Analyzing games of chance

This is a concept development lesson that is designed to help students to:

• Overcome common misconceptions about probability
• Count equally likely outcomes using diagrams
• Discuss relationships between theoretical probabilities, observed outcomes and sample sizes

The lesson begins with a horse ‘race’ game. A grid is given with horses numbered from 2 to 12 along the left hand edge, with each horse having to move 12 squares to cross the finishing line. Two dice are rolled and their scores are added, the horse with that number advances by one square. It is intended that students play in pairs, so that there are several horse races to review as a class.

Having worked on the initial race together, various other rules are presented for the horse race. The task is to assess which horses are most likely to win, and then test out the games to see if the predictions are correct.

There are pre-lesson and post-lesson formative assessment tasks. Detailed teacher notes give suggestions on questioning and how to use the resources. Full solutions are given for each of the sections.

This is a concept development lesson from the Mathematics Assessment Resource Service, a collaboration between UC Berkeley and the Shell Centre team at the University of Nottingham. Further information on the collection is given here.