Maths through Hampton Court Palace
Lesson 2: Symmetry
LEARNING OBJECTIVES:
RESOURCES:
1. Investigate lines of symmetry.
2. Infer a link between the number of sides of a regular shape and the number of lines of symmetry.
3. Apply this knowledge to predict the number of lines of symmetry in other polygons.
4. Test their predictions against less regular polygons.
1. PowerPoint “Shapes and symmetry at Hampton Court Palace”
2. Squares of paper
3. PowerPoint “Categorising shapes”
4. Worksheet “Shapes with equal length sides”
5. Worksheet “Shapes with different length sides”
ACTIVITY:
Look together at PowerPoint “Shapes and symmetry at Hampton Court Palace” Discuss the
properties of the shapes.
Give each child a paper square. Discuss shape and properties. Draw attention to equal length sides and
equal angles. Ask children to predict how many ways they might be able to fold the square so that each
side fits exactly on top of the other. Predict, discuss, experiment (NB: children will often miss the ‘corner to corner’ lines of symmetry,
particularly in hexagons and octagons. Use this opportunity to remind them to think about ‘corner to
corner’ lines of symmetry during their investigations.)
Ask the children to draw down the folds. What do we call these lines? Explain we are going to be looking at the number of lines of symmetry of shapes with sides of equal length
and equal angles.
PowerPoint “Categorising shapes” – those with equal sides and angles, those without. Get the children to discuss and assess which shapes should go on which side.
Give out the worksheet “Shapes with equal length sides”. Children to cut and fold the shapes exactly in
half in as many ways as they can to find the number of lines of symmetry. Use this information to fill in the
table on the worksheet. Children hypothesise how many lines of symmetry other regular polygons might
have.
As an extension, you may want to repeat the folding activity using the worksheet “Shapes with different lengths”. QUESTIONS TO DEVELOP THINKING:
Do the children notice anything different about the number of lines of symmetry for shapes with unequal sides or angles?
Can they guess how many lines of symmetry a circle might have?
VOCABULARY:
Hypothesise, polygon, predictions, symmetry
Hampton Court Palace and St John the Baptist Church of England Junior School
Worksheet
Shapes with
equal-length sides
2
Shapes with
equal-length sides
Worksheet
Name of shape
Number of sides
Using this information, can you predict how many lines of symmetry the following shapes
will have:
Name of shape
Number of sides
A regular heptagon
A regular pentagon
A regular nonagon
(nine sides)
A regular decagon
(ten sides)
Number of lines
of symmetry
2a
Number of lines
of symmetry
Shapes with
different length sides
Worksheet
3