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

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?

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

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

An interactive activity for one to experiment with a tricky tessellation

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

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?

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?

Play this well-known game against the computer where each player is equally likely to choose scissors, paper or rock. Why not try the variations too?

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

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

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

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

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

Use the interactivities to complete these Venn diagrams.

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

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

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

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

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 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?

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?

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. . . .

Use the interactivity to sort these numbers into sets. Can you give each set a name?

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

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?

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 the chairs?

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

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

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.

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!

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

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

A shape and space game for 2,3 or 4 players. Be the last person to be able to place a pentomino piece on the playing board. Play with card, or on the computer.

Can you fit the tangram pieces into the outlines of the watering can and man in a boat?