What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one?

We went to the cinema and decided to buy some bags of popcorn so we asked about the prices. Investigate how much popcorn each bag holds so find out which we might have bought.

What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?

What do these two triangles have in common? How are they related?

Make a cube out of straws and have a go at this practical challenge.

Exploring and predicting folding, cutting and punching holes and making spirals.

Follow these instructions to make a three-piece and/or seven-piece tangram.

Can you fit the tangram pieces into the outline of Mai Ling?

Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?

Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.

Can you fit the tangram pieces into the outlines of these people?

Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?

Using these kite and dart templates, you could try to recreate part of Penrose's famous tessellation or design one yourself.

This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?

Can you fit the tangram pieces into the outline of Little Fung at the table?

Can you fit the tangram pieces into the outline of Little Ming?

Make a cube with three strips of paper. Colour three faces or use the numbers 1 to 6 to make a die.

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

Can you fit the tangram pieces into the outlines of these clocks?

Make a flower design using the same shape made out of different sizes of paper.

Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?

Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?

Can you fit the tangram pieces into the outline of these rabbits?

Can you fit the tangram pieces into the outline of the telescope and microscope?

Can you fit the tangram pieces into the outline of this goat and giraffe?

Can you fit the tangram pieces into the outline of this plaque design?

How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?

Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?

Have you noticed that triangles are used in manmade structures? Perhaps there is a good reason for this? 'Test a Triangle' and see how rigid triangles are.

Can you fit the tangram pieces into the outline of this shape. How would you describe it?

Can you fit the tangram pieces into the outlines of the chairs?

Did you know mazes tell stories? Find out more about mazes and make one of your own.

Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?

Can you fit the tangram pieces into the outline of the child walking home from school?

Surprise your friends with this magic square trick.

Can you work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?

Can you visualise what shape this piece of paper will make when it is folded?

Can you fit the tangram pieces into the outline of the rocket?

Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?

These practical challenges are all about making a 'tray' and covering it with paper.

Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.

Have a look at what happens when you pull a reef knot and a granny knot tight. Which do you think is best for securing things together? Why?

Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.

Can you fit the tangram pieces into the outline of Granma T?

Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?

You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.

Can you logically construct these silhouettes using the tangram pieces?

How many models can you find which obey these rules?