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Finding Fifteen


Tim had nine cards, each with a different number from 1 to 9 on it.
He put the cards into three piles so that the total in each pile was 15.
How could he have done this?

Can you find all the different ways Tim could have done this?

You may like to print off and cut out these digit cards to help you.

Why do this problem?

This task will encourage children to develop a systematic approach. It will also give them opportunities to practise simple addition.

Possible approach

Introduce the problem without saying too much more and then give children chance to have a go in pairs.  Having digit cards will help them try out their ideas without feeling inhibited.  Suggest that they record each solution on a different piece of paper, large enough so that it could be seen from some distance away.

After a while, bring the whole group together and invite several pupils to come up holding one of their solutions.  Keep adding to those standing at the front until the group doesn't have any more different solutions.  How do we know that there aren't any other solutions?  If no-one offers an idea, suggest to the children that they arrange the solutions in some kind of order or pattern which will then reveal any that are missing.  In this way, a system is imposed afterwards.  This will help them to see the value of working systematically on this kind of problem.

Key questions

How do you know you haven't got that solution already?
How will you know when you have found them all?
Can you convince me that you haven't left any out?

Possible extension

Investigating magic squares is a nice follow-on activity. The Fifteen game also links well.

Possible support

Having digit cards available will make this activity accessible for most children.