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

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?

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

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

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 this shape. How would you describe it?

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

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

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

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

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?

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

Can you cut up a square in the way shown and make the pieces into a triangle?

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?

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

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.

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

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

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

Make a mobius band and investigate its properties.

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?

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 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?

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 outline of this plaque design?

Can you logically construct these silhouettes using the tangram pieces?

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

Can you fit the tangram pieces into the outline of this sports car?

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 ...

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

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.

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?

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

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.

How many models can you find which obey these rules?

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?

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 telephone?

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