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.

Two circles of equal radius touch at P. One circle is fixed whilst the other moves, rolling without slipping, all the way round. How many times does the moving coin revolve before returning to P?

Use the blue spot to help you move the yellow spot from one star to the other. How are the trails of the blue and yellow spots related?

Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.

Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.

Can you make the green spot travel through the tube by moving the yellow spot? Could you draw a tube that both spots would follow?

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 fit the tangram pieces into the outline of the child walking home from school?

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

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

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 the chairs?

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

Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?

A red square and a blue square overlap so that the corner of the red square rests on the centre of the blue square. Show that, whatever the orientation of the red square, it covers a quarter of the. . . .

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

Show how this pentagonal tile can be used to tile the plane and describe the transformations which map this pentagon to its images in the tiling.

An interactive game to be played on your own or with friends. Imagine you are having a party. Each person takes it in turns to stand behind the chair where they will get the most chocolate.

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?

Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?

A game for 2 people that everybody knows. You can play with a friend or online. If you play correctly you never lose!

Overlaying pentominoes can produce some effective patterns. Why not use LOGO to try out some of the ideas suggested here?

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

Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?

Can you complete this jigsaw of the multiplication square?

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

Use the interactivity to move Mr Pearson and his dog. Can you move him so that the graph shows a curve?

Can you create a story that would describe the movement of the man shown on these graphs? Use the interactivity to try out our ideas.

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

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?

Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.

An interactive game for 1 person. You are given a rectangle with 50 squares on it. Roll the dice to get a percentage between 2 and 100. How many squares is this? Keep going until you get 100. . . .

This rectangle is cut into five pieces which fit exactly into a triangular outline and also into a square outline where the triangle, the rectangle and the square have equal areas.

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

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.

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

How many times in twelve hours do the hands of a clock form a right angle? Use the interactivity to check your answers.

What are the coordinates of the coloured dots that mark out the tangram? Try changing the position of the origin. What happens to the coordinates now?

An interactive activity for one to experiment with a tricky tessellation

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?

Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!

These interactive dominoes can be dragged around the screen.

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

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

If you have only four weights, where could you place them in order to balance this equaliser?