Title
Westy's United Nations Committee (Liz Sansone)
Goals
Students will explore the concept of fair division as it relates to apportioning discrete objects (legislative seats) among members of a group
Abstract
Students are asked to form groups and devise a method that fairly apportions "seats" among a legislative group. Each group is then asked to present and explain their method to the class.
Problem Statement
Discuss with your students that everyone at one time or another has felt frustrated that they did not get their fair share in being represented in a legislative committee. This activity will allow students to explore a division situation and employ discrete mathematics in devising a method that fairly distributes power among a legislative group.
Instructor Suggestions
1) Discuss "Problem Statement" from above with your students.
2) Decide on a method to have students form small groups
3) Distribute "Westy's United Nations Committee" activity sheet, also distribute a transparency and a marker to each group, one person needs to illustrate the groups' approach..
4) When the small groups are finished, have a spokesperson for each group share their method using the transparency that they prepared.
5) Discuss the students' work as it relates to fair division
Materials
"Westy's United Nations Committee" activity sheet, transparencies, markers.
Time
Introduction (5 min.) small group work (20 min.), presentation of small group work and large group discussion (20 min.).
Mathematics Concepts
Discrete Mathematics Concepts
Apportionment, Algorithms for Fair Division, Fairness
Related Mathematics Concepts
Matrices, Ratios, Arithmetic Mean., Geometric Mean, Statistics
NCTM Standards Addressed
Problem Solving, Communication, Reasoning, Connections, Algebra, Geometry, Discrete Math.
Colorado Model Content Standards Addressed
Algebraic Techniques (2), Problem Solving Techniques (5), Linking Concepts and Procedures (6)
Curriculum Integration
This activity could be integrated into a traditional or Integrated Algebra and/or Geometry class as the topics of matrices, quotas and/or ratios are examined.
Further Investigation
Extend the problem by increasing the number of seats or people involved , introduce another nationality., ask students to formally define what is means to be "fair"
Variations/Comments
In the large group have students use seats so they can refine and test their fair division method.
References/Resources
Crisler, N., Fisher, P., & Froelich, G. (199410. Discrete mathematics through applications. New York: W.H. Freeman and Company.