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

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?

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?

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?

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

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

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

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

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

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

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

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

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.

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....?

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

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

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

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

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

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

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

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

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?

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

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

Train game for an adult and child. Who will be the first to make the train?

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

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

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

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

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!

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

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

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

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

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

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?

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.

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