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Flippin' Discs

Age 11 to 14 Challenge Level:

Why do this problem?

This problem offers an opportunity to explore and discuss two types of probability: experimental and theoretical. The simulation generates lots of experimental data quickly, freeing time to focus on predictions, analysis and justifications. 

The interactivity starts with a simple context of just two discs with two equally likely outcomes, together with a visual way of representing successive trials. As students work on the problem, they can increase the number of discs and switch between representations, before moving on to other related probability tasks. For more information about Low Threshold High Ceiling tasks, you may be interested in this article.

Possible approach

Introduce the problem, and invite students to make hypotheses about the likelihood of winning with two discs. Encourage them to explain their thinking and try to justify their hypotheses.

Run the simulation, once, then again and again, so that pupils are confident with what the computer is doing. Then run it 100 times and ask the pupils to comment on/explain the result. (Click on the tabs in the right hand pane of the interactivity to switch between the graphical visualisation and the table of results.)
 
Record the result for two discs on the board before moving onto three discs.

Invite students to think for a minute on their own about what will happen with three discs. Ask them to justify their conjectures with a partner and then the whole class. Use the interactivity to demonstrate what happens. Students could then work in pairs, to explain the results.

You may like to stop the group part way through their work in order to talk about useful representations that they have devised. This could be an opportunity to introduce tree diagrams, sample space diagrams, or the systematic listing of outcomes.

Students could then use the different representations to work out the theoretical probability of winning for 4, 5, and $n$ discs.
 

Key questions

What does it mean if a game is fair?
How can you decide if a game is fair?
How many trials do we need to be confident of the likelihood of winning?
How can we record all the different possible combinations?
How do we know we haven't missed any possibilities?
 

Possible support

Students could use coins or double-sided counters to help them see all the possible outcomes, and this Recording Sheet to keep a record of the outcomes.

Teachers can also use this recording tool to gather the results of other similar experiments that their students are carrying out:
 

Possible extension

Students could also work on Odds and Evens, Cosy Corner, and Two's Company.