I cut this square into two different shapes. What can you say about the relationship between them?

Use the information on these cards to draw the shape that is being described.

Can you draw a square in which the perimeter is numerically equal to the area?

These rectangles have been torn. How many squares did each one have inside it before it was ripped?

Cut a square of paper into three pieces as shown. Now,can you use the 3 pieces to make a large triangle, a parallelogram and the square again?

The large rectangle is divided into a series of smaller quadrilaterals and triangles. Can you untangle what fractional part is represented by each of the shapes?

A task which depends on members of the group noticing the needs of others and responding.

How would you move the bands on the pegboard to alter these shapes?

Find the missing coordinates which will form these eight quadrilaterals. These coordinates themselves will then form a shape with rotational and line symmetry.

How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

Can you visualise what shape this piece of paper will make when it is folded?

Can you cut a regular hexagon into two pieces to make a parallelogram? Try cutting it into three pieces to make a rhombus!

Billy's class had a robot called Fred who could draw with chalk held underneath him. What shapes did the pupils make Fred draw?

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

Draw three straight lines to separate these shapes into four groups - each group must contain one of each shape.

This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!

How many rectangles can you find in this shape? Which ones are differently sized and which are 'similar'?

Can you draw the shape that is being described by these cards?

Can you recreate squares and rhombuses if you are only given a side or a diagonal?

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?

A game for 2 or more people, based on the traditional card game Rummy.

A game in which players take it in turns to turn up two cards. If they can draw a triangle which satisfies both properties they win the pair of cards. And a few challenging questions to follow...

A game in which players take it in turns to try to draw quadrilaterals (or triangles) with particular properties. Is it possible to fill the game grid?

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?

We started drawing some quadrilaterals - can you complete them?

How many questions do you need to identify my quadrilateral?

Four rods, two of length a and two of length b, are linked to form a kite. The linkage is moveable so that the angles change. What is the maximum area of the kite?

How many differently shaped rectangles can you build using these equilateral and isosceles triangles? Can you make a square?

Take an equilateral triangle and cut it into smaller pieces. What can you do with them?

Start with a triangle. Can you cut it up to make a rectangle?

This gives a short summary of the properties and theorems of cyclic quadrilaterals and links to some practical examples to be found elsewhere on the site.