**Title**

Counting Techniques Practice (Anne Smelker)

**Goals**

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

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

**Abstract**

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.

**Materials**

"Counting Techniques" activity sheet

**Time**

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*

Probability

**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
**

**Variations/Comments**

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

**References/Resources**

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.