Title
The Eyes Have It (John Long)
Goals:
(1)Students apply their knowledge of apportionment while working in small groups on an example in which they are to assign a committee to represent their peers who are divided by way of eye color
(2)The students should be able to explain and defend their method of apportionment before a large group.
Abstract
This activity, set in the context of finding a 7 person group using eye color as a means of group division, uses the concept of apportionment and fair division. The students will work in small groups to produce what they feel is an appropriate apportionment and will be given the opportunity to present and defend their results.
Problem Statement:
Remind students that the House of Representatives is an example of apportionment. Possibly give the students an opportunity to investigate the method in which the apportionment is done. Let students know that today they will devise a method of apportionment to represent the students of the class using eye color as group division.
Instructor Suggestions
(1)Set the stage by discussing the Problem Statement".
(2)Distribute the activity. Give an opportunity for questions.
(3)Allow students to work in small groups to devise a method of apportionment.
(4)Have groups present their solution.
(5)Re-group you students into "like eyed" groups. Have students discuss the fairness of the divisions in a small group then a large group. Concept like dictator and dummy could be discussed.
Materials
Time
Introduction (5 min.), Group Work (15 min.), Group Presentations (15 min), Re-group and discussion (15 min.)
Mathematics Concepts
Discrete Mathematics Concepts
Apportionment (Jefferson, Hamilton, Webster, Hill), Weighted Voting, Dictator, Dummy, Coalitions
NCTM Standards Addressed
Problem Solving, Reasoning, Communication, Discrete Mathematics
Colorado Model Content Standards Addressed
Algebraic Methods (2), Data Collection and Analysis (3), Problem Solving Techniques (5), Linking Concepts and Procedures (6)
Curriculum Integration
This activity can fit into any curriculum. The activity can be an introduction to apportionment techniques or a practice of the techniques once they have been discussed.
Further Investigation:
Investigate the apportionment method used by the House of Representatives.
Variations and Comments
References/Resources
None