A game for two or more players that uses a knowledge of measuring tools. Spin the spinner and identify which jobs can be done with the measuring tool shown.

Use the interactivity to move Mr Pearson and his dog. Can you move him so that the graph shows a curve?

Can you create a story that would describe the movement of the man shown on these graphs? Use the interactivity to try out our ideas.

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

Can you put these shapes in order of size? Start with the smallest.

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

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

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

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

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

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

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?

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

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

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?

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

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

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

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

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

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

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

If you have only four weights, where could you place them in order to balance this equaliser?

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

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?

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?

How many times in twelve hours do the hands of a clock form a right angle? Use the interactivity to check your answers.

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

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

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?

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?

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

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

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

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

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

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

Explore this interactivity and see if you can work out what it does. Could you use it to estimate the area of a shape?

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?

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

Can you fit the tangram pieces into the outline of this junk?

Try out the lottery that is played in a far-away land. What is the chance of winning?

Can you fit the tangram pieces into the outlines of the watering can and man in a boat?

Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?

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