Good Learning Co.
SavannahYear 8
← Maths
MathsNumber, powers and accuracy28 min★★★ difficulty

Rounding, estimating and checking

Accuracy is a judgement, not a rule. A carpenter rounds to the nearest millimetre, an astronomer to the nearest million kilometres, and both are being precise for their purpose.

Part of your national curriculum
  • Number: Round numbers and measures to an appropriate degree of accuracy and use approximation to check answers

Lesson overview

What you'll learn in this lesson

Round numbers and measures to an appropriate degree of accuracy and use approximation to check answers

Key learning points

  • • Significant figures
  • • Estimating a calculation
  • • Measurement bounds
  • • Rounding only at the end

This lesson at a glance

  • 28 minutes
  • 17 parts to scroll through
  • 4 quick checks
  • Marked quiz at the end
  • Gentle pace: short sittings with pauses

Words to know

numbersmeasuresappropriatedegreeaccuracy

Scroll down — the lesson carries on below

Part 1 of 17 · Discover6%
1

Watch & discover

Part 1 of 17

Watch first

Rounding, estimating and checking

An English teaching video on this topic from Smile and Learn - English. Watch it, then scroll down for the lesson.

In a nutshell

Round numbers and measures to an appropriate degree of accuracy and use approximation to check answers

2

Learning cycle

Part 2 of 17

Learning cycle 1 of 2

Part 1 · Significant figures

A short piece of teaching, then a check to make sure it has landed.

3

Explore the idea

Part 3 of 17

Learn

Significant figures

The first significant figure is the first non-zero digit. In 0.004072 the first significant figure is 4, so to 2 s.f. the number is 0.0041. Significant figures suit measurements of very different sizes, while decimal places suit money and quantities on a shared scale.

4

Explore the idea

Part 4 of 17

Learn

Estimating a calculation

Round every number to 1 s.f. and calculate mentally. For (48.7 × 6.1) ÷ 0.52 estimate (50 × 6) ÷ 0.5 = 300 ÷ 0.5 = 600. If your calculator gives 57 or 5,700 you have made a place-value error, and the estimate has done its job.

5

Quick check

Part 5 of 17

Quick check

0.004072 to 2 significant figures is

6

Quick check

Part 6 of 17

Quick check

Estimate 39.6 × 4.8.

7

Learning cycle

Part 7 of 17

Learning cycle 2 of 2

Part 2 · Measurement bounds

A short piece of teaching, then a check to make sure it has landed.

8

Reset break

Part 8 of 17

Pause

That's sitting 1 of 2 done

Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.

Stop here for now
9

Explore the idea

Part 9 of 17

Learn

Measurement bounds

A length recorded as 12.4 cm to 1 d.p. lies between 12.35 cm and 12.45 cm: half a unit either side. Every measurement carries this uncertainty, so quoting an answer to eight decimal places from data measured to the nearest millimetre claims precision the data cannot support.

10

Explore the idea

Part 10 of 17

Learn

Rounding only at the end

Rounding partway through a multi-step calculation makes small errors grow. Keep full accuracy in your working, use the calculator memory, and round once at the final step, stating the accuracy you used.

11

Quick check

Part 11 of 17

Quick check

A mass is 6.8 kg to 1 d.p. Its lower bound is

12

Quick check

Part 12 of 17

Quick check

Why round only at the end?

13

Explore the idea

Part 13 of 17

Worked example

Worked answer: estimate (48.7 × 6.1) ÷ 0.52 and comment on your estimate (3 marks)

Rounding to 1 s.f. gives (50 × 6) ÷ 0.5 (1). The numerator is 300 and dividing by 0.5 doubles it, giving an estimate of 600 (1). The estimate is slightly high because 48.7 and 0.52 were both rounded in directions that increase the result, so the true answer, 571 to 3 s.f., is a little lower (1).

14

Challenge round

Part 14 of 17

Game · Sort it

Which of these are true?

Drag each card into the right column. Tap a card first if dragging is fiddly.

True

Not true

15

Challenge round

Part 15 of 17

Game · Fill the gaps

Finish the sentences

Choose the word that belongs in each gap.

Keep full ____ in your working, use the calculator memory, and round once at the final step, stating the accuracy you used.

16

Mastery quiz

Part 16 of 17

Marked quiz

End of lesson quiz: Rounding, estimating and checking

4 questions, marked with the reasoning shown. No timer.

  1. 1. 0.004072 to 2 significant figures is

  2. 2. Estimate 39.6 × 4.8.

  3. 3. A mass is 6.8 kg to 1 d.p. Its lower bound is

  4. 4. Why round only at the end?

17

Lesson round-up

Part 17 of 17

Lesson round-up

Ready when you are

Quiz score

Not sat

Games

Not played

Points this lesson

0

Best run

0 in a row

Luna: 0 out of 4 on the practice checks. Only if you feel up to it — one more?

Ask Luna

Do the work

Your written work for this lesson

This is the part you'd do in your book at school. Pick the pieces below, write here or on paper, and photograph anything you draw or work out.

Article

The cost of a school trip

A school is planning a trip to a wildlife park. The coach costs £480 however many people go. Entry costs £9.50 for each pupil and each adult goes free. The school says every pupil must pay the same amount, and the trip must not lose money.

If 60 pupils go, the coach works out at £8 each, so the total for each pupil is £17.50. If only 40 pupils go, the coach works out at £12 each, so the price rises to £21.50. The teacher explains that the coach is a fixed cost and the entry is a cost per person — which is why the price per pupil changes when the number changes.

The school decides to charge £20 and to use anything left over for a second trip later in the year.

Written for Good Learning Co.

Reading questions

  1. Work out the total cost of the trip if 50 pupils go.
  2. Show why the price per pupil falls when more pupils go, using numbers.
  3. At £20 each, how many pupils must go before the trip makes money? Show your working.

  • Working out

    Working out

    Do the practice questions on paper, showing every step — not just the answer. Mark them yourself and circle anything you got wrong.

    10–15 questions

  • Worked example, explained

    Writing

    Copy one question out and write underneath, in words, why each step works.

    1 question, 4–5 sentences

  • Problem in words

    Working out

    Write your own real-life problem that uses today's method, then solve it.

    1 problem + solution

Saved as you type.

Part 1 of 17 · Watch & discover

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    Round numbers and measures to an appropriate degree of accuracy and use approximation to check answers

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