lesson
A common unit makes comparison possible
1 · Learn
Equivalent ratios multiply all parts by the same factor. A unit rate gives the quantity for one unit of another, such as price per notebook. Compare on the same basis before deciding which option has a lower unit price.
A lower unit price does not automatically make a purchase suitable: quantity needed and other conditions still matter. In a mathematical model, state which factors you are comparing.
2 · Worked example
Four identical notebooks cost £6, giving £1.50 each. Six cost £8.40, giving £1.40 each. The second has a lower price per notebook in this model.
3 · Your turn
Compare £9 for 5 identical items with £12 for 8 identical items using unit price.
Check your answer
£1.80 each versus £1.50 each; the second has the lower unit price.
4 · Apply your learning
Write a ratio table for a proportional situation and identify a case with a fixed fee that would not fit it.
Adult guidance and safety
Require a reasoned method and an independent check. Use accurate number lines, geometric drawings and data displays where the task needs them. These text models require varied practice and diagnostic assessment before curriculum approval.
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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.
Powers, roots and trigonometry · Year 7 onward
Use only when the task allows a calculator. Choose one operation at a time and record your working. Trigonometry here always uses degrees (DEG), not radians. Inverse sine, cosine and tangent return an angle, not a reciprocal. Keep exact fractions and π in answers when requested.
Approximate numerical results use up to 12 significant digits. Inverse sine returns −90° to 90°, inverse cosine 0° to 180°, and inverse tangent −90° to 90°; these are principal values, not every possible solution of a trigonometric equation.
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