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?

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

NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.

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?

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

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?

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

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

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

Make one big triangle so the numbers that touch on the small triangles add to 10.

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?

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?

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

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

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

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

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

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

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

Twenty four games for the run-up to Christmas.

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

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

How many right angles can you make using two sticks?

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

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

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....?

Ahmed has some wooden planks to use for three sides of a rabbit run against the shed. What quadrilaterals would he be able to make with the planks of different lengths?

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

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

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

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

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?

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

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

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

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

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?

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

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?

Can you logically construct these silhouettes using the tangram pieces?

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

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

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