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

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?

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?

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?

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?

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

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

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.

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?

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

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

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

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

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?

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

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

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!

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 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?

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

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

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?

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?

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

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?

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

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?

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

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.

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....?

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

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

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

Explore the different tunes you can make with these five gourds. What are the similarities and differences between the two tunes you are given?

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

A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.

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

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?

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

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