Title
Colors of the State (John Reid)
Goals
(1) Students will explore the concept of graph theory as it applies to coloring.
(2) Students will then work in small groups to plan and color a map of a selected state's counties using only three colors.
Abstract
The students will devise a way of coloring a state's counties so that counties of the same color are not touching. They first must come up with an algorithm to solve this problem. They will work in small groups and then present their method of solving this problem to the class.
Problem Statement
The students are to break up into small groups, devise and present their way of solving the problem of coloring a state's counties using only three colors.
Instructor Suggestions
(1) Introduce the topic of coloring by explaining the concept of circuits and paths.
(2) Hand 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 coloring.
Materials
An activity sheet, colored markers, map of state, and normal classroom materials.
Time
Introduction and explanation (15 min), group work and discussion (20 min), group presentation (10 min), large group discussion (10 min)
Mathematics Concepts
Discrete Mathematics Concepts
Graph Theory, Circuits, Paths, and Coloring
Related Mathematics Concepts
Graphing, Problem Solving, Patterns
NCTM Standards Addressed
Problem Solving, Communication, Reasoning, Connections, Algebra, Discrete Mathematics
Colorado Model Content Standards Addressed
Algebraic Techniques (2), Geometric Techniques (4), Problem Solving techniques (5), Linking Concepts and Procedures (6)
Curriculum Integration
(1) Algebra using graphs and logical reasoning
(2) Geometry
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.