Arrange any number of counters from these 18 on the grid to make a rectangle. What numbers of counters make rectangles? How many different rectangles can you make with each number of counters?

An interactive activity for one to experiment with a tricky tessellation

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.

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.

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

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

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

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?

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

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?

Move just three of the circles so that the triangle faces in the opposite direction.

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?

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

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

Incey Wincey Spider game for an adult and child. Will Incey get to the top of the drainpipe?

Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

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

Our 2008 Advent Calendar has a 'Making Maths' activity for every 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?

Complete the squares - but be warned some are trickier than they look!

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?

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. . . .

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

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 shape. How would you describe it?

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 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 Little Fung at the table?

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?

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

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

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!

Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?

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?

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

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