lesson
Association is not a causal experiment
1 · Learn
A scatter graph pairs two measurements for each case. A trend can show association, but another variable or reverse influence may explain it. A line of best fit summarises a pattern rather than passing through every point.
Interpolation within the observed range is usually less speculative than extrapolation beyond it, but neither is a guarantee. State uncertainty and investigate unusual points rather than deleting them automatically.
2 · Worked example
Ice-cream sales and sunhat sales may rise together because warmer weather affects both. That does not show buying ice cream causes a sunhat purchase.
3 · Your turn
A fitted trend uses heights from 140 to 180 cm. Is predicting a value for 210 cm interpolation or extrapolation?
Check your answer
Extrapolation, because 210 cm is outside the observed range.
4 · Apply your learning
Explain a plausible third-variable explanation for an invented association, clearly distinguishing explanation from evidence.
Adult guidance and safety
Require reasoning and a check. Provide accurate graphs, construction instruments and varied practice. Annual KS3 allocation is proposed; do not treat these short models as a complete assessed programme.
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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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