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?

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

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

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?

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!

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

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?

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.

Can you complete this jigsaw of the multiplication square?

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

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

A game for 1 person to play on screen. Practise your number bonds whilst improving your memory

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?

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

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?

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

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

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?

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

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

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?

Interactive game. Set your own level of challenge, practise your table skills and beat your previous best score.

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?

An environment which simulates working with Cuisenaire rods.

An interactive activity for one to experiment with a tricky tessellation

Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?

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

Practise your diamond mining skills and your x,y coordination in this homage to Pacman.

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?

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?

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

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.

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

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 can be played on line or with pens and paper. Combine your knowledege of coordinates with your skills of strategic thinking.

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

Imagine picking up a bow and some arrows and attempting to hit the target a few times. Can you work out the settings for the sight that give you the best chance of gaining a high score?

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

Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?

Carry out some time trials and gather some data to help you decide on the best training regime for your rowing crew.

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?

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

Find out what a "fault-free" rectangle is and try to make some of your own.