Title
Tendency To Be Tardy (John Long)
Goals
(1)Students will continue to explore the concepts of graph theory by devising a graph that models the students trips to and from class.
(2)Using their model, the students will be able to find the shortest route to and from their classes.
Abstract
This activity, set in the context of finding the most efficient route to and from daily classes, focuses on the idea of graph theory. Students will graph all possible routes to and from class. Using the graph they will find the shortest route.
Problem Statement
Explain to your students the stress that tardies place on teachers and administrators. This stress results in tighter restrictions on students. A solution to the problem would benefit all.
Instructor Suggestions
(1)Hand out the activity and give students an opportunity to read it
(2)Discuss various routes from class to class
(3)Have students produce their directed graphs
(4)Have students measure the distances to and from their various classes. Efficiency, not precision is the key to the measurement.
(5)Add the distance data to the graphs
(6)Using the graphs, find the shortest route. Have the students write up their solution, describing their method
Materials
Tendency to Be Tardy handout, yard and meter sticks, maps of the school, map of the school on an overhead
Time
Reading and Discussing activity (5 min.), Students Producing Graph (15 min.), Measuring Distances and adding information to graph (20 min.), Finding the shortest route (10 min.), Write Up (Homework)
Mathematics Concepts
Discrete Mathematics Concepts
Graph Theory, Critical Path, Digraphs
Related Mathematics Concepts
Measurement
NCTM Standards Addressed
Problem Solving, Communication, Reasoning, Connections (Measurement and Graph Theory), Geometry, Discrete Mathematics
Colorado Model Content Standards Addressed
Data Collection and Analysis (3), Problem Solving Techniques (5), Linking Concepts and Procedures (6)
Curriculum Integration
During a Pre-Algebra unit on measurement would be an excellent opportunity to introduce this Graph Theory activity. Also during an Algebra unit in which you are working on Rate-Time-Distance problems (see further investigation).
Further Investigation
Extend the problem by having the students approximate their rate at which they walk. Using this information, they can find the actual time it takes to get from class to class.
Variations/Comments
What is nice about Graph Theory is that it can be inserted into an existing curriculum quite easily due to the little explanation needed to understand the basics.
References/Resources