Build and annotate the model
Represent mathematical modelling with rational numbers and percentages and label the important parts, quantities or choices.
Learning goals
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
- Represent
- Reason
- Calculate
- Interpret
- 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 concept
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.
Worked examples
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.
Curriculum elaborations explicitly taught
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.
Common misconceptions
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.
Classroom activities
Compare and reason
Use the application model to compare two cases, explain the relationship and identify a likely error.
Transfer and verify
Apply the idea in an unfamiliar context and use a second method, evidence source or text feature to check it.
Revision Notes and quick mastery check
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.
Curriculum wording and references
Australian Curriculum v9.0
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
The Australian Curriculum code and wording are exact. International teachers can use the underlying mathematical concept while matching the lesson to their local grade or year outcomes.
Resources and next steps
Teacher Slides
Project the fixed, branded four-page teaching sequence.
Open Classroom ViewHomework
Use the printable activity for written practice.
Open HomeworkPractice and Test
Use supported Practice first, then the separate Test when ready.
Open PracticeOpen Test
🎥 Optional Video Lesson
The SkillrHub lesson remains the primary learning resource. This optional video reinforces the explanation; you can complete the lesson and practice without watching.
Before you watch:
- Pause after each worked example.
- Try the examples yourself.
- Return to the SkillrHub lesson before continuing.
Recommended: Finding a Percent of a Number
Math Antics — Practise the percentage calculation that can form part of a practical model; planning and interpreting the model remain in the lesson.
As you watch: Which quantity is the whole when a percentage is calculated?
Load video player Loads YouTube in this lesson. See the video notice below.
Try it: Plan the cost of four $30 tickets with a 10% group discount and a $6 booking fee. Write the operations, solve and explain your assumptions.
Video unavailable, inaccurate or unsuitable for this year? Report a video problem to SkillrHub by email. You can continue with the written lesson and practice resources.
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Curriculum equivalents: Victoria, NSW and international
Curriculum equivalents for Mathematical modelling to solve practical problems involving natural and rational...
Mapped skill: 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
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.
| Region | Curriculum framework | Closest level or code |
|---|---|---|
| Australia | Australian Curriculum v9.0 | AC9M6N09 · Year 6 |
| Victoria | Victorian Curriculum F–10 Version 2.0 — Mathematics | VC2M6N09 · Level 6 |
| New South Wales | NSW Mathematics K–10 Syllabus (2022) | MA3-RN-03 · Stage 3 |
| United States (USA) | Common Core State Standards for Mathematics | Grade 6 |
| Canada (Ontario) | Ontario Curriculum — Mathematics | Grade 6 |
| United Kingdom (England) | National Curriculum in England — Mathematics | Year 7, Key Stage 3 |
| India | NCERT / CBSE — Mathematics | Class 6 |
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.
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Topic reference: AC9M6N09 — Mathematical Modelling with Rational Numbers and Percentages
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