Can you sort these triangles into three different families and explain how you did it?

What does the overlap of these two shapes look like? Try picturing it in your head and then use the interactivity to test your prediction.

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

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

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?

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.

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?

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

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

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?

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

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

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.

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.

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

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. . . .

An interactive activity for one to experiment with a tricky tessellation

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

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

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?

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?

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

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?

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

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?

Can you make the green spot travel through the tube by moving the yellow spot? Could you draw a tube that both spots would follow?

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?

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!

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

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

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?

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

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

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

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