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

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?

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 interactivities to complete these Venn diagrams.

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

Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?

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

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

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

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

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.

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

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?

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

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

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 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?

An interactive activity for one to experiment with a tricky tessellation

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

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?

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?

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

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

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?

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

Can you complete this jigsaw of the multiplication square?

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

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. . . .

Use the interactivity to move Mr Pearson and his dog. Can you move him so that the graph shows a curve?

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

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

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

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

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.

Explore this interactivity and see if you can work out what it does. Could you use it to estimate the area of a shape?

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

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

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

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.

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?

Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?