Compound Measures

Scheme of work: GCSE Foundation: Year 10: Term 4: Compound Measures

Prerequisite Knowledge

  • know and apply formulae to calculate:
  • rectangles
  • rectilinear composite shapes
  • area of triangles
  • volume of cuboids
  • use standard units of measure and related concepts (length, area, volume/capacity, mass, time, money, etc.)

Success Criteria

  • use standard units of mass, length, time, money and other measures (including standard compound measures) using decimal quantities where appropriate
  • round numbers and measures to an appropriate degree of accuracy (e.g. to a specified number of decimal places or significant figures)
  • change freely between related standard units (e.g. time, length, area, volume/capacity, mass) and compound units (e.g. speed, rates of pay, prices, density, pressure) in numerical and algebraic contexts
  • use compound units such as speed, rates of pay, unit pricing, density and pressure

Key Concepts

  • It is useful to calculate compound measures through the unitary method where ratios are in form 1 : n.
  • Distance – Time graphs can be extended to Speed-Time/Acceleration-Time graphs.
  • Use algebraic techniques to manipulate the various formulae so that other measures can also be found.

Common Misconceptions

  • Density, pressure and time do not have to have fixed units. For instance, a speed can be m/s or mph; density can be g/cm3 or kg/3.
  • Students often have difficulty remembering which measure to divide by. The speed, pressure and density triangles are helpful to recall the relationship between the various measures.

Compound Measures Resources

Mr Mathematics Blog

Problem-Solving with Angles in Polygons

How to teach problem solving with angles in polygons through scaffolding.

The Sum to Infinity of Geometric Series – A-Level Maths Tutorial

Explore geometric series in our A-Level Maths tutorial. Perfect for students/teachers, with resources to download at

Sequences and Series

Edexcel A-Level Mathematics Year 2: Pure 2: Algebraic Methods