Skip to main content
### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Tangram Tangle

## Tangram Tangle

### Why do this problem?

### Possible approach

### Key questions

### Possible extension

### Possible support

## You may also like

### Biscuit Decorations

Links to the University of Cambridge website
Links to the NRICH website Home page

Nurturing young mathematicians: teacher webinars

30 April (Primary), 1 May (Secondary)

30 April (Primary), 1 May (Secondary)

Or search by topic

Age 5 to 7

Challenge Level

- Problem
- Getting Started
- Student Solutions
- Teachers' Resources

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 try out your ideas using the interactivity below, or download this sheet which contains four copies of the square.

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

You may like to read our Let's Get Flexible with Geometry article to find out more about developing learners' mathematical flexibility through geometry.

It is important for children to have paper or card copies of the shapes to work on the activity, or to have access to a tablet/computer in pairs so they can use the interactivity. 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.

You could introduce the task using the interactivity projected onto the board, or by inviting learners to gather round some large printed pieces. You could begin by showing them the square made of the two pieces and simply ask what they see. As there are no right/wrong answers to this question, it is an accessible entry point for all children. Use the comments that learners make to introduce the task itself.

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. (There are many ways to be systematic, so try not to assume that everyone will use the same way as you!)

If it doesn't come up naturally, it might be helpful to ask the group how they are keeping track of the shapes they have found. If they are using the interactivity, a screenshot could be useful, or they could sketch the shapes they have created whether they are working on screen or using card. It might help some children to have many copies of the pieces so they can create each new shape and not have to re-use the pieces to find others.

How will you record your findings?

How do you know you have found all the shapes?

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?

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

Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated?