Title
Jill and John's Place (Jill Long)
Goals
1) Students will begin to explore the concept of group ranking as it relates to election theory.
2) Students will work in small groups and come to a consensus on how they will solve the problem.
3) Students will be able to describe the method they used to the rest of the class.
Abstract
In this activity, students will play the role of employees who are trying to pick a radio station to listen to. Each employee is asked individually to rank the five most popular stations, and then as a group to come up with a group ranking that will be used each week.
Problem Statement
Talk to the students about my experiences working in restaurants and how real this problem really is. See if any of them have this problem where they work or even at home. If so, how did your boss or mom handle it? As a class, we are going to come up with a system for picking which radio station to play on each day of the week at my restaurant.
Instructor Suggestions
1) Set stage by discussing the problem statement.
2) Distribute the actual activity.
3) Have the students write their preferences on the board or on an overhead. It may be helpful to have a chart pre-made that they just fill in.
4) Have the students form small groups and come up with a group ranking.
5) Have the group designate a spokesperson to present their solution and method to the class.
6) Discuss how their methods relate to rank ordering/election theory.
Materials
Handout, overhead projector or dry-erase or chalkboard
Time
Introduction (5-10 min), individual ranking (5), group work (15-25), presentations(20)
Mathematical Concepts
Discrete Mathematics Concepts
Group ranking, plurality winner, majority winner, Borda method, runoff method, sequential runoff method, Condorcet method, Arrow's conditions
Related Mathematics Topics
Matrices, Sequences, Series, Problem Solving, Statistics
NCTM Standards Addressed
Problem Solving, Communication, Reasoning, Connections, Algebra, Geometry, Discrete Mathematics
Colorado Model Content Standards Addressed
Data Collection and Analysis (3), Problem Solving Techniques (5), Linking Concepts and Procedures (6)
Curriculum Integration
Further Investigation
This activity can be extended by working with the statistics determined by the group rankings.
Variations/Comments
References/Resources