Year 8 Mathematics · AC9M8M07

Mathematical Modelling with Ratios and Rates

Turn a practical situation into quantities, ratios or rates; choose a representation; solve; then interpret the result and review whether proportionality, constant speed…

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Key conceptTeach from the board

A modelling cycle is more than calculation: formulate → represent → solve → interpret → review. State what quantities vary, their units, and whether a proportional/constant-rate assumption is justified.

Equivalent ratios multiply or divide every part by the same non-zero factor. Rate models may be direct (e.g. constant speed) or include fees/brackets that break simple proportionality. If a phone plan has a fixed fee, “cost per unit” alone may not predict total cost for every usage level.

Preserve the authored elaborations: map/plan scales and mixtures, magnification, exchange-rate travel budgeting, taxation/pay/phone-plan comparisons, radiocarbon ratio contexts used to study long-term human habitation, and First Nations string/cordage ratio applications. Present cultural contexts respectfully and as mathematical applications, not decorative references.

Worked examplesWe do

Worked examples

AC9M8M07 - Mathematical Modelling with Ratios and Rates
Example 1

Scale 3:5 to an equivalent ratio with total 64.

Example 2

Use a 1:25,000 map scale to convert 6 cm to real distance.

Example 3

Find distance travelled at 80 km/h for 1.75 h.

Example 4

State one assumption in a currency-conversion model.

Curriculum examplesCopied content

Australian Curriculum v9.0 — AC9M8M07: use mathematical modelling to solve practical problems involving ratios and rates, including distance-time problems for travel at a constant speed and financial contexts; formulate problems; interpret and communicate solutions in terms of the situation, reviewing the appropriateness of the model.

Victorian Curriculum F–10 Version 2.0 — Level 8, VC2M8M07:Exact.

NSW Mathematics K–10 Syllabus (2022) — Stage 4, MA4-RAT-C-01; MA4-FRC-C-01; MAO-WM-01:Partial. NSW distributes ratio/rate, distance-time, percentage/financial and Working mathematically content across outcomes rather than mirroring the national modelling descriptor one-to-one.

LessonAC v9VictoriaNSW
Ratio/rate modellingAC9M8M07VC2M8M07 — ExactMA4-RAT-C-01; MA4-FRC-C-01; MAO-WM-01 — Partial
Questions and answersWith answers
  1. What is the modelling cycle? Formulate, represent, solve, interpret and review.
  2. How are equivalent ratios formed? Multiply/divide every term by the same non-zero factor.
  3. When is d=vt appropriate? When speed v is treated as constant over time t.
  4. Why review a rate model? Real situations may include fixed fees, changing rates, limits or uncertainty.
Practice and reviewReady for practice
  • Adding the same number to ratio terms. Equivalent ratios require multiplicative scaling.
  • Assuming every rate model passes through zero. Fixed fees or thresholds create non-proportional models.
  • Ignoring units/fees. A model can be numerically correct but contextually incomplete.
  • Not reviewing the assumption. Constant speed, exchange rate or material strength may vary in reality.
Curriculum alignmentStart here
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