Challenge Level

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?

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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?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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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?

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

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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...

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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?

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We started drawing some quadrilaterals - can you complete them?

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How many questions do you need to identify my quadrilateral?

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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?

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

Challenge Level

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

Challenge Level

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

Challenge Level

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?

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.