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Cut it Out

Can you dissect an equilateral triangle into 6 smaller ones? What number of smaller equilateral triangles is it NOT possible to dissect a larger equilateral triangle into?

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Tessellating Transformations

Can you find out how the 6-triangle shape is transformed in these tessellations? Will the tessellations go on for ever? Why or why not?

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Triangular Hexagons

Investigate these hexagons drawn from different sized equilateral triangles.


Stage: 2 Challenge Level: Challenge Level:1


Find all the DIFFERENT shapes that can be made by joining five equilateral triangles edge to edge.

Here's an example:

1 or 2?

You might like to use this interactivity to try out your ideas. Click the red triangle to make a new triangle appear. You can move the triangles around by dragging with your mouse. If you hover your mouse over a corner, you will see a white circle where you can click to rotate the triangle.

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Why do this problem?

This activity is good for giving pupils the chance to explore shapes, order their solutions and create a system for getting all the solutions. It will provoke much discussion, encouraging learners to articulate their own ideas so providing a need to use appropriate vocabulary.

Possible approach

It would be good to have some time together using the interactivity on an interactive whiteboard. You could start by making a few examples as a whole group so that the aims are clear.

Give children time to explore other arrangements in pairs, using triangles cut from paper or card, or plastic shapes if you have them. If you do not have a large supply of these, you'll perhaps want to encourage pupils to record their arrangements in some way - isometric paper would be helpful.

Key questions

How are you checking that you have not got any of them twice?
Can you tell me about the way you're finding new arrangements?

Possible extension

What about getting pupils to ask "I wonder what would happen if we ...?"

Possible support

It would be a good idea to start with the Triangle Animals problem which involves making the different arrangements of three triangles.