Good Learning Co.
SavannahYear 8
← Maths
MathsWorking out value in a real shop30 min★★ difficulty

Sale prices and offers that only look cheap

Shops are very good at making an offer feel like a saving. The maths to check one takes about ten seconds, and it regularly changes the answer.

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

  • • Two reliable methods
  • • Stacked and staged discounts
  • • Offers that need checking
  • • Was/now and the honest comparison

This lesson at a glance

  • 30 minutes
  • 18 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 18 · Discover6%
1

Watch & discover

Part 1 of 18

Watch first

Sale prices and offers that only look cheap

An English teaching video on this topic from Cognito. 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 18

Before we start

What you already know

You can find 10% and 50% of an amount and multiply decimals.

Recap: Checking a receipt and your change
3

Key words

Part 3 of 18

Key words

Words you'll need today

Percentage
A number of parts per hundred, so 20% means 20 out of every 100.
Discount
The amount taken off the original price.
Multiplier
The decimal you multiply by, so a 20% discount is × 0.8.
BOGOF
'Buy one get one free', which is a 50% saving only if you need both.
Was/now price
The old and new prices shown together, which is only useful if the 'was' was real.
4

Learning cycle

Part 4 of 18

Learning cycle 1 of 2

Working out a sale price

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

5

Explore the idea

Part 5 of 18

Learn

Two reliable methods

A £45 hoodie has 20% off. Method one: 10% of £45 is £4.50, so 20% is £9, giving £36. Method two, faster: paying 80% means × 0.8, and 45 × 0.8 = £36. The multiplier method is the one to build the habit on, because it also handles awkward percentages: 35% off is × 0.65.

6

Explore the idea

Part 6 of 18

Learn

Stacked and staged discounts

'30% off, then an extra 10% at the till' is not 40% off. It is × 0.7 then × 0.9 = × 0.63, so 37% off. On £80 that is £50.40, not £48. Two discounts never simply add, because the second one applies to an already smaller price.

7

Quick check

Part 7 of 18

Quick check

A £45 hoodie with 20% off costs

8

Reset break

Part 8 of 18

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

Quick check

Part 9 of 18

Quick check

The multiplier for a 35% discount is

10

Learning cycle

Part 10 of 18

Learning cycle 2 of 2

Judging whether an offer is real

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

11

Explore the idea

Part 11 of 18

Learn

Offers that need checking

'3 for 2' on £2.50 drinks means £5 for three, so £1.67 each — a genuine 33% saving, if you wanted three. If you only wanted one, you have spent £5 instead of £2.50 to 'save' £2.50. The same trap applies to BOGOF on food that spoils. An offer is only a saving on things you were already going to buy.

12

Explore the idea

Part 12 of 18

Learn

Was/now and the honest comparison

'Was £60, now £30' only means something if it really sold at £60. The reliable check is not the shop's old price but another shop's current price. Comparing today's prices in two places beats trusting any claimed reduction, and it takes one search.

13

Quick check

Part 13 of 18

Quick check

£80 with 30% off then a further 10% off costs

14

Quick check

Part 14 of 18

Quick check

'3 for 2' on £2.50 drinks makes each drink cost about

15

Common mix-ups

Part 15 of 18

Common mix-ups

Things people often get wrong

  • Adding two discounts together. 30% then 10% is 37%, not 40%.
  • Treating '3 for 2' as a saving when you only needed one item.
  • Trusting the 'was' price as proof of value instead of comparing another shop today.
  • Finding 20% off by working out 20% and forgetting to subtract it from the original.
16

Challenge round

Part 16 of 18

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

Mastery quiz

Part 17 of 18

Marked quiz

End of lesson quiz: Sale prices and offers that only look cheap

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

  1. 1. 20% off means you pay

  2. 2. A £24 shirt with 25% off costs

  3. 3. Two discounts of 50% and 50% together give

  4. 4. BOGOF is a real saving only when

  5. 5. The best check on a 'was £60, now £30' claim is

  6. 6. £150 with 40% off costs

18

Lesson round-up

Part 18 of 18

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 18 · Watch & discover

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