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?

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

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?

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

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

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

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?

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 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 complete this jigsaw of the multiplication square?

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

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

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

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

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

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?

An interactive activity for one to experiment with a tricky tessellation

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 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.

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?

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

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

Use the interactivity to make this Islamic star and cross design. Can you produce a tessellation of regular octagons with two different types of triangle?

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

Use the interactivity or play this dice game yourself. How could you make it fair?

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?

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

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....?

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

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?

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

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

These interactive dominoes can be dragged around the screen.

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

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

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.

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

Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

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

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 create a story that would describe the movement of the man shown on these graphs? Use the interactivity to try out our ideas.

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?