Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

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

Can you complete this jigsaw of the multiplication square?

Use the interactivities to complete these Venn diagrams.

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

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

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

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

These interactive dominoes can be dragged around the screen.

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?

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?

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.

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?

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

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?

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?

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?

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

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!

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

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.

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.

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

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

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

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

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. . . .

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

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

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 activity for one to experiment with a tricky tessellation

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!

This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.

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

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

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

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

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

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

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

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?

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

Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?

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.