Discrete Mathematics Project

Counting Techniques Activity


Rolling Dice (John Long)


(1) Students should manipulate their strategies in a way which reflects the roll of the dice.

(2) Students will compare their hypothesis of which # is rolled most often with the actual result.

(3) Students will learn the definition of probability and work with counting techniques.

Problem Statement

The game of Craps is based on an individual betting on a number that will be rolled on a pair of dice. We will be playing a modified game of craps and will be trying to guess which numbers will be rolled most often. We will then try to prove our hypothesis on what number (if there is one) that will be rolled most often.

Instructor Suggestions

(1) Introduce the problem to the students and hand out the activity and game sheet

(2) Allow the students to play the game a number of times. Then allow the students to discuss their strategies

(3) Continue the work on finding out which number will be rolled the most by doing part II of the activity. Point out how the results of the data looks like a bell curve.

(4) Part III of the activity will allow the students to put some proof to their hypothesis. Discuss the results with the class and allow them to make an "ultimate strategy". Allow the students to discuss why there strategy is better than another.


Activity Sheet

Game Board Sheet

Dry Erase Board


Part I (25 min.), Part II (25 min.), Part III (25 min.)

Mathematics Concepts

Discrete Mathematics Concepts

Counting, Probability

NCTM Standards Addressed

Problem Solving, Communication, Reasoning, Probability & Statistics, Discrete Mathematics

Colorado Model Content Standards Addressed

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

Curriculum Integration

This activity can be integrated into any probability section. The activity is recommend for Pre-Algebra or Algebra I.

Further Investigation

Have the students prove their "ultimate strategy" is better than any other group.



Crisler, N., Fisher, P., & Froelich, G. (1994). Discrete mathematics through applications. New York: W.G. Greeman and Company.

Last updated January 16, 1997