Digging Deeper into … Symmetry (2nd to 4th)

For practical suggestions for families, and links to useful digital resources, to support children learning about the topic of symmetry, please check out the following post: Dear Family, your Operation Maths Guide to Symmetry.

Symmetry is officially a strand unit for second to fourth classes, although it also features as a content objective in 2-D shapes for fifth and sixth class where the children “classify 2-D shapes according to their lines of symmetry”.

While there are different types of symmetry, the curriculum specifies line symmetry, also known as mirror symmetry, reflective or reflection symmetry.

In Operation Maths, this chapter is placed after 2-D shapes, so that the children can identify symmetry in the shapes that they have previously encountered, and, in third  and fourth class, it is placed after Lines and Angles so that they can use their knowledge of different line types when describing the lines of symmetry.

Concrete exploration

To complete or create symmetrical patterns, requires the children being able to visualise the mirror image of the given arrangement/image. But children cannot visualise what they have not experienced. Thus to experience symmetry the children must:

• be made aware of examples of symmetry all around them, and locate examples themselves e.g. flowers, leaves, objects at home and at school, numbers and letters of the alphabet.
• be afforded ample opportunities to use real mirrors to explore symmetry. The type of child-safe mirrors that are often used in science investigations (eg in the strand unit of light) are ideal for this purpose.

Using mirrors allows the children the opportunity to observe symmetry and to check the accuracy of their completed patterns.  When using mirrors:

• Try to have enough mirrors for one between two (the child-safe mirrors can often be cut into smaller sizes, 10cm x 7cm approx is big enough), or if supply is limited the mirror exploration could be incorporated as a station in a station/team teaching maths lesson.
• Initially, allow the children free exploration and then, when suitable, guide it towards a purpose using questioning:
  • What letters or numbers look the same in the mirror? What shapes or images in the environment look the same in the mirror?
  • Can you put the mirror along the middle of any shapes and numbers so that they look complete? Does this work with any shapes or images from the environment? Don’t specify “middle” as being horizontal or vertical, and then see if the children realise that, on some figures, there is more than one than one way that the mirror can be placed.
• At this point you could use this as the introduction to a separate and distinct What do you notice? What do you wonder? activity, and use the children’s wonder questions to guide the course of the rest of the lesson.
• Explain that, on the symmetrical figures, the position of the mirror, is referred to as the line of symmetry. Then ask the children to use the mirrors to identify/draw the line of symmetry on the figures or mark the line of symmetry first (more challenging) and then check using the mirror.
• Using the mirrors the children can create and check symmetrical patterns using cubes, counters, objects etc. One child can create a pattern that their partner has to complete symmetrically. Since children often incorrectly replicate the pattern (eg as done in the first image below) rather than reverse it, the mirror can show them their error (as used in second image below). Encourage the children to realise that whatever is closest to the mirror/line of symmetry on one side will also be closest to the mirror on the other side.

• The children could then progress to creating symmetrical arrangements of more than one row. The Operation Maths twenty frames (free with Operation Maths 1 and 2) can be very useful for this (see below). Again the children should be encouraged to recognise that the colour and type of object/figure that is closest to the line of symmetry on one side should also be closest to the line of symmetry on the other side.

When the children have had sufficient experience with actual mirrors they should progress to completing activities without them, although they could always be returned to again if needs arose.

Further Reading and Resources

• Dear Family, your Operation Maths Guide to Symmetry includes practical suggestions for supporting children, and links to a huge suite of digital resources, organised according to class level.
• Virtual Maths Manipulatives for Shape and Space: Lots of tools that can be used in many different ways to explore symmetry and other shape concepts.
• Shape and Space Manual from PDST
• NRICH: selection of problems, articles and games for symmetry