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

Have you ever tried tessellating capital letters? Have a look at these examples and then try some for yourself.

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

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

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

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 the telescope and microscope?

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

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

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?

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

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?

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

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?

What does the overlap of these two shapes look like? Try picturing it in your head and then use the interactivity to test your prediction.

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

Here are more buildings to picture in your mind's eye. Watch out - they become quite complicated!

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

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?

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 the child walking home from school?

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 clocks?

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

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

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 plaque design?

Can you fit the tangram pieces into the outline of this shape. How would you describe it?

Can you work out what kind of rotation produced this pattern of pegs in our pegboard?

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

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 these convex shapes?

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 junk?

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

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

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

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 picture where this letter "F" will be on the grid if you flip it in these different ways?

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

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

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?

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

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