Three Squares

What is the greatest number of squares you can make by overlapping three squares?

Chain of Changes

Arrange the shapes in a line so that you change either colour or shape in the next piece along. Can you find several ways to start with a blue triangle and end with a red circle?

Halving

These pictures show squares split into halves. Can you find other ways?

Tangrams

Tangrams

 The tangram is based on the dissection of a square into seven pieces. Can you make other squares using some, not all, of the pieces? Can you make five different squares? What is the smallest square you can make? What is the largest?

You might find it helpful to print and cut out one of the tangrams on this sheet.

Why do this problem?

Not only will children be using their knowledge of properties of squares as they try this activity , but they will also be putting into practice their visualising skills. Tangrams can be great to work on in pairs and this will encourage the pupils to talk together about what they are doing - a great opportunity for you to listen!

One of the main benefits of tangrams is the ability to manipulate the pieces; to "play" with the shapes and get a feel for the challenge. For this reason, it would be a good idea to encourage pupils to print off and cut out the shapes for themselves from this sheet.

Key questions

How many pieces have you got altogether?
What could you put with this piece to make a square?
Are all the pieces different?
What's the smallest square you can make?

Possible extension

To find more tangrams on the site (many of which have interactivities), enter 'tangram' in the top right-hand search box.

Possible support

You may have to encourage some children to experiment and 'have a go'.