Title
The Superintendent's Journey (Jill Long)
Goals
1) Students will explore the concept of paths and circuits in a familiar setting.
2) Students will be able to write in words what they are doing mathematically.
Abstract
In this activity, students will determine the shortest method of traveling to all six high schools in Boulder Valley. This activity may be used as an introduction to graphs and circuits.
Problem Statement
Inform students about the new superintendent in our district. She will have to come and personally visit each high school just as our former superintendent did. We will try to find the shortest path for her to travel, assuming that she will visit all of these schools on the same day. Let students know that they will need to be able to justify their solution.
Instructor Suggestions
1) Introduce the problem with the problem statement.
2) Allow time for individuals to work on a solution.
3) Have them pair up or form groups to share methods.
4) Ask for 3 or 4 volunteers to come to front of class to present, whether they came up with best answer or not!
5) Discuss the similarities and differences in methods.
Materials
Time
Introduction (5 min), Individual work (15-20), group discussion (10), presentations (10-15)
Mathematics Concepts
Discrete Mathematics Concepts
Weighted graphs, nearest-neighbor algorithm, heuristic method, shortest path algorithm
Related Mathematics Concepts
Problem solving, matrices, optimization
NCTM Standards Addressed
Problem Solving techniques (5), Linking Concepts and Procedures (6)
Colorado Model Content Standards Addressed
Problem Solving, reasoning, connections, algebra, geometry, discrete mathematics
Curriculum Integration
This activity could be used in any problem solving setting. You could store the data in matrices in a beginning Algebra class.
Further Investigation
Add the middle schools from the same district and repeat the whole process including all middle and high schools. See if the path is the same.
See if your original method works on a new situation.
Variations/Comments
References/Resources