Rates and Unit Rates — AC9M8M05

• Recognise rates as comparisons of unlike units.
• Calculate and interpret unit rates.
• Convert compound units such as m/s and km/h.
• Compare prices, pay, consumption and other practical rates fairly.

Recall ratios, division, fractions/decimals, metric conversions, percentages and proportional reasoning.

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.

• 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.

1. Find the unit rate for 240 km in 4 h.
2. Find $/kg for $9.60 per 3 kg.
3. Convert 12 m/s to km/h.
4. Interpret 6.8 L/100 km in words.

1. Compare $18 for 5 kg with $25 for 8 kg.
2. Convert 72 km/h to m/s.
3. A worker earns $162 for 6 h. Find hourly rate.
4. A recipe uses 450 g flour for 6 serves. Find grams per serve.
5. A team scores 96 runs in 16 overs. Find average run rate.
6. A vehicle uses 45 L over 600 km. Find L/100 km.
7. Give an example where an average rate should not be interpreted as constant at every moment.

Two mobile-data plans advertise different total prices and data allowances. Explain how to create a fair rate comparison, what other fixed fees or usage limits could make the unit-price comparison incomplete, and what information a user would need before choosing.

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.

1. Compare 750 g for $5.40 with 1.2 kg for $8.10 and identify better value.
   Convert both to the same unit price, such as $/kg.
2. A runner travels 2.4 km in 9 min. Find average speed in km/h.
   Convert 9 min to 0.15 h before dividing.
3. Two cars use 7.2 L/100 km and 9 L/120 km. Compare fuel efficiency.
   Convert the second rate to L/100 km.

• I recognise unlike-unit comparisons.
• I calculate unit rates.
• I convert compound units.
• I interpret rates rather than only compute them.

Exit ticket: Why is 60 km in 1 h easier to compare than 180 km in 3 h?

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.

• AC9M8M04 — duration/time zones
• AC9M8M07 — modelling ratios and rates

• Australian Curriculum v9.0
• Victorian Curriculum F–10 Version 2.0 Mathematics
• NSW Mathematics K–10 Syllabus (2022)

Curriculum equivalents for And use rates to solve problems involving the comparison of...

Mapped skill: recognise and use rates to solve problems involving the comparison of 2 related quantities of different units of measure

These references identify matching or closely related learning. Curriculum sequence, terminology and depth vary, so teachers should use the mapped skill and lesson difficulty to confirm suitability.

Australian Curriculum v9.0 is the canonical source for this SkillrHub lesson. Victoria and NSW entries name the closest published state codes or outcomes; international entries are planning references rather than claims of identical curricula.