Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

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

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?

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?

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?

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

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

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

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

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?

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

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

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.

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?

Find your way through the grid starting at 2 and following these operations. What number do you end on?

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?

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

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

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?

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.

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

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

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?

Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.

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

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.

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

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?

How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

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?

What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?

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?

Here are shadows of some 3D shapes. What shapes could have made them?

Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?

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

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.

Imagine a 3 by 3 by 3 cube made of 9 small cubes. Each face of the large cube is painted a different colour. How many small cubes will have two painted faces? Where are they?

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

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

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?

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

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