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.

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

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.

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

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

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?

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!

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

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

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?

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

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?

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

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?

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?

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

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

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

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

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

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

Twenty four games for the run-up to Christmas.

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?

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

Can you work out what is wrong with the cogs on a UK 2 pound coin?

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

Use the interactivity to create some steady rhythms. How could you create a rhythm which sounds the same forwards as it does backwards?

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

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

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

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

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

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

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

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

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.

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

Can you logically construct these silhouettes using the tangram pieces?

Can you fit the tangram pieces into the outline of this telephone?

Can you fit the tangram pieces into the outline of Little Fung at the table?

How many right angles can you make using two sticks?

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

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.

If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?