What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.

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?

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

This activity challenges you to make collections of shapes. Can you give your collection a name?

The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?

Complete the squares - but be warned some are trickier than they look!

If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?

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.

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?

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?

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....?

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.

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

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?

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

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

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.

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

Use the information about Sally and her brother to find out how many children there are in the Brown family.

Exchange the positions of the two sets of counters in the least possible number of moves

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

Take it in turns to make a triangle on the pegboard. Can you block your opponent?

Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?

How many different triangles can you make on a circular pegboard that has nine pegs?

Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.

Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.

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. You could use the interactivity to help you.

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

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

An interactive activity for one to experiment with a tricky tessellation

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?

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

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!

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?

How many different rhythms can you make by putting two drums on the wheel?

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?

Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?

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

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?

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

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?

You'll need two dice to play this game against a partner. Will Incey Wincey make it to the top of the drain pipe or the bottom of the drain pipe first?

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

Stop the Clock game for an adult and child. How can you make sure you always win this game?