Identify a proportional relationship and scale it consistently. Use a unit rate or equivalent ratios while keeping the meaning and units of both quantities clear.
Explain when two ratios describe the same relationship.
Find a unit rate and use it to scale a quantity.
Recognize an assumption behind a proportional model.
Keep the relationship constant
Two quantities are directly proportional when multiplying one by a factor multiplies the other by the same factor. Their ratio stays constant; a table can make that pattern visible.
Find one unit or scale both quantities
A unit rate expresses the amount for one unit. Alternatively, multiply both parts of a ratio by the same factor. Choose whichever makes the quantities easiest to interpret.
A mistake to avoid
Adding the same amount to both quantities usually changes their ratio. A fixed fee, discount threshold, or changing rate can also mean a real situation is not proportional.
Worked example
Price five identical notebooks
If 3 identical notebooks cost 6 currency units at a constant price, one costs 6 ÷ 3 = 2. Five therefore cost 5 × 2 = 10. This assumes there is no fixed fee or quantity discount.
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