Direct proportion and rates
Two quantities are in direct proportion when doubling one doubles the other. The reliable method is to find the value of one unit first.
Part of your national curriculum
- Ratio, proportion and rates of change: Solve problems involving direct and inverse proportion, including graphical and algebraic representations
- 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
Solve problems involving direct proportion
Key learning points
- • The unitary method
- • Spotting when it is not proportional
This lesson at a glance
- 25 minutes
- 15 parts to scroll through
- 3 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 15
Visual introductionPicture this
Direct proportion and rates
Two quantities are in direct proportion when doubling one doubles the other. The reliable method is to find the value of one unit first.
In a nutshell
Solve problems involving direct proportion
Explore the idea
Part 2 of 15
Learn
The unitary method
Divide to find the value of one, then multiply for the amount you need. It works for costs, distances, feed quantities and speeds alike.
Explore the idea
Part 3 of 15
Learn
Spotting when it is not proportional
If a graph of the relationship does not pass through the origin, it is not direct proportion. A fixed charge plus a rate is a different model.
Reset break
Part 4 of 15
Pause
That's sitting 1 of 4 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 15
Worked example
Worked example
7 kg of feed lasts 4 days. One day needs 7 ÷ 4 = 1.75 kg. Two weeks needs 1.75 × 14 = 24.5 kg.
Quick check
Part 6 of 15
Quick check
Part 7 of 15
Reset break
Part 8 of 15
Pause
That's sitting 2 of 4 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 15
Challenge round
Part 10 of 15
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 11 of 15
Game · Fill the gaps
Finish the sentences
Choose the word that belongs in each gap.
If a graph of the relationship does not pass through the origin, it is not ____ proportion.
Reset break
Part 12 of 15
Pause
That's sitting 3 of 4 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 13 of 15
Game · Recall cards
5 items cost £12.50. What do 8 cost?
Card 1 of 4
Mastery quiz
Part 14 of 15
Marked quiz
End of lesson quiz: Direct proportion 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 15 of 15
Lesson round-up
Ready when you are
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Luna: 0 out of 3 on the practice checks. Only if you feel up to it — one more?
Ask LunaPart 1 of 15 · Watch & discover
How this is going
- Not looked at yet
Solve problems involving direct and inverse proportion, including graphical and algebraic representations
- Not looked at yet
Use compound units such as speed, unit pricing and density to solve problems