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

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

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?

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

Can you beat the computer in the challenging strategy game?

Practise your tables skills and try to beat your previous best score in this interactive game.

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

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

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.

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?

Can you complete this jigsaw of the multiplication square?

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.

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!

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?

A game for 2 players that can be played online. Players take it in turns to select a word from the 9 words given. The aim is to select all the occurrences of the same letter.

Calculate the fractional amounts of money to match pairs of cards with the same value.

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

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

Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?

Practise your number bonds whilst improving your memory in this matching pairs game.

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

Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?

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

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

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?

Train game for an adult and child. Who will be the first to make the train?

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

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?

A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .

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?

An interactive activity for one to experiment with a tricky tessellation

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 two people that can be played with pencils and paper. Combine your knowledge of coordinates with some strategic thinking.

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.

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

The 2012 primary advent calendar features twenty-four of our posters, one for each day in the run-up to Christmas.

Can you explain the strategy for winning this game with any target?

A train building game for two players. Can you be the one to complete the train?

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

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

Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?

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

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

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....?