Good Learning Co.
SavannahYear 8
← Maths
MathsNumber, powers and accuracy30 min★★★ difficulty

Rounding, estimating and checking

Estimating is not guessing. It is a deliberate calculation with friendly numbers that tells you whether the answer you got is even possible.

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
  • • Choosing sensible accuracy
  • • Estimating with 1 s.f.
  • • Spotting an impossible answer

This lesson at a glance

  • 30 minutes
  • 19 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 19 · Discover5%
1

Watch & discover

Part 1 of 19

Watch first

Rounding, estimating and checking

An English teaching video on this topic from 1st Class Maths. 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

What you already know

Part 2 of 19

Before we start

What you already know

You can round to the nearest 10, 100 and to decimal places.

3

Key words

Part 3 of 19

Key words

Words you'll need today

significant figure
The first digits that carry the size of a number, counting from the first non-zero digit.
estimate
A rough answer found by rounding first, shown with ≈.
degree of accuracy
How precisely a measure is stated, e.g. to the nearest cm.
4

Learning cycle

Part 4 of 19

Learning cycle 1 of 2

Part 1 — Accuracy

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

5

Explore the idea

Part 5 of 19

Learn

Significant figures

In 0.004073 the first significant figure is the 4 — leading zeros only hold place value. To 2 s.f. it is 0.0041. In 28,610 the first significant figure is the 2, and to 2 s.f. it is 29,000. Significant figures keep the size right, which is what matters in measurement.

6

Explore the idea

Part 6 of 19

Learn

Choosing sensible accuracy

Accuracy should suit the context. A room is measured to the nearest cm, a person's height to the nearest cm, a journey to the nearest mile, money to the nearest penny. Writing a room as 3.4172 m pretends to a precision the tape measure never had.

7

Quick check

Part 7 of 19

Quick check

0.00568 to 2 s.f. is...

8

Quick check

Part 8 of 19

Quick check

Estimate 512 × 19.

9

Reset break

Part 9 of 19

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
10

Learning cycle

Part 10 of 19

Learning cycle 2 of 2

Part 2 — Estimating to check

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

11

Explore the idea

Part 11 of 19

Learn

Estimating with 1 s.f.

To estimate 197 × 4.1, round each to 1 s.f.: 200 × 4 = 800. The real answer is 807.7, so 800 tells you the size is right. For division, round to numbers that divide neatly: 613 ÷ 29 ≈ 600 ÷ 30 = 20.

12

Explore the idea

Part 12 of 19

Learn

Spotting an impossible answer

If you estimate 800 and your calculator says 80.7, you have a factor-of-ten error, usually a misplaced decimal point. Estimating before you calculate takes seconds and catches most slips. In exam-style questions the word 'estimate' means you must show the rounded numbers you used.

13

Quick check

Part 13 of 19

Quick check

34,721 to 2 s.f. is...

14

Quick check

Part 14 of 19

Quick check

Best accuracy for a person's height?

15

Common mix-ups

Part 15 of 19

Common mix-ups

Things people often get wrong

  • Counting leading zeros as significant figures.
  • Rounding to decimal places when the question asks for significant figures.
  • Giving an 'estimate' by doing the exact calculation then rounding it.
16

Challenge round

Part 16 of 19

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

17

Challenge round

Part 17 of 19

Game · Fill the gaps

Finish the sentences

Choose the word that belongs in each gap.

____ should suit the context.

For division, round to ____ that divide neatly: 613 ÷ 29 ≈ 600 ÷ 30 = 20.

18

Mastery quiz

Part 18 of 19

Marked quiz

End of lesson quiz: Rounding, estimating and checking

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

  1. 1. Estimate 398 ÷ 21.

  2. 2. 0.04932 to 3 s.f.

  3. 3. An estimate is written with...

  4. 4. Estimate 6.1 × 7.9.

  5. 5. Your estimate is 60 and you calculate 6.2. Likely error?

  6. 6. Round 8,499 to 1 s.f.

19

Lesson round-up

Part 19 of 19

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 19 · Watch & discover

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