Title
Checkerboard Problem (Dorothy Gieck)
Goals
Students will work with the concept of networking. Students will work in small groups in order to find solutions to problems related to a checkerboard and placement of checkers. They will be able to explain and justify, how they arrived at a method to the rest of the class.
Abstract
This activity, which is set in the context of a checkerboard, will enable students to come up with a pattern that satisfies given criteria. Students are asked to form small groups to discuss the situation and come up with a pattern that works. This activity could be used as a networking problem or when discussing patterns.
Problem Statement
Show how to place 8 checkers on an 8-by-8 checkerboard so that each row, column, and main diagonal contains exactly 1 checker.
Instructor Suggestions
1. Set the stage by discussing the "Problem Statement" (see above) with your students.
2. Distribute the "Checkerboard" activity sheet and allow the students to individually read the activity and answer the first for questions.
3. Have the students form small-groups, work with checkers and checkerboards to complete the questions on the activity sheet.
4. When the small groups are finished, have a spokesperson for each group share the group answers.
5. Discuss the students work as it relates to patterns and problem solving strategies.
Materials
"Checkerboard" activity sheet, checkerboards and checkers for each group, overhead transparencies of the checkerboard, transparent disks to be used as checkers, overhead pens, blank overhead transparency sheets.
Time
Introduction of Problem Statement (5 min.), individual work (10 min.), small group work (15 min.), presentation of small group work and large group discussion (15 min.), extension questions (5 min.)
Mathematics Concepts
Discrete Mathematics Concepts
Recursion, Networking
Related Mathematics Concepts
Ratios, Unique solutions, Problem solving strategies
NCTM Standards Addressed
Problem Solving, Communication, Reasoning, Connections, Algebra, Geometry, Discrete Mathematics
Colorado Model Content Standards Addressed
Algebraic Techniques (2), Data Collection and Analysis (3), Problem Solving Techniques (5), Linking Concepts and Procedures (6)
Curriculum Integration
This activity could be adapted for any class. It would fit into an pre-algebra, algebra or geometry class during the study of networking
Further Investigation
Are solutions unique? With 16 checkers, make sure one of each color is in each column, row and diagonal.
Variations/Comments
References/Resources
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: Author.
Colorado Model Content Standards for Mathematics (1995)
Benson, J., Dodge, S., Dodge, W., Hamberg, C., Milauskas, G., Rukin, R., (1991) Algebra 2 and trigonometry. Evanston, IL: McDougal, Littell & Company