Percentage increase and decrease
Conservation reports, prices and populations all move in percentages. Getting the direction and the base right is most of the skill.
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
Calculate percentage increase and decrease
Key learning points
- • Multipliers
- • Percentage change
This lesson at a glance
- 25 minutes
- 10 parts to scroll through
- 3 quick checks
- Marked quiz at the end
- Gentle pace: short sittings with pauses
Words to know
Scroll down — the lesson carries on below
Watch & discover
Part 1 of 10
Watch first
Percentage increase and decrease
An English teaching video on this topic from mathantics. Watch it, then scroll down for the lesson.
In a nutshell
Calculate percentage increase and decrease
Explore the idea
Part 2 of 10
Learn
Multipliers
An increase of 15% is × 1.15. A decrease of 15% is × 0.85. Multipliers chain neatly: two 10% rises make × 1.21, not × 1.20.
Explore the idea
Part 3 of 10
Learn
Percentage change
Change ÷ original × 100. The original amount is always the denominator — using the new figure is the most common mistake in the topic.
Quick check
Part 4 of 10
Quick check
620 gorillas rise to 1,020. The increase is about…
Quick check
Part 5 of 10
Quick check
A 20% decrease is the multiplier…
Quick check
Part 6 of 10
Quick check
Percentage change divides by…
Challenge round
Part 7 of 10
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
Challenge round
Part 8 of 10
Game · Fill the gaps
Finish the sentences
Choose the word that belongs in each gap.
An ____ of 15% is × 1.15.
A ____ of 15% is × 0.85.
____ chain neatly: two 10% rises make × 1.21, not × 1.20.
Mastery quiz
Part 9 of 10
Marked quiz
End of lesson quiz: Percentage increase and decrease
3 questions, marked with the reasoning shown. No timer.
1. 620 gorillas rise to 1,020. The increase is about…
2. A 20% decrease is the multiplier…
3. Percentage change divides by…
Lesson round-up
Part 10 of 10
Lesson round-up
Ready when you are
Quiz score
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Games
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Points this lesson
0
Best run
0 in a row
Luna: 0 out of 3 on the practice checks. Only if you feel up to it — one more?
Ask LunaDo 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.
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
- Work out the total cost of the trip if 50 pupils go.
- Show why the price per pupil falls when more pupils go, using numbers.
- At £20 each, how many pupils must go before the trip makes money? Show your working.
Working out
Working outDo 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
WritingCopy one question out and write underneath, in words, why each step works.
1 question, 4–5 sentences
Problem in words
Working outWrite your own real-life problem that uses today's method, then solve it.
1 problem + solution
Saved as you type.
Part 1 of 10 · Watch & discover
How this is going
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Solve problems involving percentage change, including percentage increase and decrease and original value problems