Title
Checker Tournament (Anne Smelker)
Goals
(1) Students will explore the concept of graph theory as it relates to scheduling.
(2) Students will work in small groups in discuss and derive a schedule to meet all the criteria of the tournament.
(3) Students will explain and justify how they determined a schedule to meet the needs of the tournament.
Abstract
This activity focuses on applying graph theory to derive a schedule to meet the criteria of a tournament. Students will form groups and devise a schedule so that all the criteria of the tournament are met. Each group will then present, explain, and justify their schedule and/or methods to the entire class. This activity could be used to introduce graph theory such as to develop a schedule. Discussion of the problem could extend to exploring how to determine the tournament winner or ranking schedule.
Problem Statement
Scheduling for tournaments can be very intricate due to special circumstances and criteria that needs to be met. In small groups, they are to develop a schedule that meets the criteria of the checker tournament and its players and is easy for everyone to see who plays whom each day. This activity will allow students to explore and apply graph theory.
Instructor Suggestions
(1) As a class discuss only the Problem Statement and what is expected of each group but not how to begin solving the problem.
(2) Distribute the "Checker Tournament" activity sheet and have students work in groups to develop their own solutions and methods.
(3) When the groups are finished, have each group have a spokesperson share their methods and the processes they used to develop a schedule.
(4) Discuss each of their methods as it relates to graph theory.
Materials
"Checker Tournament" activity sheet
Time
Introduction of Problem Statement (5 minutes), Group Work (20 minutes>, Presentations/Class Discussion (20 minutes)
Mathematics Concepts
Discrete Mathematics Concepts
Graph Theory, Scheduling, Critical Paths, Modeling Projects
Related Mathematics Concepts
Graphs and their Applications
NCTM Standards Addressed
Problem Solving, Communication, Reasoning, Connections (within mathematics and across disciplines), Geometry, Discrete Mathematics
Colorado Model Content Standards Addressed
Geometric Techniques (4), Problem Solving Techniques (5), Linking Concepts and Procedures (6)
Curriculum Integration
This activity could be integrated in a Algebra or Geometry class as the topic of graph theory or patterns.
Further Investigation
Extend the problem to explore the tournament on how to determine the winner or ranking schedule.
Variations/Comments
Conduct an actual Checker Tournament in the classroom with each group as one player and discuss their schedules, which was the easiest to follow, which schedule was more time efficient, etc.
References/Resources
Crisler, N., Fisher, P., and Froelich, G. (1994). Discrete Mathematics Through Applications. New York: W.H. Freeman and Company.
Kenney, M. J., and Hirsch, C. R. (Eds.). (1991). Discrete Mathematics Across the Curriculum, K - 12. Reston, VA: National Council of Teachers of Mathematics.
Lynch, D., Martin, W., and Porter, B. (1995). Higher Expectations - Better Results Assessment Workbook. Colorado State Board of Education.
National Council of Teachers of Mathematics. (1989). Curriculum and Evaluation Standards for School Mathematics. Reston, VA: Author.