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?

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

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 Mai Ling?

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

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

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

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

This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?

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

We can cut a small triangle off the corner of a square and then fit the two pieces together. Can you work out how these shapes are made from the two pieces?

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?

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.

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 outlines of these clocks?

Can you fit the tangram pieces into the outline of Little Fung at the table?

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 this goat and giraffe?

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 Little Ming playing the board game?

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

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 this sports car?

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

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

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

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

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

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

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 outlines of these people?

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?

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

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

Can you split each of the shapes below in half so that the two parts are exactly the same?

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

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

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?

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

Draw three straight lines to separate these shapes into four groups - each group must contain one of each shape.

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

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?

Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?

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?

Design an arrangement of display boards in the school hall which fits the requirements of different people.