Choose exam board for KS4 Computer Science (GCSE)
Choose exam board for KS4 English
Choose exam board for KS4 French
Choose exam board for KS4 Geography
Choose exam board for KS4 German
Choose exam board for KS4 History
Choose tier for KS4 Maths
Choose exam board for KS4 Music
Choose exam board for KS4 Physical education (GCSE)
Choose exam board for KS4 Religious education (GCSE)
Choose exam board for KS4 Spanish

      Describe the relationship between scale factors and perimeters of two shapes

      Lesson details

      Learning outcome

      I can describe the relationship between scale factors and side lengths and perimeters of two shapes.

      Key learning points

      1. If the lengths of the sides of a shape have been doubled, the perimeter will be double.
      2. If the side lengths of a shape are multiplied by the same factor the perimeter will be multiplied by the same factor.
      3. The number which all the sides have been multiplied by is called a scale factor.

      Keywords

      • Perimeter - Perimeter is the distance around a two-dimensional shape.

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

      • Similar - Two shapes are similar when one shape can become the other after a resize, flip, slide or turn.

      Common misconception

      Pupils may remember to scale one of the sides (or pairs of sides) of a shape but forget to scale the others.

      Focus attention on what it means when a shape is similar, drawing on examples and non-examples to support learners to understand how scaling affects all side lengths.

      Teacher tip

      Providing to-scale examples of scaled polygons initially may support all learners to practically see and measure the scaling that has taken place.

      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

      Loading...

      Prior knowledge starter quiz

      6 Questions

      Q1.
      Double 17 is

      Correct Answer: 34

      Q2.
      Multiply 16 by 4

      Correct Answer: 64

      Q3.
      Which of these is the same as dividing by two?

      Dividing by one-half
      Correct answer: Multiplying by one-half
      Adding one-half
      Multiplying by one-quarter

      Q4.
      Match the words to their correct definitions.

      Correct Answer:Transform ,Change something

      Change something

      Correct Answer:Enlarge ,Make something larger

      Make something larger

      Correct Answer:Reduce ,Make something smaller

      Make something smaller

      Q5.
      Match the equations to the correct product.

      Correct Answer:5 × 6 = ,30

      30

      Correct Answer:4 × 7 = ,28

      28

      Correct Answer:12 × 2 = ,24

      24

      Correct Answer:3 × 9 =,27

      27

      Q6.
      Which of the following are multiples of 7?

      Correct answer: 28
      34
      40
      Correct answer: 42
      Correct answer: 49

      6 Questions

      Q1.
      Select all of the scale factors where the result would be a shape with a greater length and width than the original.

      Scale factor of 1
      Scale factor of one-half
      Correct answer: Scale factor of 2
      Scale factor of one-third
      Correct answer: Scale factor of 3

      Q2.
      Shape A is a square with a side length of 3 cm and Shape B is a square with a side length of 12 cm. Shape A has been scaled by a scale factor of to create Shape B.

      Correct Answer: 4, four

      Q3.
      Shape A is an equilateral triangle with a side length of 3 cm and Shape B is an equilateral triangle with a side length of 9 cm. Shape A has been scaled by a scale factor of to create Shape B.

      Correct Answer: 3, three

      Q4.
      Shape A is a square with a side length of 3 cm which has been scaled by a scale factor of 3 to get Shape B. What is the perimeter of Shape B? cm.

      Correct Answer: 36

      Q5.
      Shape A is a triangle with a side length of 3 cm which has been scaled by a scale factor of 4 to get Shape B. What is the perimeter of Shape B? cm.

      Correct Answer: 36

      Q6.
      Select all of the scale factors where the result would be a shape with a smaller length and width than the original.

      Correct answer: Scale factor of one-half
      Scale factor of 2
      Correct answer: Scale factor of one-third
      Scale factor of 3
      Correct answer: Scale factor of one-quarter

      To help you plan your 6 maths lesson on: Describe the relationship between scale factors and perimeters of two shapes, download all teaching resources for free and adapt to suit your pupils' needs...