Mathematics
Advanced
50 mins
Teacher/Student led
Learning Goals
Learning Outcomes
Lesson Files
+65 XP
What you need:
IWB/Projector/Large Screen

Rotation of Shapes About a Point

Rotate shapes around a fixed point by 90°, 180° and other angles in both clockwise and anticlockwise directions. Predict where corners will land, then check your predictions.

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    1 - Getting Started ~4 mins

    Key point

    Your teacher is going to pin a flag at one point and turn it a quarter-turn clockwise around that pin. A quarter-turn is the same as a 90° turn, and a half-turn is the same as a 180° turn.

    Illustration for Getting StartedWhat changed about the flag when it turned? What stayed exactly the same?

    👇 Mark your steps as done as you complete them.

    +5 XP

    2 - Watch and Notice ~10 mins

    Your teacher will show some rotations, each around a fixed point called the marked point. A vertex is a corner of the shape. Watch the shape's facing direction in each turn, and be ready to say what stayed the same.

    For one turn, think quietly to yourself: where has the chosen corner landed? Then put your hand up. The last one is different. It starts with the shape already turned, and we work backwards. Look at where one corner started and where it ended, count the quarter-turns, and say which way it went.

    👇 Mark your steps as done as you complete them.

    +10 XP

    3 - Try It Together ~8 mins

    Today we work through these rotations together, one at a time.

    Key point

    First we turn the flag 90° clockwise about the marked point.

    Next we turn it 180° about the marked point.

    Then we turn it 90° anticlockwise about a corner of the shape.

    Tip

    Before each turn we predict where a chosen corner will land. Then we check it.

    Turn the shape about a point

    +15 XP

    4 - Turn It in Your Copy ~3 mins

    COPYBOOK MOMENT

    First we work one full example together on the board so everyone sees how to sketch a rotation on squared paper. Then you try your own in your maths copy.

    Mark a centre C on the grid. Draw a small L-shape with one corner, A, three squares right and one square up from C.

    To move corner A through a 90° clockwise turn about C:

    • From C to A is 3 right and 1 up.
    • After a quarter-turn clockwise that landing spot is 1 right and 3 down from C. Mark it A′.
    • Do the same count for every other corner, then join the new corners to sketch the image. Label it 90° clockwise about C.

    For a 180° turn about C, the same corner at 3 right and 1 up lands at 3 left and 1 down. Same distance from C, opposite side. Sketch and label that image too.

    Now in your maths copy, draw a simple shape on squared paper and mark a centre of rotation with a clear dot. Sketch its image after a 90° clockwise turn, then sketch its image after a 180° turn. Label each image with the turn you made.

    +10 XP

    5 - Class Challenge ~9 mins

    Key point

    Today we match the shape onto the dashed target outline. To match it, we turn the shape so it lands exactly on top of the target.

    First we make a single 90° clockwise turn.

    Next we make a 180° turn.

    Then we make a 90° anticlockwise turn about a corner.

    Finally you work out which rotation lands the shape exactly on top of its target.

    Match the target

    +15 XP
    Pupil practice
    Module 8 · Location, Transformations and Scale Shape & Space
    Lesson 94 · Rotation of Shapes About a Point
    Download Activity Book page (PDF)
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