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?

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

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

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.

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?

An interactive activity for one to experiment with a tricky tessellation

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?

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

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!

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.

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. . . .

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

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?

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

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

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

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

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

Use the interactivity to sort these numbers into sets. Can you give each set a name?

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

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

A game for 1 person. Can you work out how the dice must be rolled from the start position to the finish? Play on line.

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

Stop the Clock game for an adult and child. How can you make sure you always win this game?

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.

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 fit the tangram pieces into the outline of Little Ming playing the board game?

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

What is the greatest number of squares you can make by overlapping three squares?

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

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

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

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

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

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!