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 does the overlap of these two shapes look like? Try picturing it in your head and then use the interactivity to test your prediction.

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

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

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

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?

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

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

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

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

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

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

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 different rhythms can you make by putting two drums 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?

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

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

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

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

Board Block game for two. Can you stop your partner from being able to make a shape on the board?

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.

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

An interactive activity for one to experiment with a tricky tessellation

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

You'll need two dice to play this game against a partner. Will Incey Wincey make it to the top of the drain pipe or the bottom of the drain pipe first?

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?

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

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

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.

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?

Can you find all the different triangles on these peg boards, and find their angles?

Incey Wincey Spider game for an adult and child. Will Incey get to the top of the drainpipe?

Stop the Clock game for an adult and child. How can you make sure you always win this game?

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

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

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

Train game for an adult and child. Who will be the first to make the train?

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

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

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

If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?

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