment. This chapter uses simple and fun videos that are about five minutes long, plus lesson quizzes and a chapter exam to ensure you learn the essentials of apportionment in math.

Who's It For?

Anyone who needs help learning or mastering apportionment math material will benefit from the lessons in this chapter. There is no faster or easier way to learn mathematics of apportionment. Among those who would benefit are:

  • Students who have fallen behind in understanding working with apportionment in math
  • Students who struggle with learning disabilities or learning differences, including autism and ADHD
  • Students who prefer multiple ways of learning math (visual or auditory)
  • Students who have missed class time and need to catch up
  • Students who need an efficient way to learn about apportionment mathematics
  • Students who struggle to understand their teachers
  • Students who attend schools without extra math learning resources

How It Works:

  • Find videos in our course that cover what you need to learn or review.
  • Press play and watch the video lesson.
  • Refer to the video transcripts to reinforce your learning.
  • Test your understanding of each lesson with short quizzes.
  • Verify you're ready by completing the mathematics of apportionment chapter exam.

Why It Works:

  • Study Efficiently: Skip what you know, review what you don't.
  • Retain What You Learn: Engaging animations and real-life examples make topics easy to grasp.
  • Be Ready on Test Day: Use the math of apportionment chapter exam to be prepared.
  • Get Extra Support: Ask our subject-matter experts any math question. They're here to help!
  • Study With Flexibility: Watch videos on any web-ready device.

Students Will Review:

This chapter helps students review the concepts in an apportionment unit of a standard contemporary math course. Topics covered include:

  • Apportionment in politics, such as upper and lower quotas
  • Hamilton's, Jefferson's, Adams', Webster's and Huntington-Hill's methods to solve apportionment problems
  • The quota rule
  • How Hamilton's method applies to the Alabama, New States and Population paradoxes
  • Balanski and Young's impossibility theorem

9 Lessons in Chapter 8: The Mathematics of Apportionment: Help and Review
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

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