Title:
The Lost Souls of the Math Department (John Long)
Goals
(1)Students will apply their knowledge of fair division and estate division in an example that does not fit the mold of problems that are generally found with those topics.
(2)Be able to defend their method using legitimate and logical reasoning
Abstract
This activity is set in the context of finding a fair method of assigning classrooms to teachers. Students are put into small groups and asked to devise a method to fairly assign the rooms using estate division as a basis of their work. Their solution will be presented to the teachers whom the method will affect.
Problem Statement
Suggest to your students the importance of this type of division. The moral of a department can be damaged if an individual feels he or she has been dealt with unfairly. Methods that involve seniority as a means of division, may be simple, but leaves many teachers feeling as if they had no power in the decision. There must be a better way. Allow students to explore a variety of division techniques. This question is left quite open ended to allow for creativity. Estate Division becomes a framework in which to model the solution, but is not the algorithm to the solution.
Instructor Suggestions
(1)Distribute "The Lost Souls of the Math Department". Describe specific examples of other "valuables" in your department so students can use those in their work.
(2)Allow students to work in groups. As the teacher, act as a sounding board to the students ideas. Push for mathematical support to their method. Continually question the "fairness" of their method.
(3)In a large group discuss the student work as it relates to fair division and estate division.
Materials
Time:
Introduction (20 min.), Small Group Work (40+min.), Preparation for presentations (30+(hw)min.), Presentations (5-10 min./group)
Math Concepts
Discrete Math Concepts
Estate division, Fair Division, Fairness
NCTM Standards
Problem Solving, Communication, Reasoning, Discrete Math
Colorado Model Content Standards Addressed
Data Collection and Analysis (3), Problem Solving Techniques (5), Linking Concepts and Procedures (6)
Curriculum Integration
This activity should be introduced after through work with fair division topics. I would recommend doing this activity with students of an Algebra two level or above.
Further Investigation
Have students describe what they feel the definition of "Fairness" is . Is there a way to measure the fairness of a method?
Variations/Comments
Instead of the distribution of classrooms to teachers, the focus could be on the yearly distribution of funds and materials to departments.
References/Resources
None