MA19.FM.27

Mathematics (2019) Grade(s): 09-12 - Applications of Finite Mathematics

MA19.FM.27
Identify and apply historic methods of apportionment for voting districts including Hamilton, Jefferson, Adams, Webster, and Huntington-Hill. Identify issues of fairness and paradoxes that may result from methods.

Unpacked Content

Knowledge

Students know:

Apportionment is a method of dividing based on population.

Skills

Students are able to:

Calculate an ideal ratio for diving objects based on populations.
Use the ideal ratio to determine exact district quotas and apply a variety of apportionment methods to determine apportionment of discrete objects such as representative seats.
Use a variety of apportionment methods to adjust the divisor and calculate subsequent quotas.
Identify specific examples of paradoxes or violation of the quota rule.

Understanding

Students understand that:

Some methods result in unfair paradoxes and may favor larger or smaller districts.
Apportionment methods are used to divide discrete objects when they cannot be divided exactly proportional to the populations.

Vocabulary

Ideal ratio
Quota
Hamilton method
Jefferson method
Adams method
Arithmetic mean
Geometric mean
Webster method
Huntington-Hill method
Population paradox
Alabama paradox
Quota rule

COS Examples

Examples: the Alabama paradox, population paradox

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