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      Use multiplication and division to calculate unknown values in ratio problems

      Lesson details

      Learning outcome

      You can use multiplication and division to calculate unknown values in ratio problems.

      Key learning points

      1. Different representations can be used to show the same mathematical structure.
      2. Ratio tables show the multiplicative relationship between variables.

      Keywords

      • Ratio - A ratio shows the relative sizes of 2 or more values and allows you to compare a part with another part in a whole

      • For every - For every allows you to talk about the relative sizes of the values e.g. for every 2 squares there is 1 triangle

      Common misconception

      Seeing multiplication and division as inverse operations e.g. dividing by 2 and multiplying by half.

      Encourage pupils to express the relationships between values using both multiplication and division.

      Teacher tip

      Make links to known times table facts and encourage pupils to think about the relationships between values as both multiplication and division. Ask them to explain which relationship they find easier to think about and why.

      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.
      What is 8 times as many as 5?

      Correct Answer: 40, Forty, Fourty

      Q2.
      How many 8s are there in 24?

      Correct Answer: 3, Three, three

      Q3.
      How many times greater than 3 is 27?

      24
      3
      6
      Correct answer: 9
      10

      Q4.
      Which phrases describe the quiz team in this image

      An image in a quiz
      For every 2 chidlren there are 3 adults
      For every 3 adults there are 3 children
      For every 3 children there are 4 adults
      Correct answer: For every 4 children there are 3 adults
      Correct answer: For every 3 adults there are 4 children

      Q5.
      Each quiz team is made up of 3 adults and 4 children. If there are 35 people taking part, which equation represents how many of them are adults?

      $$3 + 35 = 38$$
      $$4 \times 5 = 20$$
      Correct answer: $$3 \times 5 = 15$$
      $$3 \times 7 = 21$$

      Q6.
      Each quiz team is made up of 3 adults and 4 children. If there are 5 teams taking part, how many children will there be in total?

      7
      15
      Correct answer: 20
      32
      31

      6 Questions

      Q1.
      A quiz team is made up of 2 adults and 3 children. How many quiz teams does this image represent?

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

      Q2.
      How many children are represented in this image?

      An image in a quiz
      3
      4
      9
      Correct answer: 12

      Q3.
      How many adults are represented in this image?

      An image in a quiz
      2
      Correct answer: 8
      4
      6

      Q4.
      How many people in total are represented in this image?

      An image in a quiz
      5
      16
      25
      Correct answer: 20

      Q5.
      What does the 5 in this equation represent in the image? $$5 \times 4 = 20$$

      An image in a quiz
      The number of children
      The number of adults
      Correct answer: The number of people in one team
      The number of people doing the quiz altogether
      The number of teams taking part

      Q6.
      What does the 4 in this equation represent in the image? $$5 \times 4 = 20$$

      An image in a quiz
      The number of children
      The number of adults
      The number of people in one team
      The number of people doing the quiz altogether
      Correct answer: The number of teams taking part

      To help you plan your 6 maths lesson on: Use multiplication and division to calculate unknown values in ratio problems, download all teaching resources for free and adapt to suit your pupils' needs...