## Teddy Bear Line-up

Lachlan was playing with his bear counters.

He had four blue, then four red followed by four yellow and finally four green bears.

"What are you doing now?" Jenni asked.

"I want to arrange them so that no two bears of the same colour are next to each other", he said.

"That's easy!" cried Jenni.

"Ah, but you have to do it in the least number of moves possible", replied Lachlan.

What's the least number of moves you can take to rearrange the bears?

### Why do this problem?

This problem requires children to develop a logical way of moving the teddy bears and in doing this they may well use visualisation to plan ahead. Therefore, it offers an opportunity to talk about visualisation with young children.

### Possible approach

Many opportunities arise in the classroom for you to invite children to explore this task, for example after a story or poem relating to bears or as an extension to another mathematical activity when children are using counters. The initial part of the activity, when the arrangement of bears is set up, involves counting, sorting and pattern, and so is valuable in itself.

It would be a good idea to begin by introducing the problem with just four bears, two of one colour and two of another colour. If you don't have any plastic bears, you could use any other suitable toys which are differently coloured. (Or counters as a last resort!) Line the bears up so that those of the same colour are next to each other and ask children to think on their own which bear they would move first, and then to talk to a partner. Share ideas, and encourage learners to give a reason for their suggestions. Some children will be picturing the new line-up of bears and this is a good opportunity to draw attention to how useful 'seeing something in your mind' can be for planning what to do in this problem. Of course there are different ways to arrive at a solution, so it would be useful to record them (the children may have good ideas about how to do this). Make sure the group can see that in this case, we can do it in just one move. You could then introduce a third colour bear so that you have nine bears altogether, before going on to the main challenge of sixteen bears.

Ask the children to work together so they have to engage in mathematical conversation as they explain their plans and negotiate which strategy requires the least number of moves. When you bring the whole group together, you can ask for suggestions as to how to solve the challenges, but you may also want to encourage children to notice the similarities between the strategies for two, three and four bears of each colour and so to try and make some general observations.

### Key questions

Have you got a good idea about how to move the bears?
Which bear could you move next?
How do you know how many moves you have made?
How will you remember the moves you have made?

### Possible extension

Some children will be able to extend the activity by using sets of five or more bears. To extend their thinking and use their prior experience, before carrying out the follow up activity children should be encouraged to predict how many moves it will take to rearrange sets of five or more bears and to explain what evidence they are basing their prediction on.

### Possible support

It might help some children to label the bears with numbers or letters to help with recording. Alternatively, taking pictures of each move would be a nice way to display a strategy.