Compound measures and proportion

AQA GCSE Maths

8 ready-made resources for teaching Compound measures and proportion, written for AQA GCSE Maths. Slides, worksheets, mark schemes, homework, an assessment and retrieval quizzes, all with SEN-friendly scaffolding built in as standard. Below is what the topic requires and where students usually go wrong, free to read whether or not you sign up.

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What is in this bundle

Assessment mark schemeWord, editable
End-of-topic assessmentWord, editable
HomeworkWord, editable
Retrieval-practice quizzesWord, editable
SlidesPowerPoint, editable
Starter & exit ticketWord, editable
Tiered worksheetWord, editable
Worksheet mark schemeWord, editable

Foundation tier

Calculate speed, distance, or time using speed = distance ÷ time.
Calculate density, mass, or volume using density = mass ÷ volume.
Convert between units of speed (for example km/h to m/s).
Understand direct proportion (y is directly proportional to x, written y = kx), find the constant k, and use it to solve problems.
Solve direct proportion problems using scaling or ratio methods.

Higher tier, in addition

Calculate pressure, force, or area using pressure = force ÷ area.
Set up and use formulae connecting compound measures, including working with compound units.
Understand inverse proportion (y is inversely proportional to x, written y = k ÷ x) and use it to solve problems.
Recognise and interpret graphs of direct proportion (a straight line through the origin) and inverse proportion (a reciprocal curve).
Solve growth and decay problems using multipliers, including compounding over more than one time period.

Where students go wrong

Using the wrong rearrangement of a compound measure formula (for example dividing when multiplication is needed).
Forgetting to convert units before calculating, mixing for example km and m in the same calculation.
Assuming every proportion relationship is direct when it may be inverse.
Setting up y = kx when the relationship is actually y = k ÷ x, or vice versa.
Using an incorrect multiplier in growth or decay problems, or forgetting to compound it over multiple time periods.

How it gets asked in the exam

"Work out the speed of...", "y is directly proportional to x. Find the value of...", "y is inversely proportional to x². Find...", "Work out the density of...", "The value increases by 3% each year. Find...".

Key vocabulary

Speed, density, pressure, compound measure, compound unit, direct proportion, inverse proportion, proportionality constant, multiplier, growth, decay.

Assumed prior knowledge

Percentages, including percentage change.
Ratio and proportion.
Rearranging and solving simple formulae.
Recognising straight-line and reciprocal graphs.

How Speca scaffolds this topic

Provide a formula-triangle reference card for each compound measure (speed/distance/time; density/mass/volume; pressure/force/area): covering the unknown quantity reveals the correct rearrangement.
Give every proportion question a sentence-starter prompt, "as ___ increases, ___ (increases/decreases)", to decide direct versus inverse before an equation is set up.
Use a colour-coded multiplier reference table for growth and decay (increase → multiplier greater than 1 in one colour; decrease → multiplier less than 1 in a second colour), explicitly linked back to the equivalent percentage-change method already taught in the percentages topic.

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