lesson
Identify what the ratio compares
1 · Learn
A ratio compares specified quantities, while a fraction often compares one part with the whole. In red:blue = 3:2, red is 3/5 of all counters, not 3/2 of all counters. Label the quantities before calculating.
If a total changes because one group changes, the new ratio must use the new amounts. Do not preserve an old ratio automatically after adding items to only one group.
2 · Worked example
With 40 counters, each ratio part is 8, so red = 24 and blue = 16. Adding 8 blue gives 24:24 = 1:1.
3 · Your turn
A:B = 2:5 and A + B = 56. Find A and B.
Check your answer
A = 16 and B = 40.
4 · Apply your learning
Explain the difference between A/B and A/(A+B) using the same quantities.
Adult guidance and safety
Check prerequisites, units and reasoning. Provide accurate diagrams and varied practice. Extension content needs suitable prior understanding; no GCSE board, tier or examination readiness is implied by this proposed sequence.
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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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