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

Combining Transformations

Apply two transformations one after the other to a shape, discover when order matters, and find different pairs of moves that reach the same target.

Teacher Class Feed

Load previous activity

    1 - Getting Started ~4 mins

    Here is a triangle on a grid. The straight up-and-down line through the middle is our mirror line. When we flip the triangle, it swaps to the other side of that line, the same way your reflection swaps sides in a mirror.

    Watch what I do

    First I flip the triangle across the mirror line. Then I slide the flipped triangle three squares down.

    Now the question: if I had slid it down first and flipped it second, would it finish in the same square?

    2 - Watch and Notice ~9 mins

    We use two mirror lines: the y-axis goes straight up and down, the x-axis goes flat across. The interactive shows three two-step journeys, each moving the same starting triangle twice. Watch where it sits after the first move, then where it lands after the second.

    After Journey 1 we will settle the order question with one clear check. We take the same two moves from Journey 1, slide 4 right and flip across the y-axis, and run them both ways from the same start:

    • Order A: slide 4 right first, then flip across the y-axis. Mark the finish square.
    • Order B: flip across the y-axis first, then slide 4 right. Mark that finish square.

    Compare the two finish squares. Then look at Journey 3 (two slides) and ask whether swapping those two slides changes the finish or not.

    3 - Try It Together ~10 mins

    A vertex is a corner of the shape. Our triangle has three vertices, and we'll call them A, B and C. After each move we'll say where each corner ends up.

    Key point

    Today we work through three two-step sequences together on the board:

    • flip across the y-axis, then slide 3 down
    • slide 4 right, then turn a quarter-turn clockwise
    • slide 3 right, then slide 3 left

    After each step we'll read out where each corner has moved to. For the last sequence, watch where the shape finishes.

    Two moves, one after the other

    4 - Record Each Step in Your Copy ~3 mins

    COPYBOOK MOMENT

    Illustration for Record Each Step in Your CopyIn your maths copy, plot a small triangle on a grid. Label its three corners (vertices) A, B and C. Then apply flip across the y-axis, then slide 3 down. Record the co-ordinates after each step in a small table, like this:

    • Start: A, B, C
    • After flip across y-axis: A′, B′, C′
    • After slide 3 down: A″, B″, C″

    Fill in the actual co-ordinates for your triangle in each row.

    5 - Class Challenge ~8 mins

    Today we match the shape to the dashed target outline using two moves. The rounds build up:

    • a slide, then a flip
    • a flip, then a turn
    • two slides in a row
    • find a different pair of moves that reaches the target on the board

    Match the target with two moves

    Pupil practice
    Module 8 · Location, Transformations and Scale Algebra
    Lesson 88 · Combining Transformations
    Download Activity Book page (PDF)
    123learn · Online learning platform

    Unlock the full learning experience

    You're previewing this lesson. Get full access to this lesson and hundreds more — each one ready to teach, with interactive activities, printable resources and pupil progress tracking built in.

    Hundreds of curriculum-aligned lessons
    Interactive activities in every lesson
    Printable resources & progress tracking
    Copyright Notice
    This lesson is copyright of Coding Ireland 2017 - 2025. Unauthorised use, copying or distribution is not allowed.
    🍪 Our website uses cookies to make your browsing experience better. By using our website you agree to our use of cookies. Learn more