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The 24 Game

Age 7 to 11 Challenge Level:

Why do this problem?

Many people are familiar with the 'four fours' problem, in which four 4s are combined using different operations to produce all the numbers up to 100 (and beyond). This problem which is inspired by the 24 game is a variation on this, reinforcing mental arithmetic, estimation and the importance of the order of operations.

Possible approach

You could begin this with a brief whole class introduction and then give the children time to work in pairs. Write $4+6+6+8$ and ask what the end answer is ($24$).
Write $8\times 6 - 4 \times 6$.
What do the children notice? If necessary, write another calculation such as $(6 + 6) \times8 \div 4$ and again ask what they notice. You may need to remind them about the order of operations. By now there should be a consensus that the answers are the same, and so are the numbers used to make them.

As the children find other solutions, collect them somewhere centrally (and preferably where they won't be erased). Looking at ideas that others have had often provokes children into trying new ideas themselves.

Key questions

Does the order in which we write and do the calculation matter?
How many different solutions do you think there will be?

Possible extension

You could read Opening Out by Bernard Bagnall for ideas for extension activities.

Possible support

You could provide cut out cards with the four numbers and several copies of each symbol for manipulation, and perhaps a calculator for checking the answer. In that way all the class are taking part in the same activity, rather than some doing a simplified version.