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?

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

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

Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?

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?

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.

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

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

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....?

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!

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 everybody knows. You can play with a friend or online. If you play correctly you never lose!

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

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

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

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

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?

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?

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

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

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

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

Can you fit the tangram pieces into the outline of this telephone?

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

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

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

Can you fit the tangram pieces into the outline of this junk?

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

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

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

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!

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 fit the tangram pieces into the outlines of the lobster, yacht and cyclist?

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?

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

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?

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 six toy ladybirds into the box so that there are two ladybirds in every column and every row.

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?

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

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.

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 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.

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?