Good Learning Co.
SavannahYear 8
← Maths
MathsRatio, proportion and rates of change30 min★★★ difficulty

Percentage change and original values

Percentage change questions are everywhere: sale prices, wage rises, interest and population growth. The reliable method is always the multiplier.

Part of your national curriculum
  • Ratio, proportion and rates of change: Solve problems involving percentage change, including percentage increase and decrease and original value problems

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

  • • Change as a proportion of the original
  • • Increase and decrease multipliers
  • • Reverse percentages
  • • Simple and compound

This lesson at a glance

  • 30 minutes
  • 17 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 17 · Discover6%
1

Watch & discover

Part 1 of 17

Watch first

Percentage change and original values

An English teaching video on this topic from The Organic Chemistry Tutor. 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

Learning cycle

Part 2 of 17

Learning cycle 1 of 2

Part 1 · Change as a proportion of the original

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

3

Explore the idea

Part 3 of 17

Learn

Change as a proportion of the original

Percentage change is the change divided by the original amount, multiplied by 100. A rise from £40 to £46 is a change of £6 on an original of £40, which is 15%. Dividing by the new amount instead of the original is the most common mistake.

4

Explore the idea

Part 4 of 17

Learn

Increase and decrease multipliers

A 15% increase multiplies by 1.15; a 15% decrease multiplies by 0.85. One multiplication replaces two steps and works just as well for repeated change: three years of 4% growth is × 1.04³.

5

Quick check

Part 5 of 17

Quick check

A price rises from £40 to £46. The percentage increase is

6

Quick check

Part 6 of 17

Quick check

The multiplier for three years of 4% growth is

7

Learning cycle

Part 7 of 17

Learning cycle 2 of 2

Part 2 · Reverse percentages

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

Reverse percentages

If a jacket costs £68 after a 15% reduction, the £68 represents 85% of the original. Dividing by 0.85 gives £80. Adding 15% back to £68 gives £78.20, which is wrong, because the 15% was calculated on the larger original price.

10

Explore the idea

Part 10 of 17

Learn

Simple and compound

Simple interest adds the same amount each year; compound interest adds a percentage of the growing balance. £2,000 at 3.5% for four years gives £2,280 simple but 2000 × 1.035⁴ = £2,295.02 compound, and the gap widens with time.

11

Quick check

Part 11 of 17

Quick check

After a 20% decrease an item costs £64. The original was

12

Quick check

Part 12 of 17

Quick check

Compound interest differs from simple because it

13

Explore the idea

Part 13 of 17

Worked example

Worked answer: after a 15% reduction a coat costs £68. Find the original price (3 marks)

The sale price represents 100% − 15% = 85% of the original (1). The multiplier is therefore 0.85, so the original is 68 ÷ 0.85 (1), which equals £80 (1). Checking: 15% of £80 is £12, and £80 − £12 = £68.

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.

____ change is the change divided by the original amount, multiplied by 100.

A rise from £40 to £46 is a ____ of £6 on an original of £40, which is 15%.

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

16

Mastery quiz

Part 16 of 17

Marked quiz

End of lesson quiz: Percentage change and original values

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

  1. 1. A price rises from £40 to £46. The percentage increase is

  2. 2. The multiplier for three years of 4% growth is

  3. 3. After a 20% decrease an item costs £64. The original was

  4. 4. Compound interest differs from simple because it

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

How this is going

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

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