Title
I Cut, You Choose (Greta Lawlor)
Goals
1) Students will explore the concept of fair division.
2) Students will work in groups to develop a plan to share a piece of cake fairly among several groups of different sizes.
3) Students will present and justify there methods.
Abstract
This activity asks students to divide a piece of cake "fairly" between different numbers of people. The focus is to establish a method that will work for any size group through the development of an algorithm.
Problem Statement
Discuss with the students times that they have had to share with others. Discuss methods they have used for fair division. If no one mentions the "I cut, you choose," method, introduce it to them. Let students know that today they will be using this method to develop a plan that will work for more than just two people.
Instructor Suggestions
1) Set the stage by discussing the problem statement.
2) Distribute the "I Cut, You Choose" activity and allow them to read it individually. Answer any questions they may have about the activity.
3) Have the students work in groups to find a method that will work with 2 people, 3 people and so on generalizing to n people.
4) Have the students present their solutions and justify that they are fair solutions.
Materials
"I Cut, You Choose" activity sheet, transparencies, markers, (option: have a small cake for each group to divide and share)
Time
Introduction of problem statement (5 minutes), group work (20 minutes), presentations (20 minutes), "let them eat cake" (10 minutes.)
Mathematics Concepts
Discrete Mathematics Concepts
Fair division, election theory
Related Mathematics Concepts
Algebra, fractions, patterns, functions
NCTM Standards Addressed
Problem Solving, Communications, Reasoning, Connections, Algebra, Discrete Mathematics.
Colorado Model Content Standards Addressed
Number Sense (1), Algebraic Techniques (2), Problem Solving Techniques (5)
Curriculum Integration
This activity could be introduced with patterns or in algebra where an algorithm is developed. It could be used when election theory is introduced and fair division is explored.
Further Investigation
This activity could be extended by adding the restriction that some people get a piece that is a multiple of the size of others. Ask the students to divide up a portion of a piece that one person did not want.
Variations/Comments
This activity is an exploratory activity and would be useful in the development of patterns. It also points out some very interesting concepts of fractions. If the students do not obtain a method for three people, it may be necessary to bring the groups back to one large group and discuss the solution for three people.
References/Resources
Colorado Model Mathematics Standards Task Force. (1995) Colorado Model Content Standards for Mathematics.
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