Evens and Odds (Jill Long)
1) Students will begin to look at the strategies behind playing games.
2) Students will work in groups to come up with a group solution.
This activity starts off with a skit where a swindler is trying to con a young college student into playing a game. It seems apparent to all that it is a fair game. The students will be playing the same game in their groups. They need to try and decide if the game really is fair, what the best possible strategy is, and which player they would choose to be.
I would let the skit speak for itself. You may want to talk about games like this in New York for example where people really do get swindled.
1) Have a couple of the students act out the skit for the class.
2) Have the same two students actually play a round or two.
3) Break off into pairs and get started. Stop and trade partners after 5 minutes.
4) Have the small groups work on answering the questions asked.
5) Come back as a class and discuss findings. Maybe have a couple of groups play each other using their strategies to see if they work.
Skit (5 min), group playing time (10 min), group work (15 min), presentations (10 min)
Discrete Mathematics Concepts
Game theory, strategies, payoff matrix, row minimum and maximum, strictly determined game
Related Mathematics Concepts
NCTM Standards Addressed
Problem solving, communication, reasoning, connections, algebra, probability, discrete mathematics
Colorado Model Content Standards Addressed
Algebraic Techniques (2), Problem Solving Techniques (5), Linking Concepts and Procedures (6)
This activity could be used at any level when looking at matrices. It could be integrated into a discrete mathematics unit at any level also.
After working with this particular game, look at another simple game such as rock, paper, scissors.
Crisler, N., Fisher, P., & Froelich, G. (1994). Discrete mathematics through applications. New York: W.H. Freeman and Company.
Fisher, David. (1996) University of Colorado at Denver. Math 5794.