Good Learning Co.
SavannahYear 8
← Maths
MathsThe maths behind the money30 min★★★ difficulty

Unit pricing and value for money

The bigger box is not always cheaper. Unit pricing — cost per gram, per litre, per wash, per mile — turns marketing back into arithmetic you can compare.

Lesson overview

What you'll learn in this lesson

Use compound units such as speed, unit pricing and density to solve problems

Key learning points

  • • Divide to compare
  • • When the deal is not a deal
  • • Other rates that decide money
  • • Cost per use

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

compoundpricingdensityproblemsdivide

Scroll down — the lesson carries on below

Part 1 of 19 · Discover5%
1

Watch & discover

Part 1 of 19

Watch first

Unit pricing and value for money

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

In a nutshell

Use compound units such as speed, unit pricing and density to solve problems

2

What you already know

Part 2 of 19

Before we start

What you already know

You can divide decimals and convert between grams and kilograms, millilitres and litres.

Recap: Percentages of money you can do in your head
3

Key words

Part 3 of 19

Key words

Words you'll need today

Unit price
Cost per one unit of measure, such as pence per 100 g.
Compound unit
A unit built from two measures, such as £/kg or miles per gallon.
Best value
The lowest cost per unit, provided you can actually use the quantity.
Multibuy
An offer on quantity, which may or may not lower the unit price.
4

Learning cycle

Part 4 of 19

Learning cycle 1 of 2

Comparing by unit price

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

5

Explore the idea

Part 5 of 19

Learn

Divide to compare

Cereal comes as 500 g for £2.40 and 750 g for £3.30. Per 100 g that is 48p and 44p, so the large box is better value. Always divide price by quantity, and use the same unit for both. Shelf labels usually show a unit price precisely because comparing raw prices is unreliable.

6

Explore the idea

Part 6 of 19

Learn

When the deal is not a deal

'3 for £5' on £1.80 items is a genuine saving of 40p. '2 for £4' on items priced £1.95 costs you 10p more than buying two separately. And a lower unit price is worthless if half the food spoils before you eat it — value for money includes whether you can use what you buy.

7

Quick check

Part 7 of 19

Quick check

500 g for £2.40 or 750 g for £3.30. Which has the lower unit price?

8

Quick check

Part 8 of 19

Quick check

Items cost £1.95 each; '2 for £4' means you

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

Rates in real decisions

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

11

Explore the idea

Part 11 of 19

Learn

Other rates that decide money

Compound units run through household costs. Electricity is priced in pence per kilowatt-hour, so a 2 kW heater for three hours uses 6 kWh; at 25p per kWh that is £1.50. Fuel economy in miles per gallon, or pence per mile, tells you the real cost of a journey. A phone contract at £22 a month is £264 a year, which is the figure worth comparing.

12

Explore the idea

Part 12 of 19

Learn

Cost per use

Two pairs of boots: £40 lasting one winter, or £90 lasting four. Cost per winter is £40 against £22.50, so the expensive pair is cheaper in the end — the reason 'buying cheap twice' is a real trap. Cost per use only works with honest estimates of lifetime, and it explains why upfront price alone is a poor guide.

13

Quick check

Part 13 of 19

Quick check

A 2 kW heater for 3 hours at 25p per kWh costs

14

Quick check

Part 14 of 19

Quick check

£40 boots lasting one winter versus £90 lasting four. Cost per winter is

15

Common mix-ups

Part 15 of 19

Common mix-ups

Things people often get wrong

  • Assuming the largest pack always has the lowest unit price. Shops price to habit, not logic.
  • Comparing prices without matching units, such as grams against kilograms.
  • Believing every multibuy saves money. Check it against the single price.
  • Ignoring waste. Cheap per unit is expensive if it is thrown away.
  • Comparing monthly contract prices without multiplying up to the full term.
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.

Always ____ price by quantity, and use the same unit for both.

____ units run through household costs.

18

Mastery quiz

Part 18 of 19

Marked quiz

End of lesson quiz: Unit pricing and value for money

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

  1. 1. A unit price lets you compare

  2. 2. £22 a month over a year is

  3. 3. 1.5 litres for £1.20 is, per 100 ml,

  4. 4. Miles per gallon is an example of

  5. 5. Best value should also consider

  6. 6. '3 for £5' on £1.80 items saves

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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