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

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

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

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.

An interactive activity for one to experiment with a tricky tessellation

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

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

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

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

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

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 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. . . .

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

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

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!

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?

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

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

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 happens when you turn these cogs? Investigate the differences between turning two cogs of different sizes and two cogs which are the same.

Can you fit the tangram pieces into the outline of Mai Ling?

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

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 these clocks?

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 outlines of the chairs?

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

Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?

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 this junk?

Can you fit the tangram pieces into the outlines of the candle and sundial?

Use the interactivities to complete these Venn diagrams.

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.

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

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

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

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?

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

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

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.

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 complete this jigsaw of the multiplication square?

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!

These interactive dominoes can be dragged around the screen.

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