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?

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

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

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

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?

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

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?

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

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

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

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

Investigate the different sounds you can make by putting the owls and donkeys on the wheel.

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.

Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!

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

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

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

Find out what a "fault-free" rectangle is and try to make some of your own.

Use your mouse to move the red and green parts of this disc. Can you make images which show the turnings described?

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?

Terry and Ali are playing a game with three balls. Is it fair that Terry wins when the middle ball is red?

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

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

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

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

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?

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.

An interactive activity for one to experiment with a tricky tessellation

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

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. . . .

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

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

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

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?

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

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

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

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

Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.

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!

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?