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.

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

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

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.

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

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 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 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.

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

A toy has a regular tetrahedron, a cube and a base with triangular and square hollows. If you fit a shape into the correct hollow a bell rings. How many times does the bell ring in a complete game?

Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?

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?

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 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?

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

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!

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

How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?

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

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

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 shape. How would you describe it?

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

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

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

Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

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?

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

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 the watering can and man in a boat?

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.

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

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

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

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

A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?

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

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

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 Ming playing the board game?

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

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 chairs?

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

Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.

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

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