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      Deepening understanding with fractions of a given amount

      Lesson details

      Learning outcome

      I can find the original amount when given a fraction and the result.

      Key learning points

      1. To find the original amount, the result is divided by the fraction.
      2. This can be seen visually through use of a bar model.
      3. A double number line can also be used.

      Keywords

      • Reciprocal - The reciprocal is the multiplicative inverse of any non-zero number. Any non-zero number multiplied by its reciprocal is equal to 1

      Common misconception

      Only seeing the amount, not proportion. E.g £30 from £100 is no different to £30 from £60.

      Referring to the whole using bar models or fractions can emphasise the amount with respect to the whole.

      Teacher tip

      After the 'think of a number' explanation. pupils get into pairs and find a fraction of 'their number', share the fraction and result and the other pupil has the work out the 'number' their partner was thinking of.

      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 of the following is not the reciprocal of 3?

      $$12\over36$$
      $$9\over27$$
      Correct answer: $$2\over3$$
      $$1\over3$$

      Q2.
      Use a bar model to calculate $$5\over8$$ of 32.

      Correct Answer: 20, twenty

      Q3.
      Calculate 45 × $$4\over5$$.

      Correct Answer: 36, thirty-six, thirty six, thirtysix

      Q4.
      Which of the following are equivalent calculations for $$5\over6$$ of 66?

      Correct answer: 66 × $$5\over6$$
      Correct answer: (66 ÷ 6) × 5
      Correct answer: $$5\over6$$ × $${6\times11}\over{1}$$
      (66 ÷ 5) × 6
      Correct answer: $$66\over6$$ × 5

      Q5.
      Calculate $$3 {{3} \over {4}}$$ × $$5\over6$$, give your answer in its simplest form.

      $$2{{7} \over {8}}$$
      $$3 {{8} \over {24}}$$
      Correct answer: $$3 {{1} \over {8}}$$
      $$3 {{1} \over {4}}$$

      Q6.
      Find $$11 {{3} \over {4}}$$ of 32.

      Correct Answer: 376

      6 Questions

      Q1.
      Match the following to the correct reciprocal.

      Correct Answer:2,$$1\over2$$

      $$1\over2$$

      Correct Answer:$$3\over2$$,$$2\over3$$

      $$2\over3$$

      Correct Answer:2.5,$$2\over5$$

      $$2\over5$$

      Correct Answer:$$4\over5$$,1.25

      1.25

      Correct Answer:$$6\over8$$,$$4\over3$$

      $$4\over3$$

      Q2.
      A shop has a sale saving you $$1\over3$$ off the original price. You pay £40 for a sweatshirt. How much was it originally?

      Correct Answer: £60, 60, £60.00, 60.00

      Q3.
      $$1\over5$$ of 60 = $$4\over5$$ of $$\square$$.

      Correct Answer: 15, fifteen

      Q4.
      I think of a number. $$3\over8$$ of my number is 15. What is my number?

      Correct Answer: 40, forty

      Q5.
      The cost of a TV increases by $$1\over8$$. It now costs £450. How much was it originally?

      Correct Answer: £400, £400.00, 400, 400.00

      Q6.
      Alex's cat loses $$1\over6$$ of it's weight. It now weighs 4.2 kg, how heavy was it last year?

      Correct Answer: 5.04 kg, 5.04kg, 5.04, 5.04 kilograms, 5.04kilograms

      To help you plan your 7 maths lesson on: Deepening understanding with fractions of a given amount, download all teaching resources for free and adapt to suit your pupils' needs...