Title
The "Out of State Estate" Dilemma (Liz Sansone)
Goals
Students will explore the concept of fair division as it relates to apportioning discrete objects in an estate among members of a group
Abstract
Students are asked to form groups and devise a method that fairly divides the defined estate. Each group is then asked to present and explain their method to the class.
Problem Statement
Discuss with your students that everyone at one time or another has felt frustrated that they did not get their fair share when something they desired had been divided up. This activity will allow students to explore a division situation and employ discrete mathematics in devising a method that fairly distributes
Instructor Suggestions
1) Discuss "Problem Statement" from above with your students.
2) Decide on a method to have students form small groups
3) Distribute "Out of State Estate" activity sheet, also distribute a transparency and a marker to each group, one person needs to illustrate the groups' approach..
4) When the small groups are finished, have a spokesperson for each group share their method using the transparency that they prepared.
5) Discuss the students' work as it relates to fair division
Materials
"Out of State Estate" activity sheet, transparencies, markers.
Time
Introduction (5 min.) small group work (20 min.), presentation of small group work and large group discussion (20 min.).
Mathematics Concepts
Discrete Mathematics Concepts
Estate Division, Apportionment, Algorithms for Fair Division, Fairness
Related Mathematics Concepts
Matrices, Ratios, Arithmetic Mean.
NCTM Standards Addressed
Problem Solving, Communication, Reasoning, Connections, Algebra, Geometry, Discrete Math.
Colorado model Content Standards Addressed
Algebraic Techniques (2), Problem Solving Techniques (5), Linking Concepts and Procedures (6)
Curriculum Integration
This activity could be integrated into a traditional or Integrated Algebra and/or Geometry class as the topics of matrices, and/or ratios are examined.
Further Investigation
Extend the problem by having more assets or people in the estate, include heirs receiving percentages of estate, use a computer spreadsheet to perform the estate division, and/or illustrate the bids and the items awarded using matrices and then multiply them.
Variations/Comments
Provide students with Monopoly money.
References/Resources
Crisler, N., Fisher, P., & Froelich, G. (199410. Discrete mathematics through applications. New York: W.H. Freeman and Company.