Title
Where Will You Live? (Dorothy Gieck)
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 in order to arrive at a group ranking for the entire class and be able to explain, and justify, how they arrived at this group ranking to the rest of the class.
Abstract
This activity, which is set in the context of having students vote on where they would prefer to live, focuses on group ranking. Students are asked to individually determine a rank ordering of how the four cities listed should be ranked. These individual preferences are then tallied, and the students are asked to determine one rank order for the entire class. This activity could be used to introduce Election Theory.
Problem Statement
Many students feel that their choice is the best for everyone. We will discuss the relative advantages and disadvantages of choosing one place to live versus another. We will come to a consensus of what this class feels is the appropriate ranking for these cities.
Instructor Suggestions
(1) Set the stage by discussing the problem statement above with your students.
(2) Distribute the "Where Will You Live?" activity sheet and allow the students to individually read and complete the first part of the activity.
(3) When all of the students are finished, have each student write their preference on the overhead template.
(4) After all of the preferences have been recorded, have the students form small groups and determine a class ranking based on the individual rankings.
(5) When the small groups are finished, have a spokesperson for each group share their ranking and explain their method and reasoning involved in arriving at their solution.
(6) Discuss the students' work as it relates to the concept of rank ordering.
Materials
"Where Will You Live?" activity sheet, overhead projector, ranking template
Time
Introduction of problem (5 min), individual work (5 min), small group work (20 min), small group presentations and whole class discussion (15 min), extension questions (5 min)
Mathematics Concepts
Discrete Mathematics Concepts
group ranking, plurality winner, majority winner, Borda method, runoff method, sequential runoff method, Condorcet method, Arrow's conditions, recurrence relations
Related Mathematics Concepts
matrices, sequences and series
NCTM Standards Addressed
Problem Solving, Communication, Reasoning, Connections
Colorado Model Content Standards Addressed
Number Sense (1), Data Collection and Analysis (3), Problem Solving Techniques (5), Linking Concepts and Procedures (6)
Curriculum Integration
This activity could be integrated into most any level. Discussion could include all discrete mathematics topics. With a lower level class you might use this activity to discuss how elections are not always as straightforward as we think. This activity could also be used with a traditional Advanced Algebra or Pre-calculus class when the topics of sequences and series are examined.
Further Investigation
This activity can be extended by asking students to research the population increases of the cities over the past five year period.
Variations/Comments
References/Resources
Crisler, N., Fisher, P., & Froelich, G. (1994). Discrete mathematics through applications. New York: W. H. Freeman and Company.
National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.
Colorado Model Content Standards for Mathematics (1995)