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?

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?

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

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

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

An interactive activity for one to experiment with a tricky tessellation

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

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

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

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

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

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?

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

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

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.

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

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?

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

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?

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?

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

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. . . .

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 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.

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?

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

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.

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

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

Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?

Can you create a story that would describe the movement of the man shown on these graphs? Use the interactivity to try out our ideas.

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

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

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

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?

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

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

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

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

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

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 lobster, yacht and cyclist?

Can you fit the tangram pieces into the outline of the child walking home from school?