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

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

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?

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

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

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?

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

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?

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.

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.

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

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

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

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

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?

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

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

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?

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

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

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

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

Use the interactivity to find out how many quarter turns the man must rotate through to look like each of the pictures.

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

How many trains can you make which are the same length as Matt's, using rods that are identical?

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

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?

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?

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

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

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

Take it in turns to place a domino on the grid. One to be placed horizontally and the other vertically. Can you make it impossible for your opponent to play?

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 outlines of these people?

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

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

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

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

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?

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