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

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?

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!

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.

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

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

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?

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.

Use the interactivities to complete these Venn diagrams.

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

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?

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

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

An interactive activity for one to experiment with a tricky tessellation

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. . . .

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?

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.

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

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?

Can you complete this jigsaw of the multiplication square?

NRICH December 2006 advent calendar - a new tangram for each 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?

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

Can you explain the strategy for winning this game with any target?

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?

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

Here is a solitaire type environment for you to experiment with. Which targets can you reach?

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

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 these clocks?

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

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

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

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!

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 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?

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

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.

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

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?