Price per 100 g and splitting a bill fairly
Two boxes of cereal, different sizes, different prices. The bigger one is usually better value, except when it is not. Unit pricing settles it, and the same division sorts out who owes what after a meal.
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
- • Cereal on a real shelf
- • When bigger is worse
- • Splitting a bill
- • Fair is not always equal
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
Scroll down — the lesson carries on below
Watch & discover
Part 1 of 18
Watch first
Price per 100 g and splitting a bill fairly
An English teaching video on this topic from Cognito. Watch it, then scroll down for the lesson.
In a nutshell
Use compound units such as speed, unit pricing and density to solve problems
What you already know
Part 2 of 18
Before we start
What you already know
You can divide with decimals and work out a percentage of an amount.
Key words
Part 3 of 18
Key words
Words you'll need today
- Unit price
- The cost of one standard amount, such as per 100 g or per litre.
- Value for money
- The best price for the amount and quality you actually need.
- Multipack
- Several items sold together, sometimes cheaper per item and sometimes not.
- Service charge
- An amount added to a restaurant bill, often 10% or 12.5%.
- Per person share
- The bill divided by the number of people paying.
Learning cycle
Part 4 of 18
Learning cycle 1 of 2
Comparing with unit price
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 5 of 18
Learn
Cereal on a real shelf
Box A: 500 g for £2.40. Box B: 750 g for £3.45. Per 100 g: A is 240 ÷ 5 = 48p, B is 345 ÷ 7.5 = 46p. B is better value by 2p per 100 g — genuinely cheaper, but only about 15p across the box, and only if you eat it all before it goes stale. Unit price gives the answer; you still decide whether the answer matters.
Explore the idea
Part 6 of 18
Learn
When bigger is worse
Shops rely on the assumption that larger is cheaper, and it is often wrong, especially on multipacks and offers. A 6-pack of crisps at £2.10 is 35p a bag; the same bags loose at 30p are cheaper. Always divide. Supermarket shelf labels show price per 100 g in small print, which does the work for you when you remember to look.
Quick check
Part 7 of 18
Quick check
500 g for £2.40 is, per 100 g,
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.
Quick check
Part 9 of 18
Quick check
750 g for £3.45 is, per 100 g,
Learning cycle
Part 10 of 18
Learning cycle 2 of 2
Splitting a real bill
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 11 of 18
Learn
Splitting a bill
Four friends eat out. The food comes to £58 and a 10% service charge is added: £58 × 1.1 = £63.80. Split four ways that is £63.80 ÷ 4 = £15.95 each. If one person had a £4 drink nobody else had, fair splitting means taking that off first: £54 shared plus £4 to them, service applied to each share.
Explore the idea
Part 12 of 18
Learn
Fair is not always equal
An equal split is simplest and fine when everyone ate similarly. When one person had much more, an itemised split is fairer and worth the extra minute. Agreeing which method you are using before you order avoids the awkward conversation afterwards, and stops the person who ordered least paying for the person who ordered most.
Quick check
Part 13 of 18
Quick check
A £58 bill with 10% service comes to
Quick check
Part 14 of 18
Quick check
£63.80 split between four people is
Common mix-ups
Part 15 of 18
Common mix-ups
Things people often get wrong
- Assuming the largest pack is always the best value without dividing.
- Comparing per-item prices when the items are different sizes; convert to a common unit first.
- Adding 10% service by adding £10 rather than multiplying by 1.1.
- Splitting equally when one person's order was far larger, then feeling resentful about it.
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
Mastery quiz
Part 17 of 18
Marked quiz
End of lesson quiz: Price per 100 g and splitting a bill fairly
6 questions, marked with the reasoning shown. No timer.
1. Unit price lets you
2. A 6-pack at £2.10 costs per bag
3. A 12.5% service charge on £40 is
4. 2 litres for £1.80 versus 1.5 litres for £1.20: the better value is
5. Which split is fairest when one person ate far more?
6. The best time to agree how to split is
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 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 18 · Watch & discover