MathsPercentages and data25 min★★ difficulty

Percentage increase and decrease

Percentage change compares the change to the original amount — not to the new one. Multipliers make it fast and reversible.

Part of your national curriculum

Number: Work interchangeably with terminating decimals and their corresponding fractions, and define percentage as 'number of parts per hundred'
Ratio, proportion and rates of change: Solve problems involving percentage change, including percentage increase and decrease and original value problems
Statistics: Describe, interpret and compare observed distributions of a single variable through appropriate measures of central tendency and spread
Financial capability: Understand the functions and uses of money, the importance and practice of budgeting, and managing risk
Financial capability: Understand income, spending, saving and the choices involved in managing personal finances

Lesson overview

What you'll learn in this lesson

Calculate percentage increase and decrease

Key learning points

• Using multipliers
• Percentage change formula

This lesson at a glance

25 minutes
12 parts to scroll through
3 quick checks
Marked quiz at the end
Gentle pace: short sittings with pauses

Words to know

calculatepercentageincreasedecreasemultipliers

Scroll down — the lesson carries on below

Part 1 of 12 · Discover8%

Watch & discover

Part 1 of 12

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 12

Learn

Using multipliers

A 12% increase is × 1.12. A 12% decrease is × 0.88. Chain multipliers to apply several changes in a row.

Explore the idea

Part 3 of 12

Learn

Percentage change formula

change ÷ original × 100. Watch the sign: a fall is a negative change, usually reported as a percentage decrease.

Explore the idea

Part 4 of 12

Worked example

Worked example — a population count

A monitored population falls from 480 to 372. Change = 108. 108 ÷ 480 × 100 = 22.5% decrease.

Reset break

Part 5 of 12

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

Quick check

Part 6 of 12

Quick check

Increase 240 by 15%.

Quick check

Part 7 of 12

Quick check

A count drops from 200 to 150. The percentage decrease is…

Quick check

Part 8 of 12

Quick check

Which multiplier applies a 7% decrease?

Challenge round

Part 9 of 12

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 10 of 12

Game · Fill the gaps

Finish the sentences

Choose the word that belongs in each gap.

A 12% ____ is × 1.12.

A 12% ____ is × 0.88.

Chain ____ to apply several changes in a row.

Mastery quiz

Part 11 of 12

Marked quiz

End of lesson quiz: Percentage increase and decrease

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

1. Increase 240 by 15%.
2. A count drops from 200 to 150. The percentage decrease is…
3. Which multiplier applies a 7% decrease?

Lesson round-up

Part 12 of 12

Lesson round-up

Ready when you are

Quiz score

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Games

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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

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 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

Write your answer, notes or working here

Saved as you type.

Photos of paper work, diagrams or working outHow many minutes did the written work take?

Part 1 of 12 · Watch & discover

0 points

How this is going

Not looked at yet
Work interchangeably with terminating decimals and their corresponding fractions, and define percentage as 'number of parts per hundred'
Not looked at yet
Solve problems involving percentage change, including percentage increase and decrease and original value problems
Not looked at yet
Describe, interpret and compare observed distributions of a single variable through appropriate measures of central tendency and spread
Not looked at yet
Understand the functions and uses of money, the importance and practice of budgeting, and managing risk
Not looked at yet
Understand income, spending, saving and the choices involved in managing personal finances