2. Apportionment Apportionment means distribution or allotment in proper shares. (related to “Fair Division”)

3. In the context of the Constitution, apportionment means that each state gets a number appropriate to its population. For example, Representatives are apportioned among the states, with the most populous getting the greater share.

4. Two terms that need to be understood: Standard Divisor (what you divide by) Standard Quota (the result of your division)

5. Standard Divisor The Standard Divisor determines the number of people needed to get one seat in Congress Standard Divisor = Total Population # of seats

6. Standard Quota The Standard Quota determines the number of seats a particular group deserves Standard Quota = population of subgroup standard divisor

7. Example 1440 students at CHS and 30 seats in the student senate 1440/30 = 48 needed to get a seat (Standard Divisor) Senior class has 328 students 328/48 = 6.83 seats for Seniors in the student senate (Standard Quota) 6.83 Seats = 6.83 Seniors???

8. The Apportionment Problem How do we turn the fractions into whole people?

9. Lower & Upper Quotas The standard quota numbers need to be rounded to a whole number. The Lower Quota is the standard quota rounded down to the nearest whole number The Upper Quota is the standard quota rounded up to the nearest whole number

10. There have been four different apportionment methods over the history of this country. Today we will learn about the simplest method…

11. Hamilton’s Method This was Alexander Hamilton’s attempt to deal with the Apportionment Problem There are 3 steps to Hamilton’s Method: 1) Calculate each group’s standard quota 2) Round each standard quota down (lower quota), and give each group that number 3) Give the surplus items one at a time to the groups with the largest decimal parts

12. For Example… CHS = 1440 students with 30 seats in student senate Number of students in each grade: Seniors = 328 Juniors = 346 Sophomores = 351 Freshmen = 415

13. Hamilton’s Method There are 3 steps to Hamilton’s Method: 1) Calculate each group’s standard quota Standard divisor = 1440/30 = 48 students per seat Standard quotas : Seniors = 328/48 =6.83 Juniors = 346/48 =7.21 Sophomores = 351/48 = 7.31 Freshmen = 415/48 = 8.65

14. Hamilton’s Method There are 3 steps to Hamilton’s Method: 2) Round each standard quota down (lower quota), and give each group that number of seats Standard quotas (adjusted) : Seniors = 328/48 =6.83 becomes 6 Juniors = 346/48 =7.21 becomes 7 Sophomores = 351/48 = 7.31 becomes 7 Freshmen = 415/48 = 8.65 becomes 8

15. Hamilton’s Method There are 3 steps to Hamilton’s Method: 3) Give the surplus items one at a time to the groups with the largest decimal parts Standard quotas (adjusted) : Seniors = 328/48 =6.83 becomes 6Only 28 seats have Juniors = 346/48 =7.21 becomes 7been used… Sophomores = 351/48 = 7.31 becomes 7 Freshmen = 415/48 = 8.65 becomes 8

16. Hamilton’s Method There are 3 steps to Hamilton’s Method: 3) Give the surplus items one at a time to the groups with the largest decimal parts Standard quotas (adjusted) : Seniors = 328/48 =6. 83 becomes 7 (gets an additional seat) Juniors = 346/48 =7.21 becomes 7 Sophomores = 351/48 = 7.31 becomes 7 Freshmen = 415/48 = 8. 65 becomes 9 (gets an additional seat)

17. Hamilton’s Method There are 3 steps to Hamilton’s Method: 3) Give the surplus items one at a time to the groups with the largest decimal parts Standard quotas (adjusted) : Final Apportionment: Seniors = 328/48 =6.83 became 7Seniors have 7 seats Juniors = 346/48 =7.21 remained 7Juniors have 7 seats Sophomores = 351/48 = 7.31 remained 7Sophomores have 7 seats Freshmen = 415/48 = 8.65 became 9Freshmen have 9 seats

18. Homework, Homework, Homework; I know you love your homework… P. 760-761; #1-5