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The Twelve Pointed Star Game

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

The Twelve Pointed Star Game

The game is for two or more players.
Each player chooses one, two or three numbers.
Players then take it in turns to roll two dice and add the scores.

The player who has chosen that number puts a counter on the appropriate circle.
(So for example there's me and my friend Zac. I choose $2$,$4$ and $6$, Zac chooses $7$,$8$ and $9$. Zac rolls the dice and it's a $4$ and a $2$ - so I can put a counter on $6$)
The winner is the first player to have counters on all three circles belonging to one of their chosen numbers.

board for game with 12 pointed star

Play the game a few times.
Here is a copy of the star which you can print off and use.

Which are good numbers to choose? Why?
Which are poor numbers to choose? Why?
Which is the worst number to choose? Why?

Why do this problem?

This game 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 made.

Possible approach

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.

Key questions

What totals are possible when you roll two dice?
Which totals are more likely to come up? Why?

Possible extension

Pupils could be challenged to make a version of the game which was fairer.

Possible support

Some children will find it useful to manipulate dice as they work out the possible outcomes.