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?

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 Mai Ling?

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!

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

Move just three of the circles so that the triangle faces in the opposite direction.

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.

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.

Take it in turns to place a domino on the grid. One to be placed horizontally and the other vertically. Can you make it impossible for your opponent to play?

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

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?

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

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

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

What happens when you try and fit the triomino pieces into these two grids?

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

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

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

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

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 brazier for roasting chestnuts?

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

Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?

Exchange the positions of the two sets of counters in the least possible number of moves

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

If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?

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

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

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 child walking home from school?

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?

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 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 outline of these rabbits?

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

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

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

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

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

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

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

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

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