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

This was a problem for our birthday website. Can you use four of these pieces to form a square? How about making a square with all five pieces?

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

NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.

Sort the houses in my street into different groups. Can you do it in any other ways?

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

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.

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

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

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. . . .

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

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?

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

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

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

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.

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.

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

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 the child walking home from school?

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

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.

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?

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?

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

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

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?

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?

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

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?

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

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.

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

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?

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

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

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

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

An interactive activity for one to experiment with a tricky tessellation

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