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      Representing ratio in different ways

      Lesson details

      Learning outcome

      You can explain how to use multiplication and division to calculate unknown values with two variables.

      Key learning points

      1. Bar models can represent unequal sharing or many to many sharing.
      2. Representations show the relationship between the two variables.
      3. The representation helps to identify the calculations needed to solve the problem.

      Keywords

      • Many to many - Use many to many to describe ratios where each value is more than one

      Common misconception

      Using addition and subtraction rather than multiplication and division to solve problems.

      Continue to model the use of the language and notation of multiplication to calculate missing values.

      Teacher tip

      Make sure that pupils can explain how the numbers in the caluclation relate to the objects and bar models. Make sure they understand what the answer represents and whether they are calculating a part or the whole.

      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.
      Which image can be described by this statement 'For every 3 birds there are 4 squirrels'?

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

      Q2.
      Write a sentence using 'for every' to describe this image

      An image in a quiz
      For every 2 triangles there are 3 circles
      Correct answer: For every 3 triangles there are 2 circles
      Correct answer: For every 9 triangles there are 6 circles
      For every three triangles there are 3 circles

      Q3.
      What does the number 8 in this equation $$2 \times 4 = 8$$ represent in relation to this image?

      An image in a quiz
      Correct Answer: The total number of circles, All the circles, 4 lots of 2 circles

      Q4.
      What does the number 4 this equation $$3 \times 4 = 12$$ represent in relation to this image?

      An image in a quiz
      Correct Answer: The pattern is shown 4 times, There are 4 basic patterns, There are 4 lots of pattern

      Q5.
      What does the number 12 this equation $$3 \times 4 = 12$$ represent in relation to this image?

      An image in a quiz
      Correct Answer: The number of triangles, There are 12 triangles, 4 lots of 3 triangles

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

      An image in a quiz
      Correct Answer: The total number of shapes, All the triangles and circles, All the shapes in the image

      6 Questions

      Q1.
      Which statment matches this image?

      An image in a quiz
      For every 1 orange marble there are 3 blue marbles
      For every 3 orange marbles there are 2 blue marbles
      For every 3 blue marbles there are 2 orange marbles
      Correct answer: For every 3 orange marbles there is 1 blue marble

      Q2.
      Which of the images show a 'many to many' ratio?

      Correct answer: For every 2 orange marbles there are 3 blue marbles
      For every 1 orange marble there are 2 blue marbles
      Correct answer: For every 2 blue marbles there are 5 orange marbles
      For every 3 orange marbles there is 1 blue marble

      Q3.
      What multiplication would you use to work out the missing number? If there are 12 blue marbles, there will be __ orange marbles.

      An image in a quiz
      $$5 \times 2 = 10$$
      $$2 \times 3 = 6$$
      Correct answer: $$2 \times 4 = 8$$
      $$5 \times 4 = 20$$

      Q4.
      Which equation represents the total number of marbles?

      An image in a quiz
      $$5 \times 2 = 10$$
      $$2 \times 3 = 6$$
      $$2 \times 4 = 8$$
      Correct answer: $$5 \times 4 = 20$$

      Q5.
      A recipe uses 3 eggs for every 4 spoons of sugar. If you use 15 eggs, how many spoons of sugar will you need?

      25
      Correct answer: 20
      19
      16

      Q6.
      A recipe uses 3 eggs for every 4 spoons of sugar. If you use 40 spoons of sugar, how many eggs will you need?

      39
      70
      40
      Correct answer: 30

      To help you plan your 6 maths lesson on: Representing ratio in different ways, download all teaching resources for free and adapt to suit your pupils' needs...