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?

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

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?

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.

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

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?

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

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

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 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?

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

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

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

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

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

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 the lobster, yacht and cyclist?

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

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

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

Twenty four games for the run-up to Christmas.

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.

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?

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?

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

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 information about Sally and her brother to find out how many children there are in the Brown family.

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

Can you logically construct these silhouettes using the tangram pieces?

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?

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

How many right angles can you make using two sticks?

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?

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....?

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

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

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?

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?

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!

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