## The Twelve Pointed Star Game

This game is for two or more players.

You will need a copy of the star board, counters and two 1-6 dice.

Each player chooses three numbers on the star. (If you play with more than four players, each player chooses two 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.* *

The winner is the first player to have counters on all three circles belonging to one of their chosen numbers.

*For example I'm playing with my friend Zac. I choose the numbers 2, 4 and 6; Zac chooses 7, 8 and 9.*

Zac rolls the dice and it's a 4 and a 2, which makes a total of 6.

This means I can put a counter on one of the circles next to the 6.

Play the game a few times.

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, or one pair playing against another pair so that they are able to talk through their ideas with a partner.

Once they have got a good 'feel' for the game, you could ask them:

Which are good numbers to choose? Why?

Which are poor numbers to choose? Why?

Which is the worst number to choose? Why?

Give them time to consider these questions and as they work, listen out for pairs who have a sense of being able to make the totals in different ways. In a mini plenary, you could encourage some learners to share ways of working, which might include ways of working systematically to find all possibilities for each total.

The 'Why' part of the questions is very important - encourage children to justify their responses based on the number of ways of making the numbers using two dice. You may like to bring everyone together to work on finding all possibilities together as a whole group.

### 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.