MA21-01 Maths Coming soon
Solve direct proportion problems
MA21-01
This lesson is coming soon.
In this lesson
Solve a direct-proportion word problem by finding the single multiplier connecting two quantities and using it to scale a given value up or down.
What it covers
- Recognising a direct-proportion word problem (quantities grow or shrink together)
- The unitary method: find the value for one unit, then scale
- The multiplier/scale-factor method as an equivalent shortcut
- Linking y = kx to the statement 'y is proportional to x'
- Linking the ratio between two direct-proportion quantities to a fraction and to the gradient of the line through the origin (CAN-RAT-012)
- Proportion as equality of two ratios, e.g. scaling a recipe (CAN-RAT-011)
Key words
For: AQA GCSE 8300, Cambridge IGCSE 0580, Edexcel GCSE 1MA1, Edexcel IGCSE 4MA1, Eduqas GCSE C300, OCR GCSE J560
On the specification
| Board | Spec | Statement |
|---|---|---|
| AQA GCSE 8300 | R10 | Solve problems involving direct and inverse proportion, including graphical and algebraic representations |
| AQA GCSE 8300 | R7 | Understand and use proportion as equality of ratios |
| AQA GCSE 8300 | R8 | Relate ratios to fractions and to linear functions |
| Cambridge IGCSE 0580 | E2.8 | Express direct and inverse proportion in algebraic terms and use this form of expression to find unknown quantities. |
| Cambridge IGCSE 0580 | C1.11 | Ratio and proportion |
| Cambridge IGCSE 0580 | E1.11 | Ratio and proportion |
| Edexcel GCSE 1MA1 | R10 | Solve problems involving direct and inverse proportion, including graphical and algebraic representations |
| Edexcel GCSE 1MA1 | R7 | Understand and use proportion as equality of ratios |
| Edexcel GCSE 1MA1 | R8 | Relate ratios to fractions and to linear functions |
| Edexcel IGCSE 4MA1 | F1.7D | Calculate an unknown quantity from quantities that vary in direct proportion |
| Edexcel IGCSE 4MA1 | H2.5A | Set up problems involving direct or inverse proportion and relate algebraic solutions to graphical representation of the equations |
| Edexcel IGCSE 4MA1 | F1.7C | Use the process of proportionality to evaluate unknown quantities |
| Edexcel IGCSE 4MA1 | F1.7E | Solve word problems about ratio and proportion |
| Eduqas GCSE C300 | FR11 | Solve problems involving direct and inverse proportion, including graphical and algebraic representations |
| Eduqas GCSE C300 | HR11 | Solve problems involving direct and inverse proportion, including graphical and algebraic representations |
| Eduqas GCSE C300 | FR8 | Understand and use proportion as equality of ratios |
| Eduqas GCSE C300 | HR8 | Understand and use proportion as equality of ratios |
| Eduqas GCSE C300 | FR9 | Relate ratios to fractions and to linear functions |
| Eduqas GCSE C300 | HR9 | Relate ratios to fractions and to linear functions |
| OCR GCSE J560 | 5.02a | Solve simple problems involving quantities in direct proportion including algebraic proportions. |
| OCR GCSE J560 | 5.01d | Solve simple ratio and proportion problems. Understand the relationship between ratio and linear functions. |
For teachers
This GCSE Maths lesson teaches solve direct proportion problems. By the end, students should be able to solve a direct-proportion word problem by finding the single multiplier connecting two quantities and using it to scale a given value up or down. It works through two worked examples and the mistakes examiners report.