Direct proportion and best value
If two quantities double together, they are in direct proportion. That single idea handles recipes, currency, fuel and every 'best value' shelf label in a supermarket.
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
- • Comparing deals
This lesson at a glance
- 25 minutes
- 13 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 13
Visual introductionPicture this
Direct proportion and best value
If two quantities double together, they are in direct proportion. That single idea handles recipes, currency, fuel and every 'best value' shelf label in a supermarket.
In a nutshell
Solve problems involving direct proportion
Explore the idea
Part 2 of 13
Learn
The unitary method
Find the value of one, then multiply. If 6 kg of feed costs £9, one kilogram costs £1.50, so 11 kg costs £16.50.
Explore the idea
Part 3 of 13
Learn
Comparing deals
Best value means the lowest cost per unit, not the lowest price. Convert both offers to the same unit before you judge.
Reset break
Part 4 of 13
Pause
That's sitting 1 of 3 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 13
Worked example
Worked example
A zoo feeds 15 penguins 9 kg of fish a day. For 25 penguins: 9 ÷ 15 = 0.6 kg each, 0.6 × 25 = 15 kg a day.
Quick check
Part 6 of 13
Quick check
Part 7 of 13
Reset break
Part 8 of 13
Pause
That's sitting 2 of 3 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 13
Challenge round
Part 10 of 13
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 13
Game · Recall cards
5 items cost £12.50. What do 8 cost?
Card 1 of 4
Mastery quiz
Part 12 of 13
Marked quiz
End of lesson quiz: Direct proportion and best value
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 13 of 13
Lesson round-up
Ready when you are
Quiz score
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Points this lesson
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Best run
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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 13 · 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