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      Lesson details

      Learning outcome

      I can rotate objects using information about centre, size and direction of rotation

      Key learning points

      1. Tracing paper can be a helpful tool to perform a rotation.
      2. The image and the object should be congruent.
      3. Unless a full rotation occurs, the object and its image will not have the same orientation.

      Keywords

      • Clockwise - A clockwise direction is the direction in which the hands of an analogue clock travel.

      • Anti-clockwise - An anti-clockwise direction is the opposite direction to which the hands of an analogue clock travel.

      • Centre of rotation - The centre of rotation is the fixed point about which an object is rotated. It fixes the location of the image after it is rotated.

      • Degrees - Degrees are the most common unit of measurement for angle. One whole turn is equal to 360 degrees, written 360°.

      Common misconception

      After drawing an object on the tracing paper, you take the tracing paper off the table to rotate it.

      This is especially dangerous if the centre of rotation wasn't drawn on the tracing paper, too. The image will lose its correct location.

      Teacher tip

      For all diagrams where vertices or the centre of rotation overlap inside the object, students need to press hard enough through the tracing paper so that they can see the mark on the paper.

      Licence

      This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0
      except where otherwise stated. See Oak's terms & conditions
      (Collection 2).

      Lesson video

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      Prior knowledge starter quiz

      6 Questions

      Q1.
      Match the size an angle in degrees to its description.

      Correct Answer:90°,a quarter turn
      Correct Answer:180°,a half turn
      Correct Answer:270°,a three-quarter turn
      Correct Answer:360°,a full turn
      Correct Answer:540°,a one-and-a-half turn
      Correct Answer:630°,a one-and-three-quarter turn

      Q2.
      Which of these is an accurate description for this rotation?

      An image in a quiz
      Correct answer: Rotated clockwise by 90°.
      Rotated clockwise by 270°.
      Rotated anti-clockwise by 90°.
      Correct answer: Rotated anti-clockwise by 270°.

      Q3.
      What is the centre of rotation for this rotation?

      An image in a quiz
      Correct Answer: (4, 1), (4,1)

      Q4.
      This object has been rotated clockwise. By how many degrees did this object rotate?

      An image in a quiz
      Correct Answer: 180, 180°, 180 degrees, 180degrees

      Q5.
      A pair of corresponding vertices on the object and image are joined with a line segment. Join a second pair of vertices to find the coordinates of the centre of rotation.

      An image in a quiz
      (3, 4)
      (11, 8)
      (7, 4)
      Correct answer: (7, 6)
      (9, 7)

      Q6.
      This object has been rotated by 180°. The image overlaps its object. Find the coordinates of the centre of rotation.

      An image in a quiz
      Correct Answer: (6, 7), (6,7)

      6 Questions

      Q1.
      When you use tracing paper to rotate an object, which two things should you draw onto the tracing paper?

      the origin
      Correct answer: the whole object
      exactly two vertices of the object
      both the $$x$$-axis and $$y$$-axis
      Correct answer: the centre of rotation

      Q2.
      After which step can you remove the tracing paper in order to progress onto the next step in completing your rotation?

      after drawing the object and centre of rotation on the tracing paper
      after drawing the image on the paper underneath
      after pushing your pencil onto the centre of rotation to use it as a pivot
      Correct answer: after pushing your pencil onto each of the vertices to leave an imprint
      after rotating the tracing paper

      Q3.
      This object will be rotated 90° anti-clockwise with the centre of rotation of (6, 6). Where will the image of vertex A end up after this rotation?

      An image in a quiz
      (4, 10)
      Correct answer: (2, 6)
      (8, 6)
      (6, 6)
      (6, 2)

      Q4.
      This object will be rotated 180° with the centre of rotation of (6, 6). Where will the image of vertex B end up after this rotation?

      An image in a quiz
      Correct Answer: (4, 6), (4,6)

      Q5.
      This object will be rotated 90° clockwise with the centre of rotation of (9, 4). Where will the image of vertex C end up after this rotation?

      An image in a quiz
      (9, 4)
      (9, 6)
      Correct answer: (9, 7)
      (9, 8)
      (9, 10)

      Q6.
      This object will be rotated 90° clockwise with the centre of rotation of (9, 4). Where will the image of vertex D end up after this rotation?

      An image in a quiz
      Correct Answer: (15, 10), (15,10)

      To help you plan your 7 maths lesson on: Rotating objects, download all teaching resources for free and adapt to suit your pupils' needs...