Two engines, at opposite ends of a single track railway line, set off towards one another just as a fly, sitting on the front of one of the engines, sets off flying along the railway line...

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its vertical and horizontal movement at each stage.

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.

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

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

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

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

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

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

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 the child walking home from school?

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

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

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

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

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?

A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?

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?

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

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

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

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

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.

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?

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

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

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?

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

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

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

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects the distance it travels at each stage.

Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its speed at each stage.

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 Granma T?

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

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?

Explore displacement/time and velocity/time graphs with this mouse motion sensor.

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?

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

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.

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 outline of Little Ming and Little Fung dancing?

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

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

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