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?

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

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?

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

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.

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?

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?

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?

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

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

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

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?

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

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

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?

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

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

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

Which of these dice are right-handed and which are left-handed?

Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

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

A game for 2 players. Given a board of dots in a grid pattern, players take turns drawing a line by connecting 2 adjacent dots. Your goal is to complete more squares than your opponent.

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?

Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?

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

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

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

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

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 Little Fung at the table?

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 the child walking home from school?

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

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

How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!

A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?

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?

An extension of noughts and crosses in which the grid is enlarged and the length of the winning line can to altered to 3, 4 or 5.

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

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.

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

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

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

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