lesson
Use endpoints that maximise the expression
1 · Learn
Rounded positive measurements represent intervals. To bound a sum, combine the lower endpoints for its lower bound and upper endpoints for its upper bound. For a quotient of positive quantities, the largest numerator and smallest denominator give the upper bound.
Check endpoint inclusion and assumptions. A displayed measurement is not exact, and rounding an intermediate calculation can lose valid information.
2 · Worked example
If 9.5 <= a < 10.5 and 1.5 <= b < 2.5, then 11 <= a+b < 13. The upper endpoint is not attained.
3 · Your turn
Lengths round to 6 cm and 4 cm, each to the nearest centimetre. Give the interval for their sum.
Check your answer
9 cm <= sum < 11 cm under the usual halfway-up convention.
4 · Apply your learning
Test examples close to each boundary and explain why the rounded sum alone hides uncertainty.
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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