lesson
The scale compares matching lengths
1 · Learn
A scale of 1:200 means one length unit on the drawing represents 200 of the same unit in reality. Convert units after or before applying the scale consistently.
Length scale factors do not apply unchanged to areas: scaling both dimensions by 2 multiplies area by 4. A measured map length should also be interpreted at the precision the drawing allows.
2 · Worked example
At 1:200, 4 cm represents 800 cm, or 8 m. A 3 cm by 2 cm rectangle represents 6 m by 4 m, with actual area 24 m².
3 · Your turn
At scale 1:500, what actual distance is represented by 6 cm?
Check your answer
3,000 cm, or 30 m.
4 · Apply your learning
Draw a rectangular room plan for a 4 m by 3 m room at scale 1:50. Mark a door opening 0.8 m wide on one 4 m wall. Use a ruler and label the scale; check the plan's two side lengths and door width by converting back to metres.
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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