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Year 8

Checking by estimating

I can estimate and check if solutions to problems are of the correct magnitude.

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New
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Year 8

Checking by estimating

I can estimate and check if solutions to problems are of the correct magnitude.

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Share activities with pupils
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Lesson details

Key learning points

  1. Estimation should give you an idea of the size of an answer.
  2. It is useful to estimate the answer to calculations so you can check your answers make sense.
  3. Errors in calculations can be found by using estimates.

Keywords

  • Significant figures - Significant figures are the digits in a number that contribute to the accuracy of the number.

  • Estimate - A quick estimate for a calculation is obtained from using approximate values, often rounded to 1 significant figure.

Common misconception

When rounding a number, pupils write the first significant digit(s). e.g 36 789 is 4.

The use of the place value table shows the magnitude of the number, thus preserving their place value.

Give the class an answer of 300 and ask what could the unrounded calculations be. Draw out their use of rounding to significant figures or other degrees of accuracy. E.g 300 could be 148.32 x 2.16 because 148.32 rounded to 2 s.f and 2.16 is rounded to 1 s.f.
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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.
Significant figures are the digits in a number that contribute to the accuracy of the number. The first significant figure is the first __________ digit.
digit between 5 and 9
important
Correct answer: non-zero
zero
Q2.
Which of the following are good estimate calculations for 989 × 213.4?
Correct answer: 1000 × 200
Correct answer: 1000 × 210
Correct answer: 1000 × 213
9 × 2
Q3.
Which of the following are good, quick estimate calculations for 432.4 ÷ 1.85?
Correct answer: 400 ÷ 2
400 ÷ 1.85
Correct answer: 500 ÷ 2
5 ÷ 2
Q4.
Which of the following are correct estimates for $${17.9}\over {0.532}$$?
$${18}\over {0.5}$$ $$= 9$$
$${20}\over {0.5}$$ $$= 10$$
Correct answer: $${18}\over {0.5}$$ $$= 36$$
Correct answer: $${20}\over {0.5}$$ $$= 40$$
Q5.
Which of the following is the correct estimate for $${3.4\times3.92}\over {0.511}$$?
$${3\times4}\over {0.5}$$ $$= 12$$
Correct answer: $${3\times4}\over {0.5}$$ $$= 24$$
$${3\times4}\over {0.5}$$ $$= 6$$
$${3.4\times3.92}\over {0.511}$$ $$ = 26.082$$
Q6.
Horses and ponies are measured using ‘hands’ as a unit, where the width of the hand is used. This pony has a height of 9 hands. Estimate the height of the pony.
An image in a quiz
200 cm
150 cm
Correct answer: 90 cm
50 cm
10 cm

Exit quiz

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6 Questions

Q1.
Match the following numbers to the correct rounded value.
Correct Answer:9212,9000 (1 s.f.)
tick

9000 (1 s.f.)

Correct Answer:8934.89,8934.9 (1 d.p.)
tick

8934.9 (1 d.p.)

Correct Answer:8910,8900 (2 s.f.)
tick

8900 (2 s.f.)

Correct Answer:8934.894,8934.89 (2 d.p.)
tick

8934.89 (2 d.p.)

Q2.
Which of the following are sensible measurements for the lengths of an average house?
An image in a quiz
Front: 844 mm , Side: 596 mm
Front: 0.844 km, Side: 0.896 km
Correct answer: Front: 844 cm, Side: 596 cm
Correct answer: Front: 8.44 m, Side: 5.96 m
Q3.
A bookshop wants to buy the new sci-fi books to sell in their store. The bookshop has £789 and each book costs £18.99. Select the correct estimate for the number of books the bookshop can buy.
$${800} \over {20}$$ = 4 books
Correct answer: $${800} \over {20}$$ = 40 books
$${800} \over {18.99}$$ = 42.127 books
$${800} \over {20}$$ = 4000 books
Q4.
Select the approximate answer to $$\frac{8}{15}\times\ 9$$.
3
Correct answer: 5
7
12
15
Q5.
A bicycle costs £18.99 for 1 week's hire. Which of the following shows the estimate to hire 6 bicycles for 4 weeks?
£20 × 6 × 4 = £240
Correct answer: £20 × 6 × 4 = £480
£20 × 6 × 4 = £2400
£20 × 6 × 4 = £4800
£20 × 6 × 4 = £24 000
Q6.
Jun buys paper £3.25, USB £$$\square$$, stamps £4.95, crisps £0.85, staples £2.30 and plug £1.99. He pays with a £20 note and receives about £2 back in change. Estimate the cost of the USB.
£1
£2
£3
Correct answer: £5
£7