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Odds or Sixes?

Stage: 2 Challenge Level: Challenge Level:1

Odds or Sixes?

You can use the computer to see what happens when Tania and Derek are playing a game with a dice. They roll the dice. If the number is odd, Tania wins that round.
If the number is a six, Derek wins.
(It doesn't matter who throws the die.)
Who is more likely to win the game? Why? How could you make the game fair?

You might like to use the interactivity below which will roll the dice many times.
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This text is usually replaced by the Flash movie.

Why do this problem?

This problem gives learners the opportunity to describe and predict outcomes, and consider the meaning of 'fair'. The interactivity simulates the die-throwing, so data can be collected quickly and easily.

Possible approach

You could introduce this problem either by using the interactivity or by having two children come to the front to play it. Whichever way you choose, play the game a few times and if not using the interactivity, record the outcomes on the board. Ask the class to predict what would happen if the game was played many times, for example $100$ times. Take suggestions from the children, looking out for those who justify their answer based on the few games which have already been played.

Suggest that the group tests out their theories. Again, this could be done using the 'Run x100' button on the interactivity or by pairs throwing dice and then collating class results. Bring pupils together to talk about their findings and ask them whether the game is fair or not and why. Listen out for explanations which compare the number of possible winning throws using appropriate vocabulary. Some children might quantify the probability of throwing a six, for example, as $1$ out of $6$ or $\frac{1}{6}$ whereas throwing an odd number is $3$ out of $6$, or $\frac{1}{2}$.

It would be useful to encourage children to talk in pairs about what they understand as 'fair' - there will be different, but equally as valid, ideas about how to change the game.

Key questions

What numbers are possible to throw on the dice?
Who would win with each number?
Can you use this to decide how to make the game fair?

Possible extension

Learners could try Odds and Evens which extends the ideas in this problem.

Possible support

Having dice available will help those children who are not familiar with them and playing the game for themselves would also be of benefit.