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