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Why do this problem?
offers the opportunity for children to work on some mathematics that might be meaningful to them, and therefore engaging. At a basic level, it involves counting, but it is a good context in which children can be encouraged to identify and explain patterns using their knowledge of factors and remainders.
You could start by having a pair of volunteers standing up together so that everyone can see them. Ask the children to imagine that they are going to play a game of tag, or something similar. How would they choose who was going to be 'it' i.e. the person to do the chasing? Take some suggestions, which might involve some rhymes that are currently popular. You could choose to
go with one of these, or introduce the "Ip dip ..." rhyme with which some might already be familiar. (The important point at this stage is that the rhyme identifies the person to be 'it' straight away, having said it only once.)
Say the chosen rhyme together a few times so that everyone feels they know it well and then indicate that you're going to find out who is going to be 'it' from the two volunteers. Say the rhyme while pointing to the children alternately. You could then pose the question about who you would start the rhyme on if you wanted to be chosen. Give the whole group a chance to
talk in pairs about this, then test out their ideas. You can then encourage pairs to work together to discover where you would position yourself if there were three of you ... four ... five etc.
It may be appropriate to stop everyone after some time to share ideas so far. This might involve some pairs explaining how they are approaching the problem and sharing some possible ways of recording what they're doing.
In the plenary, you can agree on solutions for the different numbers of people but also encourage children to talk about what they notice and to explain why where possible. How could they predict where to stand if there were seven people, for example, or ten people or a hundred people? Some might find it tricky to articulate where to stand for fewer than eight people, but a few
demonstrations with larger numbers will mean they are able to explain where to be for eight or more relatively easily. Can they tell you why eight is the 'key' number?
What numbers of people have you tried? What did you find out?
How are you going about this problem? Tell me what you've done.
How will you remember what you've found out?
Do you notice any patterns?
Can you explain the patterns?
Some children may like to try with another version of this rhyme which makes the analysis much more tricky: "Ip dip sky blue! Who's 'it'? Not you!" so that a person is 'knocked out' each time and the only person left is 'it'. What happens when there are two people? Three? Four etc? Can they see any patterns emerging? Can they explain why the
patterns occur? Similarly, learners might like to test out the best places to be positioned for a rhyme of their choice.
Having counters or other objects available to represent people might help some children.