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Math 132: Foundations of Mathematics

Math 132: Foundations of Mathematics. Amy Lewis Math Specialist IU1 Center for STEM Education. 14.3 Apportionment Methods. Find standard divisors and standard quotas. Understand the apportionment problem. Use Hamilton’s, Jefferson’s, Adam’s, and Webster’s methods. Apportionment.

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Math 132: Foundations of Mathematics

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  1. Math 132:Foundations of Mathematics Amy Lewis Math Specialist IU1 Center for STEM Education Math 132: Foundations of Mathematics

  2. 14.3 Apportionment Methods • Find standard divisors and standard quotas. • Understand the apportionment problem. • Use Hamilton’s, Jefferson’s, Adam’s, and Webster’s methods. Math 132: Foundations of Mathematics

  3. Apportionment • Why do we have 2 houses in Congress? • How many members of the House of Representatives are there? • How do we decide how many representatives each state gets? Math 132: Foundations of Mathematics

  4. Sampling & Populations If Margaritaville has 30 seats in the Congress, how many seats should each state get? Math 132: Foundations of Mathematics

  5. Allocating Seats • Standard Divisor • The quotient of the total population under consideration and the number of items to be allocated. • What is the standard divisor for Margaritaville? • What does the standard divisor mean? Math 132: Foundations of Mathematics

  6. Allocating Seats • Standard Quota • The quotient of the group’s population and the standard divisor. • What is the standard divisor for each state in Margaritaville? Math 132: Foundations of Mathematics

  7. Sampling & Populations So, what’s the problem? Math 132: Foundations of Mathematics

  8. Sampling & Populations Math 132: Foundations of Mathematics

  9. Hamilton’s Method • Calculate each group’s standard quota. • Round each standard quota down to the nearest whole number (the lower quota). Initially, give each group its lower quota. • Give the surplus items, one at a time, to the groups with the largest decimal parts until there are no more surplus items. Math 132: Foundations of Mathematics

  10. Other Methods • Jefferson’s Method • Adam’s Method • Webster’s Method Math 132: Foundations of Mathematics

  11. Jefferson’s Method • Find a modified divisor, d, such that when each group’s modified quota is rounded down to the nearest whole number, the sum of the whole numbers for all the groups is the number of items to be apportioned. The modified quotients that are rounded down are called modified lower quotas. • Apportion to each group its modified lower quota. Math 132: Foundations of Mathematics

  12. Adam’s Method • Find a modified divisor, d, such that when each group’s modified quota is rounded up to the nearest whole number, the sum of the whole numbers for all the groups is the number of items to be apportioned. The modified quotients that are rounded up are called modified lower quotas. • Apportion to each group its modified upper quota. Math 132: Foundations of Mathematics

  13. Webster’s Method • Find a modified divisor, d, such that when each group’s modified quota is rounded to the nearest whole number, the sum of the whole numbers for all the groups is the number of items to be apportioned. The modified quotients that are rounded are called modified rounded quotas. • Apportion to each group its modified rounded quota. Math 132: Foundations of Mathematics

  14. No Homework! Next Session: Thursday, May 27 Last Class: Friday, May 28th!!! Math 132: Foundations of Mathematics

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