### Baked Bean Cans

Is there a best way to stack cans? What do different supermarkets do? How high can you safely stack the cans?

### Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

### Tea Cups

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

# Ip Dip

## Ip Dip

"Ip dip sky blue!  Who's 'it'?  It's you!"

Have you ever used this rhyme to decide who is 'it' in a game?

If you were playing a game with one friend and you wanted to be chosen to be 'it', would you start the rhyme, pointing at yourself or your friend?

If there were three of you, how would you position yourself so that you were sure you'd  be chosen?

How about with four of you?  Five ...? Six ...?  Seven ...? Eight ...? Nine ...?  Ten ...?  And so on?

How would you predict where you should stand to be chosen for any number of players?

### Why do this problem?

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.

### Possible approach

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?

### Key questions

What numbers of people have you tried?  What did you find out?