Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.

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.

Can you find all the different triangles on these peg boards, and find their angles?

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

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

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

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?

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?

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

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

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

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

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

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

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

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

Can you fit the tangram pieces into the outline of Granma T?

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

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!

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

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

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

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

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

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

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?

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

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?

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?

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 the lobster, yacht and cyclist?

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?

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....?

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

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?

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

Explore the different tunes you can make with these five gourds. What are the similarities and differences between the two tunes you are given?

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?

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?

What happens when you try and fit the triomino pieces into these two grids?

Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?