Symmetry (KS2) Explained

Young boy smiling at himself in the mirror to see the symmetry in his face.
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Image © freepik, under a Creative Commons license.

Symmetry can be defined as "the quality of being made up of exactly similar parts facing each other, or around an axis".

Sounds simple enough, right? As adults, we think we know about symmetry intuitively, but there are a few concepts children will learn in KS1 and KS2 maths that you might not have thought about for a long time.

If you're going to be teaching it at KS2 or primary level, this free resource will break down the basics.

Colourful plastic geometric shapes used to explain symmetry to KS2 kids.
Image © Marco Verch on Flickr (Creative Commons-Some Rights Reserved).

What Is The Syllabus For Symmetry At KS2?

The KS1 curriculum (Year 1 and Year 2) covers the essential concept of symmetrical shapes and lines of symmetry.

The KS2 curriculum (Years 3-6) expands on this, and tests children on their ability to identify line symmetry in various  shapes, categorise objects by whether they are symmetrical or not, and produce symmetrical shapes and patterns.

It continues to be taught from Year 7 through GCSEs, introducing more complex shapes and a few new concepts.

How Do You Explain Symmetry?

It's all about emphasising that one half of a shape or object is an exact copy of the other. If you drew a line through the middle of it, the two halves would be reflections of each other. If you held a mirror up to one half, it would look complete. Therefore any symmetrical shape has what is called a line of symmetry, or a mirror line.

Young boy holding a bunch of green apples, smiling in the garden as he looks at the symmetry of different objects.
Image © studiopeace, under a Creative Commons license.

Additional Lines Of Symmetry

At KS2, children will learn that a shape or object can have more than one line of symmetry.

A 2D shape is the easiest way to illustrate this. Take an isosceles triangle, a rectangle, an equilateral triangle, a square and a circle. The isosceles triangle has one line, the rectangle has two, the equilateral triangle has three, the square has four, and the circle has an infinite number.

Teaching Symmetry On Paper

Clearly this is a topic that is better shown, not just told. First, give children a range of shapes in different sizes and orientations and get them to draw lines of symmetry onto them (starting with one and moving up to multiple). Help them understand how to identify shapes that have no lines of symmetry, if possible by using a small mirror to show that the two sides don't have identical reflections, or else by folding the paper in half and showing that each side looks very different.

It's also key that children can draw simple pictures, shapes or patterns that mirror an existing picture, shape or pattern along a line of symmetry. For example, if they have a picture of half a butterfly or half a cake, can they complete the pictures along their central lines? Practice makes perfect, and this is a good chance to inject some colourful pens and pencils into the maths worksheets.

Close up of hands drawing shapes on a piece of paper to learn about lines of symmetry.
Image © evening_tao, under a Creative Commons license.

Examples Of Symmetry

When they've got to grip with 2D shapes, look around the room. Talk about which objects are symmetrical and why. If you took an apple or a tomato, where would you draw the line of symmetry? Again, mirrors are the perfect teaching tool to help illustrate this. Cut an apple in half, and show how, if the line of symmetry has been correctly followed, it will look whole again when held up to a mirror. You could also discuss how a different apple with a bite taken out of it would lose its symmetry.

You could gather a group of small objects, and get children to divide them into symmetrical and non-symmetrical piles. You could try a mug, a plate and a pen for your symmetrical pile, and a shoe, a wonky crisp or chunk of cheese, and a computer mouse or keyboard for your asymmetrical pile.

The Four Types Of Symmetry

Beyond KS2, the maths syllabus will cover additional types of symmetry, how shapes can be spun around on a central axis, and orders of rotational symmetry. But that's for another lesson once your child is another year older...

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