Title
Will Power and Food (John Reid)
Goals
(1) Students will explore the concept of fair division as it relates to dividing a continuous object and a discrete object
(2) Students will then work in small groups to arrive at a fair division and explain how they arrived at these results.
Abstract
The students will divide an estate and a piece of food among a group of people. The divisions that they arrive at must be explained and defended as fair. The students will work in small groups and present their results to the class.
Problem Statement
The students are to break up into small groups and devise and defend ways of dividing an estate and some form of food among a group of people.
Instructor Suggestions
(1) Begin by handing out activity sheet then break the students into small groups.
(2) Explain what is required of the students and then let them work.
(3) After students finish, each group will make a presentation explaining the groups choices and justify them.
(4) After all groups have gone, end the activity by having class discussion on fair division.
Materials
An activity sheet, and normal classroom materials.
Time
Introduction and explanation (5 min), group work and discussion (25 min), group presentation (10 min), large group discussion (15 min)
Mathematics Concepts
Discrete Mathematics Concepts
Estate Division, Apportionment Algorithms for Continuous Objects, Fairness
Related Mathematics Concepts
Matrices, Ratios
NCTM Standards Addressed
Problem Solving, Communication, Reasoning, Connections, Algebra, Discrete Mathematics
Colorado Model Content Standards Addressed
Algebraic Methods (2), Problem Solving techniques (5), Linking Concepts and Procedures (6)
Curriculum Integration
(1) Algebra using matrices and related operations
(2) Algebra use of fractions and ratios
Further Investigations
This activity could be changed to relate to students interests and the results could also be changed to reflect demographics.
Variations/Comments
The teacher can change and/or manipulate data as they feel necessary
References/Resources
Crisler, N., Fisher, P., & Froelich, G. (1994). Discrete mathematics through applications. New York: W. H. Freeman and Company.