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

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?

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?

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!

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?

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?

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

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!

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

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

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?

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 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 this telephone?

What happens when you turn these cogs? Investigate the differences between turning two cogs of different sizes and two cogs which are the same.

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?

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

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. . . .

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

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

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

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.

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

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

An interactive activity for one to experiment with a tricky tessellation

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

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?

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

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....?

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

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?

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?

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

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

Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?

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

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

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?

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.

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?

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?

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