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 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?

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

Can you logically construct these silhouettes using the tangram pieces?

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

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 outline of this goat and giraffe?

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

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

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

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

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.

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.

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

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

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 mobius band and investigate its properties.

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 Little Fung at the table?

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

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

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 this telephone?

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?

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

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 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 the rocket?

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 this shape. How would you describe it?

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

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

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

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

Watch the video to see how to fold a square of paper to create a flower. What fraction of the piece of paper is the small triangle?

What is the largest number of circles we can fit into the frame without them overlapping? How do you know? What will happen if you try the other shapes?

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

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

How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.

How many models can you find which obey these rules?

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.

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