Symmetry in everyday shapes
Look at twelve shapes from nature and daily life, from a butterfly and a snowflake to a shoe and a swirl. Find how many lines of symmetry each has, and sort them into one line, more than one, or none.
Core concept
A line of symmetry folds a shape into two halves that match exactly; some shapes have one, some have many, and some have none, even if they look balanced when turned
Topic: Maths in everyday life
Fold a picture of a butterfly down the middle and one wing lands exactly on the other. The fold line is a line of symmetry: When one half of a shape is a mirror image of the other half. All key words, and each half is the mirror image of the other. A heart and a smiling face also have one line. A five-pointed star has five lines and a snowflake six. Some shapes have none: an open hand has its thumb on one side only, and a single shoe is not the same on both sides. Some shapes, like a swirl or the yin-yang sign, match themselves when you turn them, but no fold makes the halves match; that is turning (rotational) symmetry, not line symmetry.
What you will learn
- Find the lines of symmetry of a shape by folding or with a mirror.
- Sort shapes by how many lines of symmetry they have.
- Tell line symmetry from turning symmetry.
Before you start
- Know what a straight line and a mirror image are.
Materials
- Paper, scissors and a small mirror
Equipment
- None
Procedure
- Pick a shape and find its lines of symmetry.
- Do this for at least eight shapes.
- Sort every shape into one line, more than one, or none.