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

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

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

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 outline of this junk?

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?

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

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 fit the tangram pieces into the outlines of the candle and sundial?

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

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?

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 fit the tangram pieces into the outline of this telephone?

Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?

Can you fit the tangram pieces into the outline of Mai Ling?

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

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 outline of Granma T?

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?

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.

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?

A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .

This rectangle is cut into five pieces which fit exactly into a triangular outline and also into a square outline where the triangle, the rectangle and the square have equal areas.

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?

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

A game for 2 players. Can be played online. One player has 1 red counter, the other has 4 blue. The red counter needs to reach the other side, and the blue needs to trap the red.

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

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

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

What is the greatest number of squares you can make by overlapping three squares?

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?

Can you fit the tangram pieces into the outline of the rocket?

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

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

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

Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?

Can you fit the tangram pieces into the outline of these convex shapes?

Can you fit the tangram pieces into the outline of these rabbits?

Square It game for an adult and child. Can you come up with a way of always winning this game?

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

Can you fit the tangram pieces into the outline of this shape. How would you describe 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 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?