Index

Discrete Mathematics Project

Counting Techniques Activity

Title

A Guaranteed Millionaire (October Crowell)

Goals

1. Students will determine how many possible tickets exist in the lottery using the concepts of permutations and combinations.

2. Students will work in groups to develop a scheme to ensure winning the lottery and be able to explain and justify their scheme to the class.

Abstract

This activity focuses on the application of permutations and combinations to and actual lottery. Students are asked to individually determine the total possible tickets and then work in groups to develop a scheme to guarantee winning the lottery. It is intended to be used after the students have been introduced to the concepts of counting, permutations and combinations.

Problem Statement

Tell the students that even though there are many people who play the lottery because they feel "lucky", few actually examine the chances that they will actually win. Let them know that they will be determining a method for guaranteeing that they will win the lottery regardless of the jackpot.

Instructor Suggestions

1. Introduce the activity by discussing the Problem Statement above with the students.

2. Distribute the "A Guaranteed Millionaire" activity sheet (see attached) and allow the students to individually read and complete part a.

3. Divide the students into groups and have each group complete the rest of the activity. Be sure to remind them that they have to be able to explain and justify their plan.

4. When the small groups are finished, have the groups present their plans.

5. Discuss the plans as they relate to probability and counting.

Materials

"A Guaranteed Millionaire" activity sheet, chalk or overhead materials

Time

Introduction (5 min), Individual work (5 min), Group work (30 - 45 min), Presentations and Discussion (20 min)

Mathematics Concepts

Discrete Mathematics Concepts

Counting, Permutations, Combinations

Related Mathematics Concepts

Probability, Fundamental Counting Principle, Permutations, Combinations.

Problem Solving, Communication, Reasoning, Connections, Algebra, Geometry, Discrete Mathematics

Number Sense (1), Algebraic Techniques (2), Problem Solving Techniques (5), Linking Concepts and Procedures (6)

Curriculum Integration

This activity could be integrated into any traditional class when the topic of counting is examined. It is meant to be bridged with the topics of permutations and combinations, but could be done without them.

Further Investigation

This activity could be extended by asking the students to develop a plan that uses the least number of people to win any lottery or how they might win "power ball" lotteries that involve multiple states.

This activity may take more than one traditional class period to complete. One variation would be to have the students complete the last part as homework or a project. Also, this activity assumes that there is only one winning ticket chosen by one person, with a variation being what happens if two people pick the winning numbers.

References/Resources

Crisler, N., Fisher, P., & Froelich, G. (1994). Discrete mathematics across the curriculum, K-12, Reston, VA; National Council of Teachers of Mathematics.

National Council of Teachers of Mathematics, (1989). Curriculum and evaluation standards for school mathematics. Reston, VA; Author.