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

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!

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

If you have only four weights, where could you place them in order to balance this equaliser?

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?

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. . . .

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?

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

An interactive activity for one to experiment with a tricky tessellation

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?

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?

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

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.

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

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?

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

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?

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?

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.

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?

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

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

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!

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

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

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?

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?

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

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 find all the different ways of lining up these Cuisenaire rods?

How many times in twelve hours do the hands of a clock form a right angle? Use the interactivity to check your answers.

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 outline of Granma T?

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

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?

Seeing Squares game for an adult and child. Can you come up with a way of always winning this game?

Use the interactivity to make this Islamic star and cross design. Can you produce a tessellation of regular octagons with two different types of triangle?

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

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

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

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