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The Hair Colour Game

Age 7 to 11
Challenge Level

Mrs Bunting's class was playing a game using interlocking cubes. All the boys took a red cube and all the girls took a green cube.

Then the children took a black cube if they had dark coloured hair and a yellow cube if they had light coloured hair. They stuck their two cubes together.

The pairs of cubes looked like this:

pairs of cubes
The children then got into four groups according to their pair of cubes.
Can you explain what these pairs of cubes stand for?
Mrs Bunting showed them a way of recording the way they had sorted themselves into different groups, called a tree diagram.
At the bottom were all the pairs of cubes. Then they divided into two branches. The red cubes went to the left and the green cubes went to the right.
Then they divided into whether they had black cubes or yellow cubes. Now there were four branches.
Here is the tree diagram:

tree diagram

The next day they did the same again except that this time, they had three cubes each. As well as a having a green or red and a yellow or black, they took a brown cube if they had brown eyes and a blue cube if they had blue eyes.

2 cubes
How many different groups were there then? Can you draw the new tree diagram?
What happens if no one had dark hair and blue eyes? How could you show that?