This activity challenges you to make collections of shapes. Can you give your collection a name?

The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?

Arrange any number of counters from these 18 on the grid to make a rectangle. What numbers of counters make rectangles? How many different rectangles can you make with each number of counters?

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

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!

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

Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?

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

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

Sort the houses in my street into different groups. Can you do it in any other ways?

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

What shaped overlaps can you make with two circles which are the same size? What shapes are 'left over'? What shapes can you make when the circles are different sizes?

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

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

What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.

Complete the squares - but be warned some are trickier than they look!

Can you put these shapes in order of size? Start with the smallest.

Use the interactivity to sort these numbers into sets. Can you give each set a name?

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.

A game for 2 players. Can be played online. One player has 1 red counter, the other has 4 blue. The red counter needs to reach the other side, and the blue needs to trap the red.

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

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?

Take it in turns to make a triangle on the pegboard. Can you block your opponent?

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.

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

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

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

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?

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

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?

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?

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

These interactive dominoes can be dragged around the screen.

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!

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 put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?

An interactive activity for one to experiment with a tricky tessellation

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 rhythms can you make by putting two drums on the wheel?

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

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

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

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

Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?