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      Checking and securing understanding of enlargement with positive integer scale factors

      Lesson details

      Learning outcome

      I can describe an enlargement and perform a given enlargement on an object.

      Key learning points

      1. Each length in the shape is multiplied by the scale factor.
      2. Each vertex in the object is a given distance from the centre of enlargement.
      3. This distance is also multiplied by the scale factor to give the distance of the image's vertex.
      4. A positive integer scale factor produces an image that is bigger than the original.
      5. To enlarge, you need the centre of enlargement and a scale factor.

      Keywords

      • Transformation - A transformation is a process that may change the size, orientation or position of a shape.

      • Enlargement - Enlargement is a transformation that causes a change of size.

      • Scale factor - A scale factor is the multiplier between similar shapes that describes how large one shape is compared to the other.

      • Centre of enlargement - The centre of enlargement is the point from which a shape is enlarged.

      Common misconception

      Pupils may measure/count from the object rather than the centre of enlargement.

      Have pupils check their answers using ray lines.

      Teacher tip

      Discuss how enlargements create similar shapes that are not congruent on the most part, whereas rotation, reflection and translation always create congruent shapes. When can an enlargement create congruent shapes?

      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.
      A of a shape is the mirror image of the shape.

      Correct Answer: reflection

      Q2.
      Which of these diagrams do NOT show a reflection?

      Correct Answer: An image in a quiz
      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

      Q3.
      Two shapes are similar if the only difference between them is their __________. Their side lengths are in the same proportions.

      angles
      orientation
      position
      Correct answer: size
      vertices

      Q4.
      Which of these diagrams show a reflection?

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

      Q5.
      Quadrilaterals A and B are similar. The length of the side marked $$z$$ is cm.

      An image in a quiz
      Correct Answer: 8, 8cm, 8 cm

      Q6.
      Rectangle B is an enlargement of rectangle A by scale factor 2. Rectangle A has perimeter = 18 cm and area = 18 cm². Both rectangles have integer side lengths. Find the area and perimeter of B.

      An image in a quiz
      Area = 36 cm²
      Correct answer: Area = 72 cm²
      Correct answer: Perimeter = 36 cm
      Perimeter = 72 cm

      6 Questions

      Q1.
      An enlargement will produce an image that is __________ to the object.

      congruent
      Correct answer: similar

      Q2.
      Shape A is enlarged to give shape B. The scale factor of this enlargement is .

      An image in a quiz
      Correct Answer: 3, three

      Q3.
      These two shapes are an enlargement of each other. The missing length is cm.

      An image in a quiz
      Correct Answer: 6, six, 6 cm, 6cm

      Q4.
      Shape A is enlarged to give shape B. The scale factor of this enlargement is .

      An image in a quiz
      Correct Answer: 2, two

      Q5.
      Shape A is enlarged to give shape B. What is the centre of the enlargement?

      An image in a quiz
      (0, 0)
      Correct answer: (1, 0)
      (0, 1)
      (1, 1)
      (2, 1)

      Q6.
      Shape A is enlarged by scale factor 2, centre (6, 6) to give shape B. Select the points that should be joined to give shape B.

      An image in a quiz
      Correct answer: (2, 4)
      (0, 4)
      (4, 4)
      Correct answer: (4, 0)
      Correct answer: (2, 0)

      To help you plan your 10 maths lesson on: Checking and securing understanding of enlargement with positive integer scale factors, download all teaching resources for free and adapt to suit your pupils' needs...