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?

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

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

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

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

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

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

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

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?

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

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

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!

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

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

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?

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?

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

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

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 Granma T?

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

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?

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

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?

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 everybody knows. You can play with a friend or online. If you play correctly you never lose!

A game for 1 person. Can you work out how the dice must be rolled from the start position to the finish? Play on line.

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. . . .

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

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.

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 the child walking home from school?

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

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

Can you fit the tangram pieces into the outlines of the chairs?

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

What is the greatest number of squares you can make by overlapping three squares?

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?

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?

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

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

Can you fit the tangram pieces into the outline of this shape. How would you describe it?