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

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

Can you put these shapes in order of size? Start with the smallest.

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

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

Try out the lottery that is played in a far-away land. What is the chance of winning?

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

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....?

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

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

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

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

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

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

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

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

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

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

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

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

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!

In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?

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

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

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?

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

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 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?

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

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?

A game for 2 players. Can be played online. One player has 1 red counter, the other has 4 blue. The red counter needs to reach the other side, and the blue needs to trap the red.

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?

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?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

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

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

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

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?

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.

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