MATH 411 - FALL 1996

Sample Modeling Exercise #1 - An Assignment Problem 

You are a consultant for a Middle School (grades 6-8) which accepts
students from 11 main "feeder" Elementary Schools (along with a
small number of transfer students from other schools). The
Principal of the school has hired you to assist her in the process
of assigning new, entering 6th graders from the Elementary Schools
to the variety of 6th grade classes. At this point, she has given
you a trial contract that does not concern itself with all the
classes these students will take, but just with assigning them to
Homerooms. 

Each student is assigned to a single Homeroom. There are several
different Teams of teachers (an approach to education that involves
an integrative curriculum). Teams consist of either 3,
4 or 5 teachers per team, with each teacher having one Homeroom
class. Currently, the Principal expects there to be 2 Teams of 3
teachers each, 1 Team of 4 teachers, and 1 Team of 5 teachers,
giving a total of 15 teachers and thus 15 Homerooms. Your task is
to ensure that the students assigned to each Team represent a
complete cross-section of student scolastic ability, as well as a 
cross-section of the "feeder" schools. The Principal requests that 
you tell her how to assign students to each Homeroom to meet these
goals, and has given you lists of each student coming from each
feeder school along with their scholastic class standing in the 
Elementary School.

Assignment #1: Think about the above and do the following: 

(1) Determine for yourself whether there is sufficient information
given to attempt to solve the problem posed by the Principal. 

(2) If you believe the answer to (1) is that there is sufficient
information given, give a method you suggest to solve the problem.
Don't try to derive the exact math for this, just develop an
algorithm that you think is appropriate, and explain why it is
appropriate. Carefully write a 1-2 page report explaining your
suggestion in a clear enough manner that a Principal with little
math background would understand it. Stop. 

(3) If you believe there is not sufficient information given,
derive a set of questions to ask the Principal that will provide
sufficient information. Write these up and make up a plausible
answer the Principal might give to your questions, then proceed to
(2).

Due Monday August 26, at which point you should be ready to discuss
your results in class and defend your procedure developed in (2).