The challenge for you is to make a string of six (or more!) graded cubes.

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.

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?

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

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

Can you fit the tangram pieces into the outlines of the candle and sundial?

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

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?

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

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

What are the next three numbers in this sequence? Can you explain why are they called pyramid numbers?

Make a mobius band and investigate its properties.

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?

For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...

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

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

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

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

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

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

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

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

What shape is made when you fold using this crease pattern? Can you make a ring design?

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

Can you logically construct these silhouettes using the tangram pieces?

Here's a simple way to make a Tangram without any measuring or ruling lines.

Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?

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.

This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!

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?

Have a go at drawing these stars which use six points drawn around a circle. Perhaps you can create your own designs?

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

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

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

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

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?

Can you fit the tangram pieces into the outline of this telephone?

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

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 this shape. How would you describe it?

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.

How can you make a curve from straight strips of paper?

Reasoning about the number of matches needed to build squares that share their sides.

Can you fit the tangram pieces into the outlines of the watering can and man in a boat?