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      Find the whole when the size of a non-unit fraction is known

      Lesson details

      Learning outcome

      I can find the whole when the size of a non-unit fraction is known.

      Key learning points

      1. This is __ of the whole so one part of the whole is __
      2. There will be __ of these parts in the whole
      3. If you work out the size of a unit fraction from the non-unit fraction, you can work out the size of the whole

      Keywords

      • Represent - To represent something means to show something in a different way. The same thing can be shown using multiple representations.

      • Unit fraction - A unit fraction is a fraction that has a numerator of one.

      • Non-unit fraction - A non-unit fraction is a fraction that has a numerator greater than one.

      • Denominator - The denominator is the bottom number in a fraction.

      • Numerator - The numerator is the top number in a fraction.

      Common misconception

      Pupils multiply the non-unit fraction by the denominator to create the whole.

      Ensure pupils spend time breaking down non-unit fractions back into unit fractions. Encourage pupils to recognise this as two stages. Firstly, find the unit fraction. Secondly, re-create the whole.

      Teacher tip

      Ensure you give additional time for pupils to practise, eventually moving away from representing the mathematics with a bar model every time. Whilst it is good for pupils to represent the maths in a way that makes sense to them, pupils should also be encouraged to calculate these problems mentally.

      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.
      Complete: $$ \frac{1}{4} $$ + $$ \frac{1}{4} $$ + $$ \frac{1}{4} $$ + $$ \frac{1}{4} $$ =

      Correct Answer: 1, 1 whole, one whole, four quarters

      Q2.
      The image represents $$ \frac{3}{4} $$ of the shape. Tick the image that shows $$ \frac{1}{4} $$

      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.
      The image represents $$ \frac{2}{5} $$ of the whole. Tick the image that shows $$ \frac{1}{5} $$

      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

      Q4.
      The part of the image shown by the arrow represents $$ \frac{6}{8} $$ How many intervals would represent $$ \frac{1}{8} $$

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

      Q5.
      The image represents $$ \frac{1}{4} $$ of the whole. How many cubes would be needed to make the whole? cubes

      An image in a quiz
      Correct Answer: 8

      Q6.
      The image represents $$ \frac{3}{5} $$ of the whole. How many circles would be needed to represent the whole?

      An image in a quiz
      Correct Answer: 20, twenty

      6 Questions

      Q1.
      Think about a fraction. The __________ tells us how many equal parts the whole has been divided into.

      numerator
      Correct answer: denominator
      whole fraction

      Q2.
      The image represents $$ \frac{2}{5} $$ of the whole. Tick the images that could represent the whole.

      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

      Q3.
      Tick the image that represents the whole collection. Sam says ‘This is two-quarters of the apples Mum bought on her shopping trip.’

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

      Q4.
      Which line would have the largest whole?

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

      Q5.
      If $$ \frac{5}{8} $$ of a number is 45, what is the number?

      Correct Answer: 72

      Q6.
      If $$ \frac{3}{5} $$ of a number is 330, what is the number?

      Correct Answer: 550

      To help you plan your 5 maths lesson on: Find the whole when the size of a non-unit fraction is known, download all teaching resources for free and adapt to suit your pupils' needs...