Probability exploration in a game context: The dice difference game

Abstract

Overview of lesson Learning about probability poses difficulties for students at all levels. In this lesson students are asked to make predictions about the fairness of a dice difference game and then test them by gathering and examining data. Student predictions and conclusions are examined and re‐examined in interactions among small group members and whole class or group and teacher. This lesson also addresses some common misconceptions relating to probability of simple and compound events. Learning objectives • Deriving and comparing experimental estimates with theoretical model probabilities for two‐stage experiments (e.g., tossing two dice) • Generating and comparing experimental probabilities from multiple samples • Comparing experimental probability estimates with theoretical probabilities calculated from generating the sample space for the game and using theoretical probabilities to solve problems relating to “fair games” • Conducting investigations using the PPDAC cycle from a probabilistic perspective Suggested age range With modifications, the game can be used with 11 to 14‐year‐olds. Time required Two 60‐minute lessons may be required for the main part of the investigation.