Title
Homecoming King and Queen Elections (Dan Snook)
Goals
1. Students will utilize the math lab by searching web sites to locate this problem.
2. Students will be able to employ and defend methods to determine a group ranking.
3. Students will be introduced to the concepts of group ranking, plurality and majority winners, the Borda method, and runoff elections.
Abstract
This activity asks students to develop a fair method to determine a group ranking based on previously collected data. The activity is to be implemented prior to any formal introduction to various group ranking methods and algorithms.
Problem Statement
Students must realize that a fair method of ranking is what they are after. Their service to this committee requires them to put aside personal preferences. Issues such as the class size and the fact that all electees are seniors need to be taken into consideration.
Instructor Suggestions
1. As this will be our first discrete math activity, I will have students find the DMP homepage on the web, and then locate and print this activity. (Homecoming will coincide with our new lab being up and running.)
2. After returning to the classroom, briefly explain the task to the students. Have them complete part 1 individually.
3. Split students into groups for parts 2, 3, &4. Make sure to have members of each grade level in each group, if possible.
4. Make sure the following topics are discussed in part 4:
a) Did the grade level make up of your group influence your decision ?
b) Should the freshmen and sophomores have more clout because they are the largest classes? Or, should the juniors and seniors have more influence because they are the upperclassmen?
c) Personal opinions aside, which method is most fair?
Materials
Math Lab computers and printers, "Homecoming Election" worksheet, dry erase board
Time
Introduction of discrete math project (5 minutes), Travel time to lab/ students locating activity on web/printing copies (10 minutes), Introduction of activity (5 minutes), Individual work on activity (5 minutes), Group work on activity (10 minutes), Group reports/ discussion (20 minutes)
Mathematics Concepts
Discrete Mathematics Concepts:
Group Ranking, Plurality Winner, Majority Winner, Borda Method, Runoff Method,
Fairness, Weighted Voting
Related Mathematics Concepts:
Matrices, use of technology
NCTM Standards Addressed
Problem Solving, Communication, Reasoning, Connections, Algebra, Discrete Mathematics
Colorado Model Content Standards Addressed
Data collection and analysis (3), Problem Solving Techniques (5), Linking Concepts and Procedures (6)
Curriculum Integration
This activity could be integrated into any level of high school mathematics. It would be a good
activity to introduce the idea of discrete mathematics, and the also the use of a math computer lab.
Further Investigation
This activity could be extended by having the students choose a personal favorite as the winner. The students could then develop a method to elect their personal choice. Include a discussion of the fairness of this activity.
Variations/Comments
The use of a math lab is not necessary. (It is however available in the BVSD high schools.) The worksheets simply could be given to the students. The election results could also be generated within the classroom.
References/Resources
Colorado Model Mathematics Standards Task Force. (1995) Colorado model content standards
for mathematics.
National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for
school mathematics. Reston, VA: Author: