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?

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?

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

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

How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?

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

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

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

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.

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

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?

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

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.

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

An interactive activity for one to experiment with a tricky tessellation

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. . . .

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

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

Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

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

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?

There are three versions of this challenge. The idea is to change the colour of all the spots on the grid. Can you do it in fewer throws of the dice?

Use the interactivity or play this dice game yourself. How could you make it fair?

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!

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

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

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!

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

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

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

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?

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?

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?

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

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

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?

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