Modelling Rational Numbers and Percentages — AC9M8N05

• Model signed rational-number changes in practical contexts.
• Use percentage increase/decrease and multipliers accurately.
• Interpret financial tables and percentage-of-income results.
• Model repeated change over time and review assumptions.

Recall integer/rational operations, percentages of quantities, percentage change, decimal multipliers and reading tables.

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.

• 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.

1. Interpret a temperature change from −4.5°C to 2.0°C.
2. Increase $80 by 12% using a multiplier.
3. Reduce $450 by 18%.
4. Use a supplied two-bracket tax table to calculate tax and tax as a percentage of income.

1. A depth changes from −32 m to −25.5 m. Find and interpret the change.
2. A $320 item is discounted by 25%.
3. A price of $150 is marked up by 30%.
4. A quantity decreases from 800 to 680. Find percentage decrease.
5. Model two consecutive 5% increases on $2,000.
6. Use a supplied tax table to compare tax paid at two incomes.
7. State two limitations of assuming one constant percentage growth rate for five years.

Two shops sell a $400 item. Shop A offers 30% off. Shop B offers 20% off then a further 12.5% off the reduced price. Determine which is cheaper, explain why adding Shop B’s percentages is invalid, and state what extra fees would make the model incomplete.

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.

1. A temperature rises from −6.5°C to 1.8°C. Find and interpret the signed change.
   Subtract final minus initial; explain the positive result.
2. A quantity grows 4% per year for 3 years from 12,000. Model the result and state one limitation.
   Use 12000×1.04³ and discuss the constant-rate assumption.
3. Using a supplied bracketed tax table, calculate tax for an income and express it as a percentage of income.
   Apply each bracket separately before dividing tax by total income.

• I model signed changes.
• I use percentage multipliers.
• I interpret table-based financial calculations.
• I review repeated-change assumptions.

Exit ticket: Why is a five-year 3% growth model an assumption rather than a guaranteed prediction?

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.

• AC9M8N04 — rational operations
• AC9M8M05 — rates
• AC9M8M07 — ratio/rate modelling

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

Curriculum equivalents for Mathematical modelling to solve practical problems involving rational numbers and...

Mapped skill: use mathematical modelling to solve practical problems involving rational numbers and percentages, including financial contexts; formulate problems, choosing efficient calculation strategies and using digital tools where appropriate; interpret and communicate solutions in terms of the situation, reviewing the appropriateness of the model

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.