Good Learning Co.
SavannahYear 8
← Maths
MathsThe maths behind the money30 min★★★ difficulty

Percentages of money you can do in your head

Percentage means 'parts per hundred', and once you can convert between fractions, decimals and percentages you can check a discount, a tip or a tax figure without reaching for a calculator.

Lesson overview

What you'll learn in this lesson

Work interchangeably with terminating decimals and their corresponding fractions, and define percentage as 'number of parts per hundred'

Key learning points

  • • Three ways to write one value
  • • Building blocks
  • • Multipliers do it in one step
  • • Rounding money sensibly

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

interchangeablyterminatingdecimalscorrespondingfractions

Scroll down — the lesson carries on below

Part 1 of 19 · Discover5%
1

Watch & discover

Part 1 of 19

Watch first

Percentages of money you can do in your head

An English teaching video on this topic from mathantics. Watch it, then scroll down for the lesson.

In a nutshell

Work interchangeably with terminating decimals and their corresponding fractions, and define percentage as 'number of parts per hundred'

2

What you already know

Part 2 of 19

Before we start

What you already know

You can multiply and divide decimals and find simple fractions of amounts.

3

Key words

Part 3 of 19

Key words

Words you'll need today

Percentage
A number of parts per hundred, written with the % sign.
Decimal multiplier
The decimal you multiply by, so 20% becomes 0.2.
Terminating decimal
A decimal that stops, such as 0.25 for one quarter.
Equivalent forms
The same value written as a fraction, decimal or percentage.
4

Learning cycle

Part 4 of 19

Learning cycle 1 of 2

Fractions, decimals and percentages

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

5

Explore the idea

Part 5 of 19

Learn

Three ways to write one value

A quarter is 1/4, 0.25 and 25% — the same amount in three notations. To turn a fraction into a decimal, divide the top by the bottom: 3/8 = 0.375 = 37.5%. To turn a percentage into a decimal, divide by 100: 6% = 0.06. Working interchangeably matters because money problems arrive in all three forms: '1/3 off', '0.5% interest', '20% VAT'.

6

Explore the idea

Part 6 of 19

Learn

Building blocks

Find 10% by dividing by 10. Find 1% by dividing by 100. Then combine: 15% is 10% + half of 10%; 17.5% is 10% + 5% + 2.5%; 30% is 10% × 3. So 15% of £64 is 6.40 + 3.20 = £9.60. This building-block method is how people check bills quickly, and it works because percentages add.

7

Quick check

Part 7 of 19

Quick check

3/8 as a percentage is

8

Quick check

Part 8 of 19

Quick check

15% of £64 is

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

Mental methods with money

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

11

Explore the idea

Part 11 of 19

Learn

Multipliers do it in one step

For a single calculation, use the decimal multiplier: 35% of £80 is 0.35 × 80 = £28. To add 20% VAT, multiply by 1.2. To take 25% off, multiply by 0.75. One multiplication replaces two steps and makes mistakes less likely.

12

Explore the idea

Part 12 of 19

Learn

Rounding money sensibly

Money is written to two decimal places, so answers are rounded to the nearest penny: 0.175 × 42 = 7.35 exactly, while 1/3 of £50 is £16.666… which becomes £16.67. Estimation checks the answer's size first: 19% of £203 must be a bit under £41, because 20% of £200 is £40.

13

Quick check

Part 13 of 19

Quick check

Which multiplier adds 20% VAT?

14

Quick check

Part 14 of 19

Quick check

A third of £50, to the nearest penny, is

15

Common mix-ups

Part 15 of 19

Common mix-ups

Things people often get wrong

  • Writing 6% as 0.6. Divide by 100, so 6% = 0.06.
  • Thinking a percentage must be under 100. A 150% increase is perfectly ordinary.
  • Rounding part-way through a calculation and drifting off the true answer.
  • Assuming 20% of £50 and 50% of £20 must be different. Both are £10 — multiplication commutes.
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.

Working ____ matters because money problems arrive in all three forms: '1/3 off', '0.5% interest', '20% VAT'.

18

Mastery quiz

Part 18 of 19

Marked quiz

End of lesson quiz: Percentages of money you can do in your head

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

  1. 1. 0.045 as a percentage is

  2. 2. Which multiplier takes 25% off?

  3. 3. 1% of £340 is

  4. 4. 35% of £80 is

  5. 5. A good estimate of 19% of £203 is

  6. 6. 7/20 written as a decimal is

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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