lesson
Choose which quantity is the subject
1 · Learn
A formula can be rearranged to make a different variable the subject. Apply inverse operations to the whole relevant expression. In A = bh/2, multiplying by 2 gives 2A = bh, then dividing by b gives h = 2A/b for b not equal to zero.
State restrictions that prevent division by zero. Rearranging is symbolic reasoning; substitution afterwards can check a particular case but is not the derivation itself.
2 · Worked example
From v = d/t, multiply by t to get vt = d. To make t the subject when v is non-zero, t = d/v.
3 · Your turn
Rearrange P = 2l + 2w to make l the subject.
Check your answer
l = (P - 2w)/2, equivalently P/2 - w.
4 · Apply your learning
Use a rectangle with length 6 m and width 4 m. Find P, then put P and w into l=(P-2w)/2 to recover 6 m. Explain why dividing only 2w by 2 would not undo the original formula.
Adult guidance and safety
Ask for the reasoning and a check, not only a numerical result. Supply accurate diagrams, coordinate grids and data displays where required. Use varied examples and revisit prerequisite gaps; these short teaching models are not a completed assessment 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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