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?

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?

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?

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.

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

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!

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?

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

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

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?

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

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

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

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?

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

Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?

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

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

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

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.

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

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?

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

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

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

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.

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

Can you complete this jigsaw of the multiplication square?

Can you logically construct these silhouettes using the tangram pieces?

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

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

Can you fit the tangram pieces into the outline of this telephone?

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

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

An interactive activity for one to experiment with a tricky tessellation

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.

Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?

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

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

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.