Title
Music to study by (Kim Kendrick)
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 consensual group-ranking and be able to explain, an 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 which type of music they will listen to during activities and work time, focuses on group-ranking. Students are asked to individually determine a rank-ordering of how the six music categories should be listed. These individual preferences are then tallied, and the students are asked to determine one rank-ordering for the entire class. This activity could be used to introduce Election Theory, and in particular, group-ranking.
Problem Statement
Let students know that in the past there have been disputes among members of the class which centered around what type of music should be played during the class work time. In order to eliminate the problem, you have decided to let them determine what type of music the class prefers. Because not all students will prefer the same type of music, they must decide on the best "schedule" for each type of music. As a class we must vote on the rank-order of the selections, and then determine the schedule, if necessary.
Instructor Suggestions
(1) Set the stage by discussing the "Problem Statement" (see above) with the class.
(2) Distribute the "Music to study by" activity sheet (see attachment) 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 of the students write their preference on the board.
(4) After all of the preferences have been recorded have the students form small-groups and determine a class ranking based on the individual ranking.
(5) When the small-groups are finished, have a spokesperson for each group share their preference and explain their method and reasoning involved in arriving at their ranking.
(6) Discuss the students' work as it relates to rank-ordering.
Materials
"Music to study by" activity sheet, chalk board
Time
Introduction of problem statement (5 minutes), Individual work (5 minutes), Small group work (15-20 minutes), Presentation of small-group work (15 minutes), Large group discussion (15 minutes)
Mathematics Concepts
Discrete Mathematics Concepts:
Group-Ranking, Plurality Winner, Majority Winner, Borda Method, Runoff Method, Sequential Runoff Method, Condorcet Method (paradox), Arrow's Conditions, Recurrence Relations.
Related Mathematics Concepts:
Matrices, Sequences and Series.
NCTM Standards Addressed
Problem Solving, Communication, Reasoning, Connections (within mathematics and across disciplines), 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
This activity will be used in the first year of the Integrated Math Program as a separate module. It could also be used in a traditional Algebra I class when discussing series or in an Algebra II class when discussing matrices
Further Investigation
Discuss the idea of fairness as it relates to selections especially if the students have decided to go with the majority. This will lead nicely into the next activity, "High Tech Education".
Variations/Comments
This lesson could be modified to vote on favorite sodas, class rules, or the way in which you evaluate your students.
References/Resources
Crisler, N., Fisher, P., & Froelich, G. (1994). Discrete Mathematics Through Applications. New York: W.H. Freeman and Company.