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?

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?

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

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

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

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.

Incey Wincey Spider game for an adult and child. Will Incey get to the top of the drainpipe?

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

Move just three of the circles so that the triangle faces in the opposite direction.

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

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

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

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

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?

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?

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

How many right angles can you make using two sticks?

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

Use the interactivity to find out how many quarter turns the man must rotate through to look like each of the pictures.

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

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

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

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?

Take it in turns to place a domino on the grid. One to be placed horizontally and the other vertically. Can you make it impossible for your opponent to play?

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

Play this well-known game against the computer where each player is equally likely to choose scissors, paper or rock. Why not try the variations too?

Use the number weights to find different ways of balancing the equaliser.

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

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

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

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