The unitary method
Objective. Find one unit first, then scale to the required amount.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
The unitary method solves proportion problems by first finding the value of a single unit, then scaling that value up or down to the amount required. For example, if 4 identical tickets cost £36, dividing by 4 gives the cost of one ticket, £9, and this can then be multiplied by any number of tickets needed. This method works for any proportional situation, from cost and quantity to time and distance. The key step is always isolating 'one unit' before multiplying back to the target amount.
Worked example
If 5 identical notebooks cost £17.50, use the unitary method to find the cost of 9 notebooks.
- 1Divide the total cost by the number of notebooks to find one unit: 17.50÷5=3.50.
- 2This means one notebook costs £3.50.
- 3Multiply the unit cost by 9: 3.50×9=31.50.
- 4Check by dividing the answer by 9, returning to £3.50 per notebook.
Answer: £31.50
Concept mastery
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Practice
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Start practisingCommon mistake. Pupils sometimes skip the unit step and try to scale directly between two unrelated quantities, producing an incorrect multiplier. Always find the value for exactly one unit before scaling to the required amount.
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