Downtown Utopian High is a small, private, high school has only one mathematics teacher who teaches five classes each day. One hundred students register to take one of three mathematics courses: 51 students sign up for tenth-grade geometry, 30 for eleventh-grade algebra, and 19 for twelfth-grade calculus. The school advertises small class sizes, and all classes have previously been less than 22 students.
a. Use each of the following methods to determine a quota and apportionment (number of sections) for each math class based on a class size of 22 students.
1. Jefferson Method
2. Hamilton Method
3. Webster Method
4. Hill Method
5. Adams method
Then determine the class size under each apportionment method.
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b. Which method provides the "best" distribution of the five math classes. Justify your answer.
c. Suppose that when the semester begins, the actual "Opening Day" enrollments in the three math courses have changed to Geometry - 52, Algebra - 33, and Calculus - 15. How would this change the course distribution for each of the above methods? Would this change the method you would want to use?