Year 6 Mathematics · AC9M6N09

Mathematical Modelling with Rational Numbers and Percentages

Formulate, solve, validate and justify practical and financial decisions

Ready to project and teach

Learning goalsSay it simply

Learning goal

Students identify quantities, rates, percentages, constraints and assumptions, build a model, compare scenarios and communicate a recommendation supported by calculations and sensitivity checks.

Success criteria

  • I can represent or identify the concept.
  • I can explain the underlying relationship.
  • I can select an appropriate strategy or feature.
  • I can apply it in a new context.
  • I can justify and verify the response.

Teaching routine

  1. Represent
  2. Reason
  3. Calculate
  4. Interpret
  5. Verify
Curriculum focus: use mathematical modelling to solve practical problems involving natural and rational numbers and percentages, including in financial contexts; formulate the problems, choosing operations and efficient calculation strategies, and using digital tools where appropriate; interpret and communicate solutions in terms of the situation, justifying the choices made
Key conceptTeach from the board

Compare two fundraising plans

Use the visual model first. Ask students to identify the quantities, structure or conditions before calculating or explaining.

planincomecostsnetA: 180 tickets at $12$2 160$780 fixed + 15% fee$1 056B: 150 tickets at $15$2 250$1 050 fixed + 8% fee$1 020decisionA higher netbut test attendance assumptions

The model separates revenue, percentage fees and fixed costs. A recommendation should state assumptions about tickets sold and constraints such as venue capacity.

Use a modelling and sensitivity cycle

Connect the central relationship to a new context, then verify the conclusion with a second representation, estimate, inverse operation or reasonableness check.

define decision→identify quantities/constraints→represent equations/table→calculate scenarios→validate and estimate→change one assumption→recommend and communicate

Digital spreadsheets can compare many scenarios, but formulas, units and assumptions must be explained and checked.

Clean visual examplesOne-page board

Clean one-page examples

AC9M6N09 - Mathematical Modelling with Rational Numbers and Percentages
Example 1

plan income costs net A: 180 tickets at $12 $2 160 $780 fixed + 15% fee $1 056 B: 150 tickets at $15 $2 250 $1 050 fixed + 8% fee $1 020 decision A higher net but test attendance assumptions

Example 2

define decision → identify quantities/constraints → represent equations/table → calculate scenarios → validate and estimate → change one assumption → recommend and communicate

Example 3

: modelling practical situations involving percentages using efficient calculation strategies to find solutions, such as mental calculations, spreadsheets, calculators or a variety of informal jottings, and interpreting the results in terms of the situation; for example, purchasing items during a sale

Example 4

: modelling situations involving earning money and budgeting, asking questions such as, “Can I afford it?”, “Do I need it?”, “How much do I need to save for it?”, and developing a savings plan or budget for an upcoming event or personal purchase

Curriculum examplesCopied content

AC9M6N09: use mathematical modelling to solve practical problems involving natural and rational numbers and percentages, including in financial contexts; formulate the problems, choosing operations and efficient calculation strategies, and using digital tools where appropriate; interpret and communicate solutions in terms of the situation, justifying the choices made

  • E1: modelling practical situations involving percentages using efficient calculation strategies to find solutions, such as mental calculations, spreadsheets, calculators or a variety of informal jottings, and interpreting the results in terms of the situation; for example, purchasing items during a sale
  • E2: modelling situations involving earning money and budgeting, asking questions such as, “Can I afford it?”, “Do I need it?”, “How much do I need to save for it?”, and developing a savings plan or budget for an upcoming event or personal purchase
  • E3: modelling and solving the problem of creating a budget for a class excursion or family holiday, using the internet to research costs and expenses, and representing the budget in a spreadsheet, creating and using formulas to calculate totals

Use the central and application models above to connect each elaboration to the same underlying concept.

Questions and answersWith answers

Check understanding

  • Identify a percentage fee base.
  • Write a net-income equation.
  • Check a capacity constraint.
  • Test one assumption.
  • Communicate a recommendation.

Evidence of mastery

  • Represent or identify the concept
  • Explain the underlying relationship
  • Select an appropriate strategy or feature
  • Apply it in a new context
  • Justify and verify the response

Decision: continue when students can explain the model, apply it to a new example and justify their check. Otherwise return to the central model and reduce the numerical or representational load.

Practice and reviewReady for practice
Every number in the context usedInclude only relevant quantities and relationships.
Percentage fee calculated from the wrong baseIdentify whether it applies to revenue, cost or balance.
Cheapest option selected without constraintsCheck capacity, quality and requirements.
Spreadsheet output accepted without formula auditExplain and verify formulas.
Curriculum alignmentStart here

Learning goal

Students identify quantities, rates, percentages, constraints and assumptions, build a model, compare scenarios and communicate a recommendation supported by calculations and sensitivity checks.

Success criteria

  • I can represent or identify the concept.
  • I can explain the underlying relationship.
  • I can select an appropriate strategy or feature.
  • I can apply it in a new context.
  • I can justify and verify the response.

Teaching routine

  1. Represent
  2. Reason
  3. Calculate
  4. Interpret
  5. Verify
Curriculum focus: use mathematical modelling to solve practical problems involving natural and rational numbers and percentages, including in financial contexts; formulate the problems, choosing operations and efficient calculation strategies, and using digital tools where appropriate; interpret and communicate solutions in terms of the situation, justifying the choices made
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