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?

Ahmed has some wooden planks to use for three sides of a rabbit run against the shed. What quadrilaterals would he be able to make with the planks of different lengths?

Two circles of equal radius touch at P. One circle is fixed whilst the other moves, rolling without slipping, all the way round. How many times does the moving coin revolve before returning to P?

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?

A game for two people that can be played with pencils and paper. Combine your knowledge of coordinates with some strategic thinking.

A red square and a blue square overlap so that the corner of the red square rests on the centre of the blue square. Show that, whatever the orientation of the red square, it covers a quarter of the. . . .

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?

Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

Can you work out what is wrong with the cogs on a UK 2 pound coin?

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?

How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!

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

Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.

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 make a right-angled triangle on this peg-board by joining up three points round the edge?

Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

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?

Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?

A shape and space game for 2,3 or 4 players. Be the last person to be able to place a pentomino piece on the playing board. Play with card, or on the computer.

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.

The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?

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

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?

Can you find triangles on a 9-point circle? Can you work out their angles?

This game challenges you to locate hidden triangles in The White Box by firing rays and observing where the rays exit the Box.

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

Show how this pentagonal tile can be used to tile the plane and describe the transformations which map this pentagon to its images in the tiling.

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

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.

What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.

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.

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

An interactive game to be played on your own or with friends. Imagine you are having a party. Each person takes it in turns to stand behind the chair where they will get the most chocolate.

Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.

This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.

Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?

Use the interactivity to make this Islamic star and cross design. Can you produce a tessellation of regular octagons with two different types of triangle?

What shaped overlaps can you make with two circles which are the same size? What shapes are 'left over'? What shapes can you make when the circles are different sizes?

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

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

We can show that (x + 1)² = x² + 2x + 1 by considering the area of an (x + 1) by (x + 1) square. Show in a similar way that (x + 2)² = x² + 4x + 4

Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?