Title
Transportation Dilemma (Kim Kendrick)
Goals
(1) Students will explore the concept of graph theory (maps, graphs, paths, and circuits).
(2) Students will work individually to interpret data and represent the information in graph form.
(3) Students will work in small groups and come to a consensus on the graph.
(4) Students will choose a representative to present the information to the rest of the class, and they will be able to explain and justify their solution.
(5) Students will determine how many separate cars are necessary to transport all eight people using the graph they have created.
Abstract
This activity presents students with a scheduling problem. They are asked to find transportation for eight individuals according to specific set of criteria indicating who can be grouped together and who cannot. They should be familiar with the concept of basic graph theory and the vocabulary relating to this topic.
Problem Statement
Interpreting and organizing information can be a difficult task. Trying to accommodate various schedules and preferences for all members of a group requires the 'overseer' pay close attention to all of the information. Today we will be looking at a traveling dilemma in which you will need to arrange transportation for eight of your closest friends. As you might have expected, not all of your friends are getting along. You will be given various conditions surrounding who is and is not able to get along. Your job will be to group only those individuals who like each other. Good Luck!
Instructor Suggestions
(1) Set the stage by discussing the "Problem Statement" (see above) with the class.
(2) Distribute the "Transportation Dilemma" activity sheet (see attachment) and allow the students to individually read and complete the first part of the activity.
(3) Allow students to form small groups to check over their solutions.
(4) Discuss the solutions paying close attention to the graph. Have students describe their methods for creating the graph to insure its accuracy.
Materials
"Transportation Dilemma" activity sheet, chalk board
Time
Introduction of problem statement (5 minutes), Individual work (20 minutes), mall group work (10 minutes, Present the information, explain and justify their solution (10 minutes)
Mathematics Concepts
Discrete Mathematics Concepts:
Modeling, Vocabulary and representations of graphs, circuits and paths, graph coloring
Related Mathematics Concepts:
Matrices
NCTM Standards Addressed
Problem Solving, Communication, Reasoning, Connections (within mathematics and across disciplines), Algebra, Geometry, Discrete Mathematics.
Colorado Model Content Standards Addressed
Geometric Techniques (4), Problem Solving Techniques (5), Linking Concepts and Procedures (6)
Curriculum Integration
This activity will be used in the first year of the Integrated Math Program as a separate module to extend the ideas covered in the graph section of discrete mathematics. It could also be used in a traditional Algebra I class when discussing matrices or focusing on problem solving and critical thinking skills.
Further Investigation
This project could be extended by having the students create a map and color it. The number of colors will correspond to the number of cars.
Variations/Comments
This project could have listed animals or chemicals which could not share the same space, for whatever reason.
References/Resources
Crisler, N., Fisher, P., & Froelich, G. (1994). Discrete Mathematics Through Applications. New York: W.H. Freeman and Company.