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?

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

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?

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!

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

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

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

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

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....?

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?

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

Can you complete this jigsaw of the multiplication square?

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?

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!

Here is a chance to play a version of the classic Countdown Game.

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

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

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

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

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

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

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?

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

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?

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

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

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

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

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

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

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 Granma T?

Can you fit the tangram pieces into the outline of Little Fung at the table?

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

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

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

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

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

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

Use the Cuisenaire rods environment to investigate ratio. Can you find pairs of rods in the ratio 3:2? How about 9:6?

Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.

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.

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

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

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 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.