This Popular Class Dice Game Can Be Extended Into a Whole Class Investigation

Greedy Pig

This popular class dice game can be extended into a whole class investigation.

Overview The class stands up, the teacher rolls a die and students score whatever is rolled. This is repeated, with students aggregating their scores. Students may sit down at any stage and hence keep their score to that stage. However, if the number 2 is rolled while they are standing up their entire score for that game is zero. Play 5 games. The investigative question then becomes When is the best time to sit down?

1. The class game The class all stand up and the teacher rolls a die. Everyone writes the number down in Game 1. This is their score so far. This repeats for a second number. The score for everyone so far is the total of the two rolls. Then the teacher announces: ”You get the first two rolls for free - but from now on if I roll a '2' (the 'killer' number) and you are still standing, your entire score for that game will be zero! So each player has to decide when to quit - you show this by sitting down. When you sit down, you do not add to your score anymore.” The teacher keeps rolling, pausing after each to allow students to quit if they wish. The game has a lot of 'drama' and fun. However, at this stage the teacher makes no comment at all about strategies or probabilities. That will come later. Announce you would like to play 5 games in all, and the data you are interested in is the grand total after the 5 games.

2. Collecting class data After the 5 games, invite students to come to the board and record their grand totals on a stem and leaf plot.

3. The investigative challenge: When is the best time to quit? - collecting strategies. The teacher now engages students in a discussion about what prompted them to sit down when they did? What was going through their minds that caused them to make the decision to sit down? The teacher listens to a range of reasons and lists them on the board.

Extensions : 4. Have we improved? Compare mean, mode and median. 5. Class data - 'back to back' stem and leaf graphs for comparison? 6. The 'vote' for which strategy seems best

One flexible way to use the activity is to have an initial whole class lesson as an introduction. After the context and variables have been introduced in this way, students could then extend the investigation into an individual major project . Different students could follow different investigative pathways that grow out of the initial context.