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

Can you fit the tangram pieces into the outline of this goat and giraffe?

Can you fit the tangram pieces into the outline of this sports car?

Can you fit the tangram pieces into the outline of this plaque design?

Can you fit the tangram pieces into the outline of the telescope and microscope?

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

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

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 the workmen?

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

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 fit the tangram pieces into the outline of these rabbits?

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?

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

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?

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

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 fit the tangram pieces into the outline of this junk?

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 Mai Ling?

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 outlines of the candle and sundial?

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

Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?

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?

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

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

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 chairs?

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

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

Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.

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 Little Ming playing the board game?

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

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

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

Explore the different tunes you can make with these five gourds. What are the similarities and differences between the two tunes you are given?

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 see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

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

What is the relationship between the angle at the centre and the angles at the circumference, for angles which stand on the same arc? Can you prove it?

This interactivity invites you to make conjectures and explore probabilities of outcomes related to two independent events.

Practise your diamond mining skills and your x,y coordination in this homage to Pacman.

Meg and Mo need to hang their marbles so that they balance. Use the interactivity to experiment and find out what they need to do.

The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.

A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?

Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.