Title
Color the County (Ed Snyder)
Goals
(1) Students will begin to explore the concept of coloring as it pertains to graph theory.
(2) Students will work individual using critical thinking and reasoning skills for the purpose of exploring coloring problems as it relates to graph theory.
Abstract
This activity is designed for students to work on critical thinking and reasoning skills while applying it to the concepts of graph theory, including graphing , coloring graphs and chromatic numbers.
Problem Statement
Suggest to students that maps are made of vertices and edges that divide cities, counties, states etc. Introduce the four color theorem as related to graph theory. Ask the students to color the map of Boulder utilizing no more than four colors, but as few as possible.
Instructor Suggestions
(1) Begin by discussing the problem statement.
(2) Have students work individually.
(3) Distribute the Color the County activity sheet and have students work on the problem.
(4) Have several students report their findings to the rest of the class.
Materials
"Color the County" activity sheet, colored pencils or markers.
Time
Introduction (5 min.), individual work( 20 min.), presentation of work and class discussion (20 min.)
Mathematics Concepts
Discrete Mathematics Concepts
Graph theory including coloring , vertices ,edges, chromatic number of graphs, and cycles.
Related Mathematics Concepts
Algebra, geometry.
NCTM Standards Addressed
Problem solving , Communications, Reasoning, Discrete Mathematics.
Colorado Model Content Standards Addressed
Number Sense (1), Data Collection and Analysis (3), Geometric Techniques (4), Problem Solving Techniques (5), Linking Concepts and Procedures (6)
Curriculum Integration
This particular activity could be integrated into a Integrated (1) Mathematics course during a geometry unit or when covering graphing principles.
Further Investigation
The assignment can be extended by having students design a map of their school and the color using the graph coloring principles.
Variations/Comments
References/Resources
Crisler, N., Fisher, P., & Froelich, G. (1994). Discrete mathematics through applications. New York: W. H. Freeman and Company.
Kenney, M.J., & Hirsch, C. R. (Eds.). (1991). Discrete mathematics across the curriculum, K-12. Reston. VA; National Council of Teachers of Mathematics