Q. My Year 5 and 6 pupils are keen on classifying shapes, and want to know if squares are rhombuses, rectangles are parallelograms and right-angled triangles are scalene. Can you suggest ways of exploring these ideas without confusing those who find it tricky to visualise a particular shape? Could Venn diagrams be used to create subsets of shapes?
A. Your pupils seems to be having fun with shapes and some really in-depth mathematical thinking has been stirred. Great! A Venn diagram is a good way to explore shapes. Before doing this, I get pupils to fill in a table such as the one below, which makes them focus on the properties of each quadrilateral.
Having thought about the different properties, the table suggests there are overlaps, which you quite rightly say could be effectively explored via a Venn diagram. I have done this with classes by drawing on tabletops in chalk (you could also use tape on the floor). I used this activity to explore quadrilaterals and their classification.
Divide the class into groups of four. They should each have a large Venn diagram. Have a set of shapes ready, with a list of their properties, and more than one of each type of shape. To help less able pupils grasp the individual properties, indicate the shapes' equal sides, parallel lines and 90o angles. Leave the shapes unmarked for more able or older learners.
Quadrilateral: a four-sided polygon or a closed shape made of four straight lines.
Parallelogram: a quadrilateral with both pairs of opposite sides parallel and equal in length.
Rhombus: a quadrilateral with all sides of equal length and opposite sides parallel (an equilateral parallelogram).
Rectangle: a quadrilateral with both pairs of opposite sides parallel and equal in length with four right angles (a parallelogram with four right angles).
Square: a quadrilateral with all sides of equal length and opposite sides parallel, with four right angles.
Trapezium: a quadrilateral with one pair of opposite sides parallel.
Kite: a quadrilateral with adjacent sides equal in length.
The difficulty arises with the description of the kite. A rhombus is a type of kite, but is also a type of parallelogram. This is hard to replicate as an overlap, so a rhombus would appear in two places in the Venn diagram, as I have shown in the picture above. If you would like copies of these, and of the shapes that can be cut out and the Word document with the definitions, please email me.
And, yes, you can have a right-angled scalene triangle. You can also have a right-angled isosceles triangle. You will find programs for "playing" with shape at nlvm.usu.eduennavvlibrary.html
I am grateful to Dr Steve Warr, a teacher in Horncastle, who has written to say that he has tried my ideas on standard form (November 18, 2005) with his Year 8 class and found them to be very effective. He has produced PowerPoint files, Excel starters and Word worksheets based on the ideas, and these are now available for download at www.mathagonyaunt.co.uk