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

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

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

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?

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.

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 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 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!

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

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?

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!

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

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

Explore the different tunes you can make with these five gourds. What are the similarities and differences between the two tunes you are given?

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

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

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

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

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?

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

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

Use the interactivities to complete these Venn diagrams.

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

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?

Can you complete this jigsaw of the multiplication square?

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

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

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

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

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?

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 outlines of the lobster, yacht and cyclist?

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.

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

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?