## Egyptian Rope

The ancient Egyptians were said to make right-angled triangles using a rope which was knotted to make $12$ equal sections.

If you have a rope knotted like this, what other triangles can you make? (You must have a knot at each corner.)

What regular shapes can you make - that is, shapes with equal sides and equal angles?

### Why do this problem?

This problem is one that combines knowledge of properties of shapes while using the operations of addition, subtraction, multiplication and division with small numbers. It also provides an opportunity for learners to consider the effectiveness of alternative strategies.

### Possible approach

You could use this problem during work on either number or shape. It could be introduced by looking at the picture of the triangle made from rope and asking children what they see. If it does not come up naturally, draw their attention to the fact there are twelve sections in the rope and ask learners to investigate other possible triangles, using headless matches (or something similar such as lolly sticks or cut-up drinking straws). It would be a good idea to work in pairs so that they are able to talk through their ideas with a partner.

They could then go on to the second part of the problem to find regular shapes that can be made using all twelve sticks.

At the end of the lesson it would be useful to discuss why no other triangles are possible with the twelve sticks. Some children may well have come up with 'rules' for the possible triangles which would be worth talking about together.

### Key questions

Why do you think these two sides will not make a triangle with the other sticks?
How do you know you have found them all? Can you tell me why no other ones are possible?
What numbers are factors of $12$? Can this help you to make some regular shapes?

### Possible extension

Learners could investigate the possible triangles made with different numbers of sticks as in the problem Sticks and Triangles.

### Possible support

Having twelve sticks of equal length (such as headless matches, or even pencils) to build the shapes makes this problem accessible to all children.