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

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

Use your mouse to move the red and green parts of this disc. Can you make images which show the turnings described?

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

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

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

Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?

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

Can you logically construct these silhouettes using the tangram pieces?

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

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

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.

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....?

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

Can you fit the tangram pieces into the outline of the rocket?

This was a problem for our birthday website. Can you use four of these pieces to form a square? How about making a square with all five pieces?

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

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

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

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

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

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

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

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

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 use the interactive to complete the tangrams in the shape of butterflies?

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

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

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

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

Can you sort these triangles into three different families and explain how you did it?

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

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

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

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

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

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?

If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?

Investigate the different sounds you can make by putting the owls and donkeys on the wheel.

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?

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

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?

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?

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