Discovering Dominoes (Anne Smelker)
(1) Students will explore counting techniques, permutations, and combinations.
(2) Students will develop their combinatorial reasoning and learn to count without actually counting or applying formulas to count.
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 building strong combinatorial reasoning skills and the ability to apply the tools of counting, permutations, and combinations, with the reasoning process (not just applying formulas) while developing problem solving and critical thinking skills.
A domino is a rectangle formed by two congruent squares. Each square contains an orderly pattern of "pips" or dots representing a number from zero through six. Explore and develop methods and strategies to solve the following problems involving dominoes.
(1) Discuss the problem statement with the students.
(2) Encourage students to organize the situations with dominoes.
(3) Have students work in small groups to explore and investigate the problems.
(4) As a class, have each group share and discuss their methods and/or strategies they developed to solve the problems.
(5) Discuss student's methods and/or strategies, how they developed their methods, what data organization they used, and how their methods/strategies relate to counting, permutations, combinations, and graph theory
"Discovering Dominoes" activity sheet
Introduction of Problem Statement (5 minutes), Group Work (20 minutes), Presentations/Class Discussion (20 minutes)
Discrete Mathematics Concepts
Counting Techniques, Combinatorial Reasoning, Permutations, Combinations, Graph Theory
Related Mathematics Concepts
NCTM Standards Addressed
Problem Solving, Communication, Reasoning, Connections, Algebra, Geometry, Discrete Mathematics
Colorado Model Content Standards Addressed
Geometric Techniques (4), Problem Solving Techniques (5), Linking Concepts and Procedures (6)
This activity could be integrated into an Algebra or Geometry class when introducing combinatorial reasoning.
Try other board games such as Triominoes or other related games.
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.