Title
Ted the Taxi Man (John Reid)
Goals
(1) Students will explore the concept of graph theory as it applies to circuits and paths.
(2) Students will then work in small groups to plan a route for Ted as he travels through the city using circuits and paths.
Abstract
The students will devise a plan to get around the city using Euler's circuits and paths. The trip will be done as a whole class, the second larger trip will be done in small groups. The small group will then present their results to the whole class.
Problem Statement
The students are to break up into small groups, devise and present their plan of moving around the city using Euler's circuits and paths.
Instructor Suggestions
(1) Introduce the topic of Euler's 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 circuits and paths.
Materials
An activity sheet, map of city 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
Related Mathematics Concepts
Graphing, Problem Solving, Patterns
NCTM Standards Addressed
Problem Solving, Communication, Reasoning, Connections, Algebra, Discrete Mathematics
Colorado Math Standards Addressed
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.