Title
Let's Chat (Greta Lawlor)
Goals
1) Students will apply recursion to a real-world problem.
2) Students will be able to individually use and justify a method for determining the cost of a call, and the amount of income produced by a chat line.
3) Students will present solutions and come to consensus on a solution.
Abstract
This activity, set in the context of determining the cost of a teen chat line and the income for the telephone company, asks students to use apply recursion to solve a "real" problem.
Students will also explore the profit of a chat line.
Problem Statement
Ask students if they have ever heard of a "chat" line. Have the students describe how they work. Students are ask to explore the cost of such a line and to make decisions about using such a line considering the cost. This activity should be introduced after exploration and study of recursion.
Instructor Suggestions
1) Set the stage by discussing what chat lines are and how they work.
2) Distribute the "Let's Chat" activity sheet and allow the students to read and ask questions about the activity.
3) Have students complete the activity (in groups or individually as meets the needs of your classroom.)
4) Students should be able to individually present and justify a solution.
5) Discuss the students work in relation to the cost/profit of a chat line.
Materials
"Let's Chat" activity sheet, chalk-board.
Time
Introduction of the problem (5 minutes), individual work (30 minutes), presentation and class discussion (20 minutes.)
Mathematics Concepts
Discrete Mathematics Concepts
Arithmetic sequences, geometric sequences, closed form solutions, recursion.
Related Mathematics Topics
Interest, recurrence relations, sequences
NCTM Standards Addressed
Problem Solving, Communication, Reasoning, Connections, Algebra, Geometry, Discrete Mathematics
Colorado Model Content Standards
Algebraic Techniques (2), Geometric Techniques (4)
Curriculum Integration
This activity could be introduced into an Algebra or Geometry class as an extension to sequences. It could also be introduced when interest and related problems are studied.
Further Investigation
This activity can be extended by using different payment plans to model other recursive patterns. Finite differences may be a valuable tool.
Variations/Comments
This activity could be used as a formal assessment. The students could also be asked to decide how much the phone company should charge to "come out even" or to reach certain profit levels.
References/Resources
Crisler, N., Fisher, P., & Froelich, G (1994). Discrete Mathematics Through Applications. New York: W. H. Freeman and Company