Mathematics
Intermediate
50 mins
Teacher/Student led
+65 XP
What you need:
IWB/Projector/Large Screen
Paper shapes

Line Symmetry: Finding Lines of Symmetry

Explore lines of symmetry by folding shapes and letters so their two halves match exactly. Test whether each fold is a true line of symmetry and discover how many lines different shapes have.

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    1 - Getting Started ~5 mins

    Watch as I fold this paper heart straight down the middle. The fold I make is a mirror line: the line we test to see whether the two halves match. Look closely: the two halves land exactly on top of each other, like a mirror.

    Key point

    A square is different. Where could you fold a square so that both halves match perfectly? Is there only one fold that works, or could there be more than one?

    2 - Watch and Notice ~11 mins

    A square folds four ways

    Watch the mirror line on the square. Slide it side to side, top to bottom, and corner to corner — each fold makes two halves that match. A square has four lines of symmetry.

    A rectangle folds only two ways

    Now the rectangle. The two straight-across folds match, but watch the corner-to-corner fold: the halves do not land on each other. A rectangle has only two lines of symmetry.

    The letter X folds two ways

    The capital letter X folds straight down the middle and the two halves match. It also folds straight across the middle and the halves match again. That is two lines of symmetry.

    The letter T folds once

    The capital letter T folds straight down the middle, and the two halves match. That single fold is its only line of symmetry.

    3 - Try It Together ~13 mins

    Today we explore: drag the mirror line, the fold line we test, onto each shape and letter to see whether the two halves match. We will work through a square, a rectangle, the letter T and the letter X on the shared board.

    Key point

    When the fold makes both halves land exactly on top of each other, we have found a line of symmetry. When they miss, that fold does not count.

    Test the fold lines

    4 - Rule the Lines in Your Copy ~5 mins

    COPYBOOK MOMENT

    In your maths copy, draw a square, a rectangle and the letter X. Then rule in every line of symmetry you can find on each one. Use the straight edge of your ruler to keep your lines neat.

    5 - Class Challenge ~10 mins

    Today we work through these together: the letter H, the letter X, the letter S and the letter M.

    Watch out

    Watch out — one of them has no line of symmetry at all, so check every fold carefully before you decide.

    Find every line of symmetry

    Pupil practice
    Module 8 · Symmetry, Location and Transformation Algebra
    Lesson 84 · Line Symmetry: Finding Lines of Symmetry
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