Re-arranging formula

Rearrange a given formula to make a specified variable the subject, by undoing multiplicative, additive, fractional, bracketed, or squared/rooted operations in the correct inverse order.

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Te reo Māori terms

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Learning objective overview

Master Teaching Guide coverage for this objective.

Current NZC (2007)
  • NA5-7
  • NA6-5
New NZC (2026)
  • NZC26-P4-ALG-ER-P-Y9-06

Resources

Terminology

  • re-arrange
  • change the subject
  • isolate
  • formula
  • subject

Task goals

  • Rearrange a one-step multiplicative formula, such as D = S x T, to make any one of the three variables the subject.
  • Rearrange a one-step additive or subtractive formula, such as y = x + 5, to make the unknown the subject.
  • Rearrange a one-step formula written as a fraction, such as S = D / T, to make the numerator the subject.
  • Rearrange a two-step formula that combines multiplication with addition or subtraction, such as P = 2L + 2W, v = u + at, or y = mx + c, to make a given variable the subject.
  • Rearrange a formula written as a single fraction with two terms in the numerator, such as A = (b + c) / 2, to make either variable the subject.
  • Rearrange a formula containing a squared term or a square root, such as V = pi r^2 h, A = pi r^2, or c^2 = a^2 + b^2, to make a given variable the subject.
  • Rearrange a formula containing brackets, such as y = 2(x + 3) - 5, to make x the subject.
  • Rearrange a real-world formula (for perimeter, hire cost, or temperature conversion) to make a given variable the subject, then substitute given values to find its numerical value.

Where this fits

What leads into this objective, and where it goes next.

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Re-arranging formula

Re-arranging formula

Do

Rearranging formulae (e.g. solving P = 2l + 2w for w)

Statement▸
Year 9 · Algebra · Equations and relationships
NZC26-P4-ALG-ER-P-Y9-06

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