Illustrative survey: 18 of 60 votes are for option A. A display is 25 cm long. Find the A segment.
- Fraction for A: 18/60 = 0.3.
- Model length: 0.3 × 25 = 7.5 cm.
- Check: 7.5/25 = 18/60. This is invented practice data.
Proportional problem solving
Choose a model. Check the whole. Explain the result.
Decide whether proportional reasoning fits
Identify the quantities, their units, and the condition that keeps their ratio fixed. Recipes scaled without changing ingredient balance are proportional. Fixed charges, changing rates and unrelated survey populations need different treatment.
See the quantities change.
Predict before changing a value. The written explanation below remains available without JavaScript.
Use the same reference whole
For the If… project, each category is a fraction of one clearly defined total. A category amount a out of N maps to a/N × M units in a model of total size M. The whole, category definitions and time period must be consistent.
Treat rounding as a decision
A continuous strip may show 2.4 cm accurately; a display of whole counters cannot show 2.4 counters without a partial-symbol convention. Keep unrounded calculations, choose a suitable model, and explain rounding without claiming exact equivalence.
Khan Academy
Pause the explanation before a calculation. Predict the next step and explain which quantities are being compared.
Worked examples
A recipe for 4 people needs 300 g of rice. How much for 7 people?
- Assume equal portions and the same recipe.
- Unit amount: 300 ÷ 4 = 75 g/person.
- 75 × 7 = 525 g.
Try it before checking.
In an illustrative survey, 12 of 40 choose A. How long is A on a 30 cm strip?
A first hint
Find the fraction, then multiply by the model total.
Compare your reasoning
12/40 × 30 = 9 cm. Check: 9/30 = 12/40.
Practise the skill.
Fresh questions · useful feedback
Build fluency, one decision at a time.
Work through eight questions. Two independent correct answers introduce a harder version; supported answers bring the next question back to the foundation. You can use hints at any time.
0 of 8 questions completed
This round saves on this device. It is practice, not a school mark.
Explain a little more.
Choose a model total that makes 7/24 easy to represent. Explain your choice.
Use this thinking in the If… project →