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?

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

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?

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

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.

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?

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?

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

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

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 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?

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

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?

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?

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

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

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

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

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....?

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

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

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

Investigate the different sounds you can make by putting the owls and donkeys on the wheel.

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?

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

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

A shape and space game for 2,3 or 4 players. Be the last person to be able to place a pentomino piece on the playing board. Play with card, or on the computer.

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

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

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 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.

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.

Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?

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?

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!

Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.

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

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?