Year 8 Mathematics · AC9M8N05

Modelling Rational Numbers and Percentages

Formulate real situations with signed rational numbers and percentages, choose efficient strategies, interpret financial or environmental results, and review whether the…

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Key conceptTeach from the board

Mathematical modelling is a cycle: formulate → calculate → interpret → review. Identify quantities, units and assumptions before calculating. Signed rational numbers are useful for temperature, sea depth and other change-from-reference contexts.

Percentage multipliers encode a new base: increase by p% means multiply by 1+p/100; decrease means multiply by 1−p/100. Repeated changes use the updated quantity, so equal percentage increase and decrease do not cancel.

Financial modelling may use a provided tax table. Apply each stated bracket/rule exactly, then interpret tax as an amount and, where asked, as a percentage of income. A simplified classroom table is a mathematical model, not personal tax advice.

For change over extended time, state whether a constant percentage is assumed each period and review how realistic that assumption is for population, markets or environmental measures.

Worked examplesWe do

Worked examples

AC9M8N05 - Modelling Rational Numbers and Percentages
Example 1

Interpret a temperature change from −4.5°C to 2.0°C.

Example 2

Increase $80 by 12% using a multiplier.

Example 3

Use a supplied two-bracket tax table to calculate tax and tax as a percentage of income.

Example 4

Mathematical modelling is a cycle: formulate → calculate → interpret → review . Identify quantities, units and assumptions before calculating. Signed rational numbers are useful for temperature, sea depth and other change-from-reference contexts.

Curriculum examplesCopied content

Australian Curriculum v9.0 — AC9M8N05: mathematical modelling with rational numbers and percentages, including financial contexts.

Victorian Curriculum F–10 Version 2.0 — Level 8, VC2M8N06:Exact. Victoria inserts a separate percentage-change/error descriptor at VC2M8N05.

NSW Mathematics K–10 Syllabus (2022) — Stage 4, MA4-FRC-C-01; MAO-WM-01:Partial.

FrameworkMappingRelationship
Australian CurriculumAC9M8N05Canonical
VictoriaVC2M8N06Exact
NSW Stage 4MA4-FRC-C-01; MAO-WM-01Partial
Questions and answersWith answers
  1. What are the modelling stages? Formulate, calculate, interpret and review.
  2. What multiplier gives a 17% increase? 1.17.
  3. Why do equal percentage increase/decrease not cancel? They use different base quantities.
  4. Why must a tax-table model be interpreted carefully? Its brackets and rates are assumptions supplied for that task and may not represent every real tax rule.
Practice and reviewReady for practice
  • Ignoring the sign/reference point. Interpret positive/negative quantities in context.
  • Adding/subtracting a percentage as a decimal amount. Apply it to the current base quantity.
  • Applying one tax rate to all income when a table is bracketed. Follow the supplied model’s intervals.
  • Assuming repeated percentage change is linear. Each period uses the updated amount.
Curriculum alignmentStart here
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