lesson
Scale both quantities consistently
1 · Learn
In a proportional recipe, doubling every ingredient preserves the intended ratios. A scale factor multiplies corresponding lengths of similar shapes. Adding the same length to every side usually does not preserve shape proportions.
Check that proportional reasoning fits the context: a fixed entrance charge does not necessarily double just because the group size doubles.
2 · Worked example
A model recipe uses 300 g flour for 12 equal biscuits. For 20 biscuits, one biscuit's share is 25 g, so 20 need 500 g, assuming the recipe scales proportionally.
3 · Your turn
A rectangle is 4 cm by 7 cm. Enlarge every length by scale factor 3. State the new dimensions.
Check your answer
12 cm by 21 cm. Both lengths are multiplied by 3.
4 · Apply your learning
Compare the scaled rectangle with one made by adding 3 cm to each length; explain why they are different.
Adult guidance and safety
Ask the learner to explain the method and check it using a different representation. Supply place-value grids, fraction strips, accurate diagrams and measuring tools where needed. These examples need varied practice; a short correct answer alone does not establish fluency.
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Check a calculation · Year 5 onward
Use this only when your teacher or adult allows a calculator for the task. Show your thinking first. It does not replace mental or written arithmetic and does not mark your lesson answer.
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