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## 'Posting Triangles' printed from http://nrich.maths.org/

## Posting Triangles

How many different ways can you post this triangle into the black hole?

A dot has been drawn on the triangle to help you keep track.

The triangle is yellow on the other side.

If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?

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### Why do this problem?

Tackling

this problem will give a context in which children can explore transformations and begin to get an idea of working systematically. It introduces ideas of symmetry without introducing the word itself. Instead it builds on the notion of posting shapes into a shape sorter which is part of essential pre-school mathematical experience for
all children.

### Possible approach

The activity can be introduced by using the interactive version or a real shape sorter that you might borrow from the EYFS department. Mark one corner of the shape and look at ways of posting it into the slot. Keeping track of the options you have tried is tricky and introduces the children to the importance of recording in geometric problems. They may decide to use drawings to help them.

The children could go on to try the task for themselves either working with a shape sorter or on computers.

### Key questions

How many different positions can you find for the black dot to be in when the blue side is facing up?

How about when the yellow side is facing up?

### Possible extension

Children could use other shapes from a selection to create their own 'slot' and ask their own questions.

### Possible support

Using a triangle from a selection of shapes and a shape sorter might help children picture this more easily. It might also be helpful to create laminated shapes like the triangle which are blue on one side and yellow on the other and which have one corner marked with a dot. A template sheet with black shapes which they have to match would also help. This will enable the children to make a series
of pictures showing the different way of posting the shapes and save them the task of recording their results.

This sheet of equilateral triangles could be printed off on different colours of paper/card and laminated as necessary.