Good Learning Co.
SavannahYear 8
← Maths
MathsRatio, proportion and rates30 min★★★ difficulty

Percentage change and original values

Multipliers turn percentage questions into one calculation instead of three. They also make reverse percentage questions possible.

Lesson overview

What you'll learn in this lesson

Solve problems involving percentage change, including percentage increase and decrease and original value problems

Key learning points

  • • Increase and decrease in one step
  • • Finding the percentage change
  • • Reverse percentages
  • • Repeated change

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

problemsinvolvingpercentagechangeincrease

Scroll down — the lesson carries on below

Part 1 of 19 · Discover5%
1

Watch & discover

Part 1 of 19

Watch first

Percentage change and original values

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

In a nutshell

Solve problems involving percentage change, including percentage increase and decrease and original value problems

2

What you already know

Part 2 of 19

Before we start

What you already know

You can convert between percentages and decimals and find a percentage of an amount.

Recap: Fractions, decimals and percentages as one idea
3

Key words

Part 3 of 19

Key words

Words you'll need today

multiplier
The decimal you multiply by to make a percentage change.
percentage change
The change as a percentage of the original amount.
reverse percentage
Working back to find the amount before a change.
4

Learning cycle

Part 4 of 19

Learning cycle 1 of 2

Part 1 — Multipliers

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

5

Explore the idea

Part 5 of 19

Learn

Increase and decrease in one step

A 15% increase multiplies by 1.15; a 15% decrease multiplies by 0.85. So £240 increased by 15% is 240 × 1.15 = £276. Multipliers combine, too: a 10% rise then a 10% fall is × 1.1 × 0.9 = × 0.99, so you end up 1% down — not back where you started.

6

Explore the idea

Part 6 of 19

Learn

Finding the percentage change

Percentage change = change ÷ original × 100. A price rises from £80 to £94: the change is £14, so 14 ÷ 80 × 100 = 17.5%. The denominator is always the original amount, which is why a rise of £14 on £80 is a bigger percentage than the same rise on £200.

7

Quick check

Part 7 of 19

Quick check

Increase £480 by 25%.

8

Quick check

Part 8 of 19

Quick check

A price falls from £50 to £42. The percentage decrease 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

Part 2 — Working backwards

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

11

Explore the idea

Part 11 of 19

Learn

Reverse percentages

A coat costs £68 after a 15% reduction. £68 is not the original — it is 85% of it. So original = 68 ÷ 0.85 = £80. Divide by the multiplier to go backwards. Taking 15% of £68 and adding it back gives £78.20, which is wrong, and it is the single most common error in this topic.

12

Explore the idea

Part 12 of 19

Learn

Repeated change

£2,000 in an account earning 3% a year becomes 2000 × 1.03³ = £2,185.45 after three years, because each year's interest earns interest too. Simple interest would give only £2,180. Compound growth is just the same multiplier applied again and again.

13

Quick check

Part 13 of 19

Quick check

After a 20% discount an item is £64. The original price was...

14

Quick check

Part 14 of 19

Quick check

Multiplier for a 7% increase?

15

Common mix-ups

Part 15 of 19

Common mix-ups

Things people often get wrong

  • Using the new amount as the denominator in a percentage change.
  • Adding a percentage of the reduced price to reverse a decrease.
  • Thinking a 10% rise then 10% fall returns the original.
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.

A 15% ____ multiplies by 1.15; a 15% decrease multiplies by 0.85.

____ change = change ÷ original × 100.

A price rises from £80 to £94: the ____ is £14, so 14 ÷ 80 × 100 = 17.5%.

18

Mastery quiz

Part 18 of 19

Marked quiz

End of lesson quiz: Percentage change and original values

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

  1. 1. Decrease 90 by 30%.

  2. 2. £150 grows by 4% for 2 years. Value?

  3. 3. A wage rises from £24,000 to £25,200. Increase?

  4. 4. After a 12% rise a bill is £56. Before it was...

  5. 5. A 10% rise then a 10% fall gives an overall...

  6. 6. Percentage change divides the change by the...

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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