Discrete Mathematics Project

Counting Techniques Activity


Counting Techniques Practice (Anne Smelker)


(1) Students will explore the addition and multiplication principles of counting.

(2) Students will develop an understanding of counting techniques.


This activity will allow students the opportunity to develop their abilities to count various outcomes and explore different methods and principles to counting. This activity develops the foundation to then build a strong understanding and application of probability.

Problem Statement

Explore and develop methods to solve each of the situations. Discuss in groups how the methods and/or strategies were developed, how and why the methods developed may be different, why and when different methods are used.

Instructor Suggestions

(1) Discuss the problem statement with the students.

(2) Encourage students to organize the situations.

(3) Have students work in small groups to explore and investigate the situations. Divide groups so that some groups work on problems 1-4 (3 addition principle and 1 multiplication principle) and the other groups work on problems 2, 5-7 (1 addition principle and 3 multiplication principle).

(4) As a class, have each group share and discuss their methods and/or strategies they developed.

(5) Discuss student's methods and/or strategies, how they developed their methods, what data organization they used, ideas for developing counting principles and what criteria makes counting problems different.


"Counting Techniques" activity sheet


Introduction of Problem Statement (5 minutes), Group Work (20 minutes), Presentations/Class Discussion (20 minutes)

Mathematics Concepts

Discrete Mathematics Concepts

Counting Techniques, Addition Counting Principle, Multiplication Counting Principle

Related Mathematics Concepts


NCTM Standards Addressed

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

Colorado Model Content Standards Addressed

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

Curriculum Integration

This activity could be integrated into an Algebra or Geometry class when introducing probability.

Further Investigation


Having dice available for students to work with in groups may be helpful.


Crisler, N., Fisher, P., & Froelich, G. (1994). Discrete Mathematics Through Applications. New York: W.H. Freeman and Company.

Kenney, M. J., and Hirsch, C.R. (Eds.). (1991). 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.

The University of Chicago School Mathematics Project. (1992). Functions, Statistics, and Trigonometry. Glenview, IL: Scott, Foresman and Company.

Last updated January 15, 1997