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

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

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

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

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?

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

An interactive activity for one to experiment with a tricky tessellation

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. . . .

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

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?

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?

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

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?

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

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

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

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

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?

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?

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.

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

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?

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.

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

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

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 work out what is wrong with the cogs on a UK 2 pound coin?

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

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 this telephone?

Can you fit the tangram pieces into the outline of Granma T?

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

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

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?

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

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.

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.

Explore the different tunes you can make with these five gourds. What are the similarities and differences between the two tunes you are given?

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

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