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?

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

What does the overlap of these two shapes look like? Try picturing it in your head and then use the interactivity to test your prediction.

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.

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

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

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?

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

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!

What is the greatest number of squares you can make by overlapping three squares?

Seeing Squares game for an adult and child. Can you come up with a way of always winning this game?

Can you sort these triangles into three different families and explain how you did it?

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?

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

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.

Can you fit the tangram pieces into the outlines of the chairs?

Can you fit the tangram pieces into the outline of the child walking home from school?

Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?

Can you fit the tangram pieces into the outlines of these people?

Can you fit the tangram pieces into the outlines of these clocks?

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 fit the tangram pieces into the outlines of the lobster, yacht and cyclist?

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?

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

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

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?

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

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

An interactive activity for one to experiment with a tricky tessellation

A game for 1 person. Can you work out how the dice must be rolled from the start position to the finish? Play on line.

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

How many times in twelve hours do the hands of a clock form a right angle? Use the interactivity to check your answers.

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?

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. . . .

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

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?

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

These interactive dominoes can be dragged around the screen.

Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.

Can you use the interactive to complete the tangrams in the shape of butterflies?

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.

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

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

Board Block game for two. Can you stop your partner from being able to make a shape on the board?

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