Apportionment
Common Core Standards and Mathematical Practices
This module covers the following common core standards and math practices.
7th Grade: Number Systems
7.NS.A.2.a Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.
7.NS.A.3 Solve real-world and mathematical problems involving the four operations with integers and other rational numbers.
7th Grade: Expressions and Equations
7.EE.B.3: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically.
8th Grade: Functions
8.F.A.1: Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.
Mathematical Practices
MP.2 Reason abstractly and quantitatively.
MP.3 Construct viable arguments and critique the reasoning of others.
MP.4 Modeling with Mathematics
Learning Objectives
This lesson aims to give each student a clear understanding of apportionment. The lesson pressented will primarily focus on how seats in the House of Representatives are allocated, but apportionment can be used any time where subsets of people need to elect some of their members to represent them. Throughout U.S. history, various methods have been used and this lesson will explain each of them.
Introduction
In general, apportionment means distribution in proper shares. Apportionment issues occur anytime where subsets of people need to elect some of their members to represent them. For example, it can occur in companies, organizations, and in government. In this module, we will be focusing on congressional apportionment or apportionment in government.
In the U.S. government, apportionment is the process of distributing seats to each state in the House of Representatives. There are 435 seats in the House, and the number of representatives each state receives is supposed to be proportional to its population. The current number of seats (435) was permanently set in 1940. Every ten years, seats are reapportioned to each state according to the population reported in the Census.
For example, if a state's population is 5% of the entire population of the United States, then the state should hold 5% of the seats in the House. The problem is that this might not be a whole number, but the number of representatives assigned to a state must of course be a whole number. At first, this doesn't seem to be a problem since we can simply round to the nearest whole number. However, the rounding is a bigger problem than it seems, as we will see in this lesson.
Mariela Duran - Grace Jackson - Hannah Quiroz