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?

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?

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

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

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

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?

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

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

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?

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

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

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

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.

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.

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.

An interactive activity for one to experiment with a tricky tessellation

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

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

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?

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?

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?

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

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

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

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

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?

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

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!

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

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

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

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!

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 Granma T?

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

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

Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?

Use the interactivity to create some steady rhythms. How could you create a rhythm which sounds the same forwards as it does backwards?

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

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

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

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