Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?

Can you describe a piece of paper clearly enough for your partner to know which piece it is?

This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.

Try to picture these buildings of cubes in your head. Can you make them to check whether you had imagined them correctly?

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 this plaque design?

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 outline of the rocket?

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

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?

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

On which of these shapes can you trace a path along all of its edges, without going over any edge twice?

Eight children each had a cube made from modelling clay. They cut them into four pieces which were all exactly the same shape and size. Whose pieces are the same? Can you decide who made each set?

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

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

Imagine a 3 by 3 by 3 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will have holes drilled through them?

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

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

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 Little Fung at the table?

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 the telescope and microscope?

How can you paint the faces of these eight cubes so they can be put together to make a 2 x 2 cube that is green all over AND a 2 x 2 cube that is yellow all over?

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

Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?

Can you arrange the shapes in a chain so that each one shares a face (or faces) that are the same shape as the one that follows it?

Each of the nets of nine solid shapes has been cut into two pieces. Can you see which pieces go together?

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

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 workmen?

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 outlines of the candle and sundial?

Here are shadows of some 3D shapes. What shapes could have made them?

If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?

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

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?

How many balls of modelling clay and how many straws does it take to make these skeleton shapes?

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

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 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 this goat and giraffe?

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

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

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 outline of this brazier for roasting chestnuts?

A game has a special dice with a colour spot on each face. These three pictures show different views of the same dice. What colour is opposite blue?