Line and Rotational Symmetry
Lines of symmetry
A shape has a line of symmetry if it can be folded along a line so the two halves match exactly. A heart, a square and the letter A all have one or more such lines. The line of symmetry is like a mirror down the middle: each point on one side has a matching point the same distance away on the other. Recognising lines of symmetry is the first idea of this unit, and it gives a precise meaning to the everyday sense that a shape is balanced or even — the two halves are genuine reflections of each other.
Counting the lines
Different shapes have different numbers of lines of symmetry. A square has four — two through the middles of its sides and two through its corners. A rectangle that is not a square has just two; an equilateral triangle has three; a circle has endlessly many, since any line through its centre works. Counting the lines means trying every fold that makes the halves match. This counting sharpens the idea of symmetry and reveals that some shapes are far more symmetric than others, a property worth knowing for each common shape.
Rotational symmetry
Symmetry is not only about folding. A shape has rotational symmetry if, when turned about its centre by less than a full circle, it looks exactly the same as it started. A pinwheel or a windmill turned a quarter turn looks unchanged; a square does too. This is a different kind of symmetry from a line: instead of a mirror, it is a turn that maps the shape onto itself. Recognising rotational symmetry alongside line symmetry is part of this unit, and it shows that balance in a shape can come from turning as well as from reflecting.
Completing a reflection
Symmetry can be used to build, not just to recognise. Given half a pattern beside a mirror line, the whole can be completed by reflecting: each coloured square is copied to the same distance on the far side of the line. The result is a pattern symmetric about that line. This is the practical side of symmetry — using the rule to create rather than only to spot — and it is exactly how symmetric pictures and designs are made, by reflecting one half to produce its match.
Making symmetric patterns
Going further, a whole symmetric pattern can be created from scratch. Placing a mark and its mirror image at once keeps everything balanced about the line, so any design built this way is symmetric. Creating symmetrical patterns and pictures is written into the descriptor, and it is where symmetry becomes creative and playful. Dynamic geometry software on a computer does the same with a click, reflecting and turning shapes instantly, which is why the curriculum mentions using such tools where they are available.
The symmetry of shapes
Pulling the unit together, symmetry comes in two kinds — line symmetry, where a shape folds onto itself, and rotational symmetry, where a turn leaves it unchanged — and both can be used to create patterns. A table of common shapes and their lines of symmetry fixes the facts: a square has four, a rectangle two, a triangle three, a circle endless. With lines of symmetry recognised and counted, rotational symmetry understood, reflections completed and symmetric patterns made, a child can both recognise the symmetry of shapes and use it to create, the full reach of symmetry in Year 4.