Solving measurement equations

Substitute known values into a measurement formula (perimeter, area, volume, or distance = speed x time), set it equal to a given value, and solve for the unknown, keeping units attached to the answer.

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Te reo Māori terms

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Learning objective overview

Master Teaching Guide coverage for this objective.

Resources

Terminology

  • equation
  • solve
  • formula
  • substitute

Task goals

  • Substitute known values into a measurement formula (perimeter, area, volume, or distance = speed x time) to form a one-step equation, and solve for the unknown.
  • Solve a two-step equation formed from a measurement formula where the unknown has a coefficient and a constant term, such as a rectangle's perimeter with one known side.
  • Solve an equation involving a squared unknown or a unit conversion, such as finding a square's side length from its area, or converting between litres and millilitres.
  • Form and solve an equation from a measurement context where one dimension is given as an algebraic expression, including for a triangle, trapezium, prism, or circle (using pi).
  • Form and solve an equation where two algebraic dimensions are multiplied together, producing a quadratic equation, such as a rectangle's area given as (x + 2)(x - 2).
  • Solve a measurement equation involving a cube or cube root, such as finding a sphere's radius from its volume.
  • Form and solve a measurement equation from a worded multi-step context, such as a tank filling at a constant rate over time, or two different shapes sharing the same perimeter.

Teaching guidance

  • Builds directly on T1_EX05: students already have a measurement expression or formula and must now set it equal to a given value and solve for the unknown.
  • Model substituting known values into a formula (e.g. perimeter, area, volume) before solving, and re-arranging when the unknown is not the subject.
  • Keep units attached to the answer and sense-check the solved value against the diagram (e.g. a negative or oversized length signals an error).

Key skills

  • Solving
  • Measurement
  • Equations
  • Substitution
  • Formulae

Quick stats

  • 81 total questions
  • 3 difficulty levels
  • Answers included