Title
Zoo Redo (Greta Lawlor)
Goals
1) The students will explore the concept of coloring using a slightly less obvious example than a map.
2) Students will work in groups to determine the best solution and be able to justify it.
Abstract
This activity, set in the context of keeping predators from prey, asks students to organize the zoo so that no "color" is adjacent to the same "color." The students must determine how many locations for the animals the zoo keeper will need.
Problem Statement
Conduct a short discussion on coloring, reminding the students of previous problems. Let students know that they will by applying this concept to a slightly different problem, but with a similar solution. This problem will entail finding the minimum number of locations in a zoo for animals living in their natural habitat. Predators and prey are to be put in separate locations.
Instructor Suggestions
1) Set the stage by discussing previous work with coloring.
2) Distribute the handout "Zoo Redo" and allow the students time to read over it. Have a short brainstorm session about how they might solve the problem.
3) When the students have several ideas about how they might solve the problem, let them work together in groups.
4) Have a group spokesperson present the groups solution to the rest of the class with a justification.
5) Discuss as a whole group the solutions presented and which one is the minimum number of locations.
Materials
"Zoo Redo" handout, chalk-board.
Time
Introduction (5 minutes), group work (25 minutes), presentations and discussion (20 minutes).
Mathematical Concepts
Discrete Mathematics Concepts
Graph theory, coloring
Related Mathematics Concepts
Problem solving, logic
NCTM Standards Addressed
Problem Solving, Communication, Reasoning, Discrete Mathematics
Colorado Model Content Standards
Geometric Techniques (4), Problem Solving Techniques (5), Linking Concepts and Procedures (6)
Curriculum Integration
This activity could be integrated into Algebra or Geometry as a topic associated with graph theory.
Further Investigation
This activity could be extended by having students do research on the 4 color rule for maps. The activity could be manipulated by adjusting the number of predators and prey.
Variations/Comments
This activity would be a good problem of the week. It could be introduced without the connection to coloring to assess whether the students can make a connection between this problem and graph theory.
Referenced/Resources
Dossey, John A., Otto, Albert D., et. al., Discrete Mathematics. 1972. Glenview, Illinois:Scott, Foresman and Company.