Odds or Sixes?

Play this dice game yourself. How could you make it fair?

Age

7 to 11

Challenge level

Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving

Being curious Being resourceful Being resilient Being collaborative

Problem

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?

Teachers' Resources

Odds or Sixes?

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?

Why do this problem?

This problem gives learners the opportunity to describe and predict outcomes, and consider the meaning of 'fair'.

Possible approach

You could introduce this problem either by having two children come to the front to play it. Whichever way you choose, play the game a few times and 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. This could be done 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.

Or search by topic

Number and algebra

Geometry and measure

Probability and statistics

Working mathematically

Advanced mathematics

For younger learners

Odds or Sixes?

Problem

Getting Started

Student Solutions

Teachers' Resources

Odds or Sixes?

Why do this problem?

Possible approach

Key questions

Possible extension

Possible support