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?

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

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

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

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....?

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

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

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

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?

There are three versions of this challenge. The idea is to change the colour of all the spots on the grid. Can you do it in fewer throws of the dice?

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

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

An interactive activity for one to experiment with a tricky tessellation

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

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?

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?

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?

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

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

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?

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?

Arrange any number of counters from these 18 on the grid to make a rectangle. What numbers of counters make rectangles? How many different rectangles can you make with each number of counters?

Make one big triangle so the numbers that touch on the small triangles add to 10.

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. . . .

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

Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?

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

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

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

Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?

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

These interactive dominoes can be dragged around the screen.

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

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

How many trains can you make which are the same length as Matt's, using rods that are identical?

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

If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?

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 hang weights in the right place to make the equaliser balance?

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