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

Choose a box and work out the smallest rectangle of paper needed to wrap it so that it is completely covered.

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?

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 outline of Granma T?

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?

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 outline of Little Ming?

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 telephone?

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

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 logically construct these silhouettes using the tangram pieces?

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

Can you find ways of joining cubes together so that 28 faces are visible?

10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?

Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

What is the best way to shunt these carriages so that each train can continue its journey?

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

What shape has Harry drawn on this clock face? Can you find its area? What is the largest number of square tiles that could cover this area?

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

What is the total area of the four outside triangles which are outlined in red in this arrangement of squares inside each other?

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

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 Little Fung at the table?

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.

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

Can you fit the tangram pieces into the outline of these convex shapes?

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

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

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

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

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

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

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

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

Investigate the number of paths you can take from one vertex to another in these 3D shapes. Is it possible to take an odd number and an even number of paths to the same vertex?

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 these clocks?

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 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?

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

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 this shape. How would you describe it?

Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?

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