Game ShowTask 162 ... Years 2  12SummarySo easy to state and so easy to start, but likely to lead to long debate. The compère of game show has three upsidedown opaque cups, one of which has an object underneath. The player points to the one they think has the object and the compère reveals what is underneath another that she knows doesn't have the object. The player has the opportunity to change their guess. The investigative question is Should the player change their mind or stick with the original guess?. 
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IcebergA task is the tip of a learning iceberg. There is always more to a task than is recorded on the card. 
The task invites students to design an experiment and gather empirical data. However, encourage them to first predict whether it is better to 'stick or swap'. As the cards states, whether to 'stick or swap' has caused significant argument in the past and many mathematicians who were involved in that argument reasoned incorrectly. The student's experiment will need to try the game with and without change of mind a sufficient number of times and record wins and losses. At least 20 times each way would be necessary before it becomes clear which choice is more likely to give wins. If it isn't clear after 20 experiments of each, then encourage more data to be collected. Eventually students will find that a win is more likely if the player changes their mind. In fact the statistics move towards a
One way to explain is:

Whole Class InvestigationTasks are an invitation for two students to work like a mathematician. Tasks can also be modified to become whole class investigations which model how a mathematician works. 
It's easy to get opaque plastic cups or an alternative so that this investigation can be run with the whole class and a small block, or dice, makes a perfect 'prize'. Then an outline of the lesson would be:
For more ideas and discussion about this investigation, open a new browser tab (or page) and visit Maths300 Lesson 60, Game Show, which includes software allowing many trials to be run very quickly. 
Is it in Maths With Attitude?Maths With Attitude is a set of handson learning kits available from Years 310 which structure the use of tasks and whole class investigations into a week by week planner. 
The Game Show task is an integral part of:
The Game Show lesson is an integral part of:
