Challenge Level

This problem offers a context in which children will need to look carefully at the properties of each shape. They can be encouraged to refer to the shapes by name and to visualise a possible next shape in the pattern. The problem lends itself to a trial and improvement approach, as well as providing opportunities for mathematical reasoning.

If you have sets of 'Logic Blocks', or similar, then learners would benefit from using them to tackle this challenge. (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). Alternatively, you could use sets of the shapes cut out from this sheet (which contains two of each shape). If having practical shapes is not possible, then learners could use the interactivity in pairs on a tablet or computer. The interactivity can provide a useful way of sharing ideas during the lesson, even if practical resources are being used by the children themselves.

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. In this way, you could build up the idea of the pattern in the problem. To check that learners have grasped the pattern, you could offer the images of the start of two sequences (or make them yourself using the interactivity, or the hands-on shapes) and invite them to say which obeys the 'rule' and which does not. How do they know?

Encourage the children to work in pairs or threes on the main challenge so that they are able to talk through their ideas with each other.

In the plenary, you could invite children to share some of the different patterns they have created that fit the 'rule'. How many shapes does each use? Did any pair create a pattern with more shapes? Listen out for those who have a sense of why it is not possible to use all twelve shapes following this particular rule.

The work would make an engaging display using either the children's own drawings or paper copies of the pieces using this sheet.

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

So, which shape are you going to use next?

Can you find another way of doing it?

Can you do it another way and use more of the shapes?

Can you use *all* the shapes? Why or why not?

Encouraging children to say the sequence out loud (e.g. "red circle, yellow circle, yellow rectangle, blue rectangle...") will help them identify and extend the patterns.

Those who find these tasks straightforward could use a full set of Logic Blocks and so coudl also use the attributes of size and thickness as they create their own patterns.