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?

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

Can you complete this jigsaw of the multiplication square?

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!

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

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 make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

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

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

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

An environment which simulates working with Cuisenaire rods.

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

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?

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

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

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

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

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

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?

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

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

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

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

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....?

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.

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?

Try out the lottery that is played in a far-away land. What is the chance of winning?

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

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.

Can you locate the lost giraffe? Input coordinates to help you search and find the giraffe in the fewest guesses.

Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?

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?

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!

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

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

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

Can you find all the different triangles on these peg boards, and find their angles?

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

These formulae are often quoted, but rarely proved. In this article, we derive the formulae for the volumes of a square-based pyramid and a cone, using relatively simple mathematical concepts.

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!

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?

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?