Title
Scheduling Classes (Jill Long)
Goals
1) Students will explore the concepts of graph theory using a real-world problem.
2) Students will be able to represent data in a visual display.
3) Students will be able to work as a group agreeing on a method to come to a solution.
Abstract
This activity puts the students in the role of a principal, determining when classes can be offered. Students are able to use any method they can agree upon as a group to come to a solution. This activity is envisioned as an introduction to graph coloring.
Problem Statement
Talk about the work that the principals do over the summer and that one of their major tasks is class scheduling. Have them write up their method and solution in a form that could be presented to the principal.
Instructor Suggestions
1) Set the stage with the problem statement.
2) Give each group a transparency and marker to put their graph or display on.
3) When the small groups are finished, have a spokesperson go to the front of class and present.
Materials
handout, transparencies, markers
Time
Introduction (5 min), group work (15-25), presentations (10-15)
Mathematics Concepts
Discrete Mathematics Concepts
Graph coloring, chromatic numbering, paths, circuits, Euler paths and
circuits, Hamiltonian paths and circuits, degree of a vertex
Related Mathematics Concepts
Statistics(displays), matrices, problem solving
NCTM Standards Addressed
Problem Solving, communication, reasoning, connections, algebra, statistics, discrete mathematics
Colorado Model Content Standards Addressed
Problem Solving Techniques (5), Linking Concepts and Procedures (6)
Curriculum Integration
This activity could be introduced in a problem solving course as a "drawing a diagram" type of method. In Algebra, this activity could be used when discussing matrices or data displays.
Further Investigation
Explore the question "Is the solution unique?" Does it make sense to schedule 8 classes at once, etc. Bring the principal into class to talk about the method he really uses.
Variations/Comments
References/Resources