Mathematics
Intermediate
50 mins
Teacher/Student led
+80 XP
What you need:
IWB/Projector/Large Screen

Reflecting a Shape Across a Line

Learn how to flip a shape across a mirror line so it faces the opposite way, keeping every corner the same distance from the line. Work through reflections across vertical, horizontal and diagonal lines.

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    1 - Getting Started ~4 mins

    Look at this picture of a pattern-block triangle standing beside a mirror. The triangle points to the right. Its reflection sits in the mirror.

    Which way is the reflection pointing? The same way as the triangle, or the opposite way? Have a good look before any hands go up.

    2 - Watch and Notice ~12 mins

    Triangle across a vertical line

    Watch as we reflect a triangle across the mirror line, the line we flip across, that goes straight up and down. The triangle pointed one way; now it points the other way. It is still the same size, just flipped.

    Triangle across a horizontal line

    Now the same triangle reflects across a mirror line that lies flat, side to side. This time the flip is top-to-bottom.

    L-shape across a line

    Look at this L-shape. When it reflects, the foot of the L swaps to the other side. Let us check one corner together: this corner sits 2 squares to the left of the mirror line, so its reflection must land 2 squares to the right of the line. Count the squares from the line to a corner, then count the same number of squares on the other side to find where the reflection goes.

    Triangle across a diagonal line

    This time the mirror line runs on a slant, corner to corner. The flip still works the same way: each corner ends up the same distance from the line, but we count the squares along the slant rather than straight across. Watch how the triangle tips over the diagonal line to land on the other side.

    3 - Try It Together ~8 mins

    Today we explore reflections on the board. We build a small shape on one side of the mirror line, and the tool flips it across to the other side. Watch where each flipped corner lands.

    Key point

    We will try a triangle across a line, then an L-shape, checking each time that every corner is the same distance from the line.

    Reflect the shape across the line

    4 - Draw the Reflection in Your Copy ~3 mins

    COPYBOOK MOMENT

    In your maths copy on squared paper, draw a vertical mirror line. On the left of the line, draw a flag shape. Then carefully draw its reflection on the right.

    Check each corner: count how many squares the corner is from the line, then count the same number on the other side. Every corner must be the same distance from the line.

    5 - Class Challenge ~10 mins

    Key point

    Today we work through these reflections together. Remember: a reflection flips the shape; it is never just slid along.

    1. Reflect a triangle across a vertical line.
    2. Reflect the triangle across a horizontal line.
    3. Reflect an arrow so it points the opposite way.
    4. Reflect a shape that touches the line.
    Tip

    If we have time, there is an optional stretch: reflect an L across a diagonal line, just like we saw earlier.

    Reflect each shape across the line

    Pupil practice
    Module 8 · Symmetry, Location and Transformation Algebra
    Lesson 86 · Reflecting a Shape Across a Line
    Download Activity Book page (PDF)
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