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!

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

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.

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

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 brazier for roasting chestnuts?

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

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

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

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

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

Here are the six faces of a cube - in no particular order. Here are three views of the cube. Can you deduce where the faces are in relation to each other and record them on the net of this cube?

A game for 1 person. Can you work out how the dice must be rolled from the start position to the finish? Play on line.

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

Find a way to cut a 4 by 4 square into only two pieces, then rejoin the two pieces to make an L shape 6 units high.

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

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

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

Can you work out what is wrong with the cogs on a UK 2 pound coin?

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?

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?

A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.

A shape and space game for 2,3 or 4 players. Be the last person to be able to place a pentomino piece on the playing board. Play with card, or on the computer.

Can you fit the tangram pieces into the outline of Little Ming?

Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?

In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.

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

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

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 Granma T?

How many different triangles can you make on a circular pegboard that has nine pegs?

Can you make a 3x3 cube with these shapes made from small cubes?

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

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 outline of Little Ming playing the board game?

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?

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?

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

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

How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

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

What is the greatest number of squares you can make by overlapping three squares?

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

Imagine a 4 by 4 by 4 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will not have holes drilled through them?

An activity centred around observations of dots and how we visualise number arrangement patterns.

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

One face of a regular tetrahedron is painted blue and each of the remaining faces are painted using one of the colours red, green or yellow. How many different possibilities are there?