Discrete Mathematics Project

Counting Techniques Activity


Black Jack (Ed Snyder)


1. Students will explore the concept of probability while making use of counting techniques, to figure out odds in the game of Black Jack.

2. Students will work in small groups in order to discover probability.


This activity is designed for students to discover the odds of specific pairs of cards being drawn out of a 52 card deck.

Problem Statement

Suggest to students that there are many industries and businesses that make an incredible profit from projecting the odds (probability) that certain situations will occur. This activity will allow students to explore the concept of probability through the game of Black Jack.

Instructor Suggestions

1. Begin by discussing the problem statement.

2. Have students form small groups.

3. Distribute the "Black Jack" activity sheet and have students work on the problem.

4. Have each group select a spokesperson to report their results to the class.

5. Discuss students probability results.


"Black Jack" activity sheet, chalk board, overhead projector, transparencies and pens.


Introduction (5 minutes), group work (20 minutes), presentation and class discussion (20 minutes).

Mathematics Concepts

Discrete Mathematics Concepts

Counting techniques and probability

Related Mathematics Concepts


NCTM Standards Addressed

Problem solving, Communications, Reasoning, Discrete Mathematics.

Colorado Model Content Standards Addressed

Number Sense (1), Data Collection and Analysis (3), Problem Solving Techniques (5), Linking Concepts and Procedures (6)

Curriculum Integration

This activity can be integrated into a Integrated I math curriculum both as an introduction or as a more in depth understanding of a probability unit.

Further Investigation

The assignment can be extended by having students figure out the probability of other card games.



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

Kenney, M.J., & Hirsch, C. R. (Eds.). (1991). Discrete mathematics across the curriculum, K-12. Reston. VA; National Council of Teachers of Mathematics.

Last updated January 16, 1997