Index

Discrete Mathematics Project

Counting Techniques Activity

Title

Buy Me Some Peanuts And Crackerjacks (Jill Long)

Goals

Students will explore the concepts of permutation, combination, and probability.

Abstract

This activity allows the student to work with the concepts of permutation, combination, and probability in a familiar setting. Students will be able to decide which counting technique is appropriate for each individual setting.

Problem Statement

This activity doesn't need much set-up. You could talk about Coors Field and the Rockies and get a little discussion going with the students who have been there, etc. This activity could be used as an introduction to see if they can come up with a sufficient answer, or it could be used as a quick practice to review.

Instructor Suggestions

1) Discuss problem statement with class as a whole.

2) Have them work in pairs or in groups, depending on the goal of the activity. Is it a discovery type of activity or a review?

3) Just let them work without much guidance, or without giving them many hints.

4) Have groups present their strategies to the class.

Materials

Time

intro ( ~5 min), work time (10-20 min), presentations (5-10 min)

Mathematics Concepts

Discrete Mathematics Concepts

permutation, combination, probability, addition principle, factorial, mutually exclusive events

Related Mathematics Concepts

probability

Problem solving, communication, reasoning, connections, algebra, probability, discrete mathematics

Algebraic Techniques (2), Problem Solving Techniques (5), Linking Concepts and Procedures (6)

Curriculum Integration

There seems to be a unit or mention of probability in every high school math class. It could be used when discussing permutations and combinations. It is probably too simple of a task to use as a problem of a week in any class above geometry.

Further Investigation

Many other questions could have been asked here. For instance, what happens if three people go to get drinks, etc. instead of two?