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?

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

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

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

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

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

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

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

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

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

Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

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

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?

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?

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 draw on the dotty grid which each have one dot in the middle?

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

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

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?

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.

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

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?

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

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....?

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

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

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

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?

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

If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?

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

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

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

Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

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

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

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

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 these people?

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

Can you fit the tangram pieces into the outline of Little Fung at the table?