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Year 7

Deepening understanding with fractions of a given amount

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

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New
New
Year 7

Deepening understanding with fractions of a given amount

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

Download all resources
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Share activities with pupils
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Lesson details

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.

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.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), 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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Starter quiz

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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

Exit quiz

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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