Speed, density and unit pricing
Compound units are two measurements divided by each other. Once you can read the unit itself, you already know the formula.
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
- • The unit tells you the formula
- • Time traps
- • Density
- • Best value
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
Scroll down — the lesson carries on below
Watch & discover
Part 1 of 19
Watch first
Speed, density and unit pricing
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
What you already know
Part 2 of 19
Before we start
What you already know
You can rearrange simple formulae and convert between units of time.
Key words
Part 3 of 19
Key words
Words you'll need today
- compound unit
- A unit made of two others, such as km/h or g/cm³.
- density
- Mass per unit volume.
- unit price
- Cost per single unit, used to compare value.
Learning cycle
Part 4 of 19
Learning cycle 1 of 2
Part 1 — Speed
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 5 of 19
Learn
The unit tells you the formula
Miles per hour means miles ÷ hours, so speed = distance ÷ time. Rearranged: distance = speed × time and time = distance ÷ speed. You never need to memorise a triangle — read the unit and the division is written into it.
Explore the idea
Part 6 of 19
Learn
Time traps
1 hour 30 minutes is 1.5 hours, not 1.3. 40 minutes is 40/60 = 0.667 hours. A car travelling 90 km in 1 h 15 min has speed 90 ÷ 1.25 = 72 km/h. Convert time to a decimal number of hours before dividing, or every answer will be slightly wrong.
Quick check
Part 7 of 19
Quick check
A car travels 150 km in 2 hours. Its speed is...
Quick check
Part 8 of 19
Quick check
1 h 45 min in hours is...
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.
Learning cycle
Part 10 of 19
Learning cycle 2 of 2
Part 2 — Density and value for money
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 11 of 19
Learn
Density
Density = mass ÷ volume, measured in g/cm³ or kg/m³. A block of mass 240 g and volume 30 cm³ has density 8 g/cm³. Rearranging, mass = density × volume. Anything with density under 1 g/cm³ floats in water, which is why oil sits on top and ice floats.
Explore the idea
Part 12 of 19
Learn
Best value
To compare a 400 g pack at £1.80 with a 750 g pack at £3.15, find the price per 100 g: 45p and 42p. The larger pack is better value. Comparing per unit — per gram, per litre, per sheet — is the only reliable method, and it is what supermarket shelf labels do for you.
Quick check
Part 13 of 19
Quick check
Mass 500 g, volume 250 cm³. Density?
Quick check
Part 14 of 19
Quick check
Which is better value?
Common mix-ups
Part 15 of 19
Common mix-ups
Things people often get wrong
- Writing 1 h 30 min as 1.3 hours.
- Dividing volume by mass when finding density.
- Deciding best value by price alone instead of price per unit.
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
Challenge round
Part 17 of 19
Game · Fill the gaps
Finish the sentences
Choose the word that belongs in each gap.
____ = mass ÷ volume, measured in g/cm³ or kg/m³.
Mastery quiz
Part 18 of 19
Marked quiz
End of lesson quiz: Speed, density and unit pricing
6 questions, marked with the reasoning shown. No timer.
1. Time for 240 km at 80 km/h?
2. Distance in 2.5 h at 60 mph?
3. Density is measured in...
4. A 2 L bottle costs £1.60; 500 ml costs 45p. Better value?
5. Volume 4 cm³, density 3 g/cm³. Mass?
6. An object with density 0.9 g/cm³ in water will...
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 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 19 · Watch & discover