## Chain of Changes

Here is a set of shapes. For this problem we will call them *pieces*.

Each of these pieces is either a different colour or a different shape from all the others.

These problems ask you to arrange the pieces in a line so that you change either colour or shape in the next piece along. If we start with a blue triangle the next shape has to be either another triangle or another blue shape. You may want to print and cut out a set of shapes from this sheet.

The first puzzle is to arrange all the shapes in such a line starting with the blue triangle and ending with the red circle. There are lots of different ways of doing it!

The second problem is to arrange the pieces in the same way, starting with the blue triangle and ending with the red circle, but to change first colour, then shape or vice-versa.

If you put a yellow triangle after the blue one and so change the colour, next you must put another yellow piece and so change the shape.

You will not be able to use all the pieces in this way but the problem is to see how many you can use.

**Why do this problem?**

This problem will help children to refer to the shapes by name and visualise the next shape to place in the pattern. They will need to look carefully at the properties of each shape. It will also encourage them to use a trial and improvement approach in solving problems.

### Possible approach

You will need plenty of Logic Blocks or of shapes cut out from this sheet which has two copies of each of the shapes. A full set of Logic Blocks can provide enough for four children, pairs or small groups depending on how the children are working. (One group has the large, thick pieces, one the
large, thin pieces and so on).

You could start with one of the pieces and ask children to describe it. Ask if they can find one which is the same shape but a different colour. Encourage the children to work in pairs or threes on the problem so that they are able to talk through their ideas with each other.

At the end you could invite children to share the different ways that they found of doing the first part of the problem. Then discuss why there was not a way of doing the second part using all the pieces. Children could also talk about the pattern that results in changing shape and colour alternately.

The work makes a good display using either the children's own drawings or paper copies of the pieces using

this sheet.

### Key questions

Are you going to change the colour or the shape this time?

Which shape are you going to use next?

Can you find another way of doing it?

Why can't you use all the shapes this time?

### Possible extension

Those who find these tasks straightforward could use a full set of Logic Blocks and also change the size and thickness of the pieces.

### Possible support

It might help some children to make their own chains which started with the blue triangle, but without specifying the end point.