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.

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?

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?

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?

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

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

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?

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

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

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

An interactive activity for one to experiment with a tricky tessellation

A game for 2 people that can be played on line or with pens and paper. Combine your knowledege of coordinates with your skills of strategic thinking.

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 game to be played against the computer, or in groups. Pick a 7-digit number. A random digit is generated. What must you subract to remove the digit from your number? the first to zero wins.

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. . . .

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.

Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block 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.

Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?

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 complete this jigsaw of the multiplication square?

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

Use the interactivity to create some steady rhythms. How could you create a rhythm which sounds the same forwards as it does backwards?

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!

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?

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

Use the Cuisenaire rods environment to investigate ratio. Can you find pairs of rods in the ratio 3:2? How about 9:6?

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

Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.

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?

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

Explore this interactivity and see if you can work out what it does. Could you use it to estimate the area of a shape?

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

Work out the fractions to match the cards with the same amount of money.

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

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

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

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

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

Use the interactivity or play this dice game yourself. How could you make it fair?

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

Explore the different tunes you can make with these five gourds. What are the similarities and differences between the two tunes you are given?

Can you find all the different ways of lining up these Cuisenaire rods?