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

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?

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?

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

A game for 2 players. Can be played online. One player has 1 red counter, the other has 4 blue. The red counter needs to reach the other side, and the blue needs to trap the red.

An interactive activity for one to experiment with a tricky tessellation

Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

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?

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

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

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!

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.

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.

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

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

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?

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

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

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

Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.

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

Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?

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?

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?

Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?

An interactive game for 1 person. You are given a rectangle with 50 squares on it. Roll the dice to get a percentage between 2 and 100. How many squares is this? Keep going until you get 100. . . .

This is a game for two players. Can you find out how to be the first to get to 12 o'clock?

A game for 1 person to play on screen. Practise your number bonds whilst improving your memory

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

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?

An interactive game to be played on your own or with friends. Imagine you are having a party. Each person takes it in turns to stand behind the chair where they will get the most chocolate.

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?

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?

Yasmin and Zach have some bears to share. Which numbers of bears can they share so that there are none left over?

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

Arrange any number of counters from these 18 on the grid to make a rectangle. What numbers of counters make rectangles? How many different rectangles can you make with each number of counters?

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

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

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

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

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

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