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      Explain how finding a fraction of a quantity relates to multiplying by a unit fraction

      Lesson details

      Learning outcome

      I can explain how finding a fraction of a quantity relates to multiplying by a unit fraction.

      Key learning points

      1. Half of a number is the same as a half multiplied by the number.
      2. If half of 10 is 5 then 1/2 x 10 = 5
      3. Finding a fraction of a number is the same as multiplying the number by the fraction.

      Keywords

      • Relationship - A relationship is a connection between two or more things.

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

      Common misconception

      Pupils struggle to see the relationship between the different number rods.

      Take time with pupils for them to explore the use of number rods if they have not done so before. You might ask pupils to find rods that are half the size of different coloured rods, so they can estimate sizes and draw attention to the relationship.

      Teacher tip

      Make sure you give time to exploring the multiplicative relationship between the rods as both repeated addition and scaling. As you do this, you might like to replace the rods with a small piece of elastic to further demonstrate the shrinking of the whole as it becomes one-___ times the size.

      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.
      Tick the unit fractions.

      Correct answer: $$ \frac{1}{5} $$
      $$ \frac{3}{6} $$
      Correct answer: $$ \frac{1}{12} $$
      $$ \frac{6}{7} $$
      $$ \frac{8}{4} $$

      Q2.
      Look at the image and complete. Each part is one-__________ of the whole.

      An image in a quiz
      half
      Correct answer: quarter
      fifth
      sixth

      Q3.
      Look at the image. One-__________ of the whole is circled.

      An image in a quiz
      half
      third
      fifth
      Correct answer: sixth

      Q4.
      Which equations match the image?

      An image in a quiz
      orange + orange = yellow
      yellow + orange = yellow
      Correct answer: yellow + yellow = orange
      Correct answer: 2 × yellow = orange

      Q5.
      One-quarter of 28 is equal to

      An image in a quiz
      Correct Answer: 7

      Q6.
      One-fifth of 30 is equal to

      Correct Answer: 6

      6 Questions

      Q1.
      How many lots of yellow are equal to orange?

      An image in a quiz
      Correct Answer: 2, two

      Q2.
      Tick the representation that matches the equation: $$ \frac{1}{2} $$ × r = w

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

      Q3.
      Tick the equations that match the image.

      An image in a quiz
      g = r
      Correct answer: g = 3 × r
      $$ \frac{1}{3} $$ × r = g
      Correct answer: $$ \frac{1}{3} $$ × g = r

      Q4.
      Tick the operation that can replace ‘of’ in a calculation.

      +
      Correct answer: ×
      ÷

      Q5.
      Tick the equations that match the image.

      An image in a quiz
      5 = 20 × 4
      Correct answer: 20 = 4 × 5
      Correct answer: $$ \frac{1}{4} $$ × 20 = 5
      $$ \frac{1}{5} $$ × 20 = 4

      Q6.
      Tick the equations that match the image.

      An image in a quiz
      Correct answer: 18 = 6 × 3
      18 = $$ \frac{1}{3} $$ × 6
      $$ \frac{1}{6} $$ × 18 = 3
      Correct answer: $$ \frac{1}{3} $$ × 18 = 6

      To help you plan your 5 maths lesson on: Explain how finding a fraction of a quantity relates to multiplying by a unit fraction, download all teaching resources for free and adapt to suit your pupils' needs...