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

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

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

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

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?

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

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

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

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

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

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....?

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

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

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

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

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

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

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?

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?

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?

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

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?

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

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

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

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

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

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

Can you fit the tangram pieces into the outline of the child walking home from school?

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

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 outlines of the lobster, yacht and cyclist?

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

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?

Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?

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.

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

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. . . .

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?

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?

An interactive activity for one to experiment with a tricky tessellation

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

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

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!