Year 8 Mathematics · AC9M8M05

Rates and Unit Rates

A rate compares quantities measured in different units. Convert to a common or unit rate before comparing, keep units attached through calculations, and interpret the…

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Key conceptTeach from the board

A rate answers “how much of one quantity per amount of another?” Examples include km/h, $/kg, L/100 km, dollars/hour and runs/over. A unit rate makes the second quantity 1, which supports fair comparison.

When converting compound units, transform numerator and denominator consistently. For speed, 1 m/s=3.6 km/h because 1 m/s ×3600 s/h ÷1000 m/km=3.6 km/h.

Preserve the authored AC9 breadth: pay/cost/recipes/simple interest, unit conversions and exchange rates, cricket or fuel-consumption contexts, taxation tables, and First Nations land/water-management examples where rates such as fire spread or evaporation are interpreted with appropriate context and care.

Worked examplesWe do

Worked examples

AC9M8M05 - Rates and Unit Rates
Example 1

Find the unit rate for 240 km in 4 h.

Example 2

Find $/kg for $9.60 per 3 kg.

Example 3

Interpret 6.8 L/100 km in words.

Example 4

A rate answers “how much of one quantity per amount of another?” Examples include km/h, $/kg, L/100 km, dollars/hour and runs/over. A unit rate makes the second quantity 1, which supports fair comparison.

Curriculum examplesCopied content

Australian Curriculum v9.0 — AC9M8M05: recognise and use rates to solve problems involving the comparison of 2 related quantities of different units of measure.

Victorian Curriculum F–10 Version 2.0 — Level 8, VC2M8M05:Exact.

NSW Mathematics K–10 Syllabus (2022) — Stage 4, MA4-RAT-C-01; MAO-WM-01:Exact for ratios/rates and distance–time reasoning, supported by Working mathematically.

LessonAC v9VictoriaNSW
Rates and unit ratesAC9M8M05VC2M8M05 — ExactMA4-RAT-C-01; MAO-WM-01 — Exact
Questions and answersWith answers
  1. What is a rate? A comparison of two related quantities measured in different units.
  2. Why use a unit rate? It creates a common basis for comparison.
  3. What is 1 m/s in km/h? 3.6 km/h.
  4. Why keep units through calculations? They show meaning and help detect incorrect conversions.
Practice and reviewReady for practice
  • Comparing raw totals with different denominators. Convert to common/unit rates first.
  • Dropping units. Units identify what the quotient means.
  • Converting only one part of a compound unit incorrectly. Track conversion factors explicitly.
  • Assuming every rate is constant. Some contexts use average rates; state what the rate represents.
Curriculum alignmentStart here
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