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      Introduction to rotations

      Lesson details

      Learning outcome

      I can understand the nature of rotations and appreciate what changes and what is invariant.

      Key learning points

      1. The length of the lines do not change when rotated
      2. The angles inside an object do not change when rotated
      3. When an object is rotated, its image is congruent
      4. Unless a full rotation occurs, the object and its image will not have the same orientation

      Keywords

      • Rotation - The rotation of an object is the turning of an object by a fixed amount and around a fixed point (called the centre of rotation).

      Common misconception

      After an object has been rotated, the orientation stays the same if the image looks the same.

      This is only true if the object is rotated through 360°. Otherwise, the orientation is different as each vertex is in a different position.

      Teacher tip

      In Task B question 3, it is important for the projection to have 16:9 aspect ratio for the measurements to be consistent, or for the question to be printed for students to measure with a ruler.

      Equipment

      Pen or pencil, ruler, protractor.

      Licence

      This content is © Oak National Academy Limited (2026), 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.
      What is 360 - 90?

      170
      250
      260
      Correct answer: 270
      280

      Q2.
      is the process by which an object is changed into its image by moving, sliding, turning, flipping or stretching.

      Correct Answer: Transformation, transformation, transform, Transform

      Q3.
      When a vertex is labelled $$E^{\prime}$$, it means the __________ of E.

      Correct answer: image
      object
      orientation
      position
      transformation

      Q4.
      What does the term "invariant property" mean?

      A shape that hasn't changed location after a translation has been applied.
      Correct answer: A property of a mathematical object that hasn't changed after a transformation.
      A property of a mathematical object that has changed after a transformation.
      A property of a vertex that moves after a transformation.

      Q5.
      Which properties are invariant when an object is translated?

      Correct answer: length of a side
      Correct answer: size of an angle
      position
      Correct answer: orientation
      Correct answer: sense

      Q6.
      Which of these shows an arrow that has been turned round?

      An image in a quiz
      Correct Answer: An image in a quiz
      An image in a quiz
      An image in a quiz
      An image in a quiz

      5 Questions

      Q1.
      In which direction will this vehicle be facing when it is rotated so its wheels touch the road?

      An image in a quiz
      left
      Correct answer: right

      Q2.
      Which of these objects, when rotated by a quarter-turn, will fit into the space in this shape to complete a rectangle?

      An image in a quiz
      A
      Correct answer: B
      C
      D

      Q3.
      Complete this sentence: "When an object is rotated, the lengths of its sides are invariant. This means the lengths of the sides remain ."

      Correct Answer: the same, exactly the same, same, identical, unchanged

      Q4.
      Sam transforms an object and its orientation changes. Which of these describes why the orientation has changed?

      The object hasn't been rotated to become its image.
      The object has been translated right to become its image.
      Correct answer: The object has been rotated through a half turn to become its image.
      Orientation always changes when objects are translated.
      Correct answer: Orientation always changes when objects are rotated by less than a full turn.

      Q5.
      Which of these is a rotation of this object?

      An image in a quiz
      Image 1
      Correct answer: Image 2
      Correct answer: Image 3
      Image 4
      Correct answer: Image 5

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