Compound measures: speed, density and rates
A compound measure combines two units into one idea: how much of this per unit of that. Getting the units right is usually most of the mathematics.
Part of your national curriculum
- Ratio, proportion and rates of change: Use compound units such as speed, unit pricing and density to solve problems
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
- • Speed, distance, time
- • Density and mass
- • Unit pricing and best buy
- • Average speed over a journey
This lesson at a glance
- 28 minutes
- 21 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 21
Visual introductionPicture this
Compound measures: speed, density and rates
A compound measure combines two units into one idea: how much of this per unit of that. Getting the units right is usually most of the mathematics.
In a nutshell
Use compound units such as speed, unit pricing and density to solve problems
Learning cycle
Part 2 of 21
Learning cycle 1 of 2
Part 1 · Speed, distance, time
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 3 of 21
Learn
Speed, distance, time
Speed = distance ÷ time. A car covering 150 km in 2.5 hours travels at 60 km/h. Rearranging gives distance = speed × time and time = distance ÷ speed. Time in minutes must be converted to hours before dividing, or the answer will be sixty times out.
Reset break
Part 4 of 21
Pause
That's sitting 1 of 5 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.
Explore the idea
Part 5 of 21
Learn
Density and mass
Density = mass ÷ volume, measured in g/cm³ or kg/m³. A block of mass 480 g and volume 60 cm³ has density 8 g/cm³. Comparing densities explains why some objects float, and identical formulas structure pressure as force ÷ area.
Quick check
Part 6 of 21
Quick check
Part 7 of 21
Reset break
Part 8 of 21
Pause
That's sitting 2 of 5 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 9 of 21
Learning cycle 2 of 2
Part 2 · Unit pricing and best buy
A short piece of teaching, then a check to make sure it has landed.
Explore the idea
Part 10 of 21
Learn
Unit pricing and best buy
To compare a 750 g pack at £2.40 with a 1.2 kg pack at £3.72, calculate price per 100 g: 32p against 31p. The larger pack is better value, but only just, and best-buy answers must state the comparable rate for both options, not just the winner.
Explore the idea
Part 11 of 21
Learn
Average speed over a journey
Average speed is total distance divided by total time, never the mean of two speeds. Driving 60 km at 60 km/h then 60 km at 30 km/h takes 1 + 2 = 3 hours for 120 km, giving 40 km/h, not 45 km/h.
Reset break
Part 12 of 21
Pause
That's sitting 3 of 5 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 13 of 21
Quick check
Part 14 of 21
Explore the idea
Part 15 of 21
Worked example
Worked answer: a journey of 60 km at 60 km/h then 60 km at 30 km/h. Find the average speed (3 marks)
The first stage takes 60 ÷ 60 = 1 hour and the second takes 60 ÷ 30 = 2 hours, giving 3 hours in total (1). The total distance is 120 km (1). Average speed = 120 ÷ 3 = 40 km/h (1). Averaging 60 and 30 to get 45 km/h ignores the extra time spent at the slower speed.
Reset break
Part 16 of 21
Pause
That's sitting 4 of 5 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.
Challenge round
Part 17 of 21
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 18 of 21
Game · Fill the gaps
Finish the sentences
Choose the word that belongs in each gap.
Speed = ____ ÷ time.
____ = mass ÷ volume, measured in g/cm³ or kg/m³.
Challenge round
Part 19 of 21
Game · Recall cards
5 items cost £12.50. What do 8 cost?
Card 1 of 4
Mastery quiz
Part 20 of 21
Marked quiz
End of lesson quiz: Compound measures: speed, density and rates
4 questions, marked with the reasoning shown. No timer.
1. 5 items cost £12.50. What do 8 cost?
2. A graph of a proportional relationship must…
3. A tracker records 18 km in 3 hours. At the same rate, how far in 7 hours?
4. If 4 tickets cost £26, 6 tickets cost…
Lesson round-up
Part 21 of 21
Lesson round-up
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Use compound units such as speed, unit pricing and density to solve problems