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## 'Tangram Tangle' printed from http://nrich.maths.org/

## Tangram Tangle

The square below has been cut into two pieces:

It is possible to fit the pieces together again to make a new shape.

If you must match whole sides to each other so that the corners meet, how many new shapes can you make?

Watch out for shapes which are really the same but just turned round or flipped over.

You could download this sheet which contains four copies of the square.

Alternatively, experiment with the interactivity below. You can rotate a shape by holding the mouse over a corner. Click on the stars to flip the shapes over.

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### Why do this problem?

This activity invites discussion amongst pupils which will encourage them to use vocabulary associated with position and transformations.

### Possible approach

The problem could be introduced using the interactivity so that it is easy for everyone to see clearly. However, it is also important for children to have paper or card copies of the shapes to work on the activity. This sheet contains four copies of the square or you could make
your own on squared paper (the line dividing the square in two is drawn from one corner to the midpoint of the opposite side). It may be a good idea to use paper which is coloured on one side only and talk about whether the new shape should be the same colour all over.

Encouraging learners to be systematic in their discovery of 'new shapes' is important if they are going to be asked how they "know" they have found every solution. Look out for those children who have developed a system and ask them to share their method with the whole group. For example, they might keep one shape fixed and find all the ways of placing the second shape.

### Key questions

How will you record your findings?

How do you know you have found all the shapes?

### Possible extension

Invite children to make another cut so that they have three pieces. How many new shapes can they make now? What cuts make the 'best' new set of shapes?

### Possible support

Having several copies of the square will mean that children can stick down each arrangement.