Why do this problem?
offers a good context in which to explore possible outcomes and to think systematically about what scores are possible. It will be important for learners to develop a recording or listing system that they are happy with, in order to find all the possible ways in which the different totals can be
You could start by encouraging the group to try playing the game a few times and then pool their results of 'winning numbers'. It is not necessary to have the star or counters - you could just write the numbers $1$ to $12$ on a piece of paper and put ticks against the numbers that come up. However, it is more appealing to use the star. Here is a coloured copy of the board which could be printed off for pupils to use and here is one in black and white
that can be photocopied .
Then learners could then work in pairs so that they are able to talk through their ideas with a partner. Encourage them to make a table of possible outcomes.
At the end you could ask them the questions which conclude the actual problem:
Which are good numbers to choose? Why?
Which are poor numbers to choose? Why?
Which is the worst number to choose? Why?
The 'Why' part of the question is very important - encourage children to justify their responses based on the number of ways of making the numbers using two dice.
What totals are possible when you roll two dice?
Which totals are more likely to come up? Why?
Pupils could be challenged to make a version of the game which was fairer.
Some children will find it useful to manipulate dice as they work out the possible outcomes.