Putting Two and Two Together

This problem encourages children to work in a systematic way to find all possibilities and it gives a context for analysing properties of triangles.

It is essential to have cut-out triangles available for the children to manipulate while working on this problem. You can print off these sheets, if possible on coloured card.

A good way to introduce the problem would be for children themselves to investigate the different ways (in fact only one) you can put two yellow (equilateral) triangles together. This will allow you to emphasise what we mean by "different". Using the interactivity on the interactive whiteboard will allow the children to show you the ways they have found and then you can look at them all together as a group, focusing on whether they really are different from each other. When looking at two green triangles, you could ask children to work in pairs. How do they know they have all the possibilities? You could invite some pairs to share the ways that they had worked systematically in order to know they hadn't missed any out.

Then give everyone an opportunity to predict how many ways two blue triangles can be fitted together - ask them to think carefully on their own, then chat to a partner, then talk about their predictions as a class. In discussion, encourage pupils to justify their predictions and then invite them to test them out.

How many ways have you found for putting together the yellow/ green/ blue triangles?

How do you know you have found all the possible ones?

Can you think of a reason why this is so?

How many sides of different lengths does that triangle have?