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Enlarging shapes to explore their properties

Monday, 16 April 2018
A good way for children to understand the properties of polygons is to construct them precisely and accurately. Using a sharp pencil, a ruler and a protractor to draw and measure different shapes, they can then compare and ask questions about them. One issue with this for teachers is that progression in geometry is not clear, often because of the difficulty in breaking down the broad statements in the NC Programmes of Study. My Small Steps of Progression for geometry may help, which is followed by an 'enlarging shapes' activity.


If we focus on properties of 2-D shapes, these are the relevant Programmes of Study shown in the blue box. The detail gets a little more explicit in Y5 and Y6 but on the whole there is not a lot to help here with planning and teaching. What is very clear is that you cannot plan and teach by only using the statements in the Programmes of Study.  A careful breakdown of the expected outcomes and learning objectives in each year is needed to ensure the necessary depth of experience.

·   recognise and name common 2-D shapes
·   identify and describe the properties of 2-D shapes, including the number of sides and symmetry in a vertical line
·   identify 2-D shapes on the surface of 3-D shapes
·   compare and sort common 2-D shapes and everyday objects 
·   draw 2-D shapes
·   recognise that angles are a property of shape or a description of a turn
·   compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes 
·   distinguish between regular and irregular polygons based on reasoning about equal sides and angles
·   draw 2-D shapes using given dimensions and angles
·   compare and classify geometric shapes based on their properties and sizes and find unknown angles in any triangles, quadrilaterals, and regular polygons

This breakdown of the Programme of Study statements for geometry into small steps (on the right) are taken from Broadbent Maths Small Steps of Progression. They give an idea of some of the gaps and the range of experiences needed to ensure knowledge and understanding.

Take a look  if you are a Broadbent Maths subscriber.
2D shape

Try Enlarging Shapes

This is a great way to explore similar shapes. Give these instructions to your class as a method to enlarge shapes and pictures.

1. Draw a triangle. 
Draw a dot about 3cm to one side of the triangle. 

shape 1

2. Draw straight lines from the dot to go through each vertex of the triangle.

shape 2

3. Measure and put marks so that:

shape 3

4. Join EFG.

shape 4

Ask children to look at the two triangles and discuss what they notice. Encourage them to measure lengths and angles to compare the similar triangles.

What if you made:

AE = 2 x OA
BF = 2 x OB
CG = 2 x OC

Children can then draw some shapes of their own choice and enlarge them. Discuss ratio when comparing lengths of sides and ask the children to look for generalisations in their findings.

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