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

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?

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

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?

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

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

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?

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

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

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

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

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?

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

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?

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?

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

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

Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!

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?

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

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

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

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

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?

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

An interactive activity for one to experiment with a tricky tessellation

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

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

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

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....?

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

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

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?

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

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. . . .

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

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

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

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.

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

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?