Year 3 Mathematics · AC9M3N06

Use mathematical modelling to solve practical problems involving additive and multiplicative situations including financial contexts

use mathematical modelling to solve practical problems involving additive and multiplicative situations including financial contexts; formulate problems using number…

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Learning goalsSay it simply

Mathematical modelling turns a practical situation into a diagram, table or number sentence, then connects the solution back to the context.

Learning routine: Understand context → Choose representation → Formulate → Solve → Check → Interpret

Success looks like

  • Represent situations
  • Formulate number sentences
  • Use multiple operations
  • Use financial contexts
  • Interpret solutions

Success criteria:

  • Represent situations
  • Formulate number sentences
  • Use multiple operations
  • Use financial contexts
  • Interpret solutions
Key conceptTeach from the board

Key idea: Mathematical modelling turns a practical situation into a diagram, table or number sentence, then connects the solution back to the context.

Learning routine: Understand context → Choose representation → Formulate → Solve → Check → Interpret

mathematical model
a diagram, number sentence or representation of a situation
strategy
a chosen method for solving a problem
interpret
explain what an answer means in its situation
Clean visual examplesOne-page board

Clean one-page examples

AC9M3N06 - Use mathematical modelling to solve practical problems involving additive and multiplicative situations including financial contexts; formulate problems using number sentences and choose calculation strategies, using digital tools where appropriate; interpret and communicate solutions in terms of the situation
Example 1

4 boxes × 6 → 24 items → share among 3 → 8 each

Example 2

calculation answer context sentence

Example 3

Model a multi-step shopping problem 3 × notebook 3 × $4 5 × pencil 5 × $2 Total $22 Three $4 notebooks cost $12 and five $2 pencils cost $10; the total is $22. Read every label and identify what each quantity or feature represents. Describe the relationship shown by the model. Check that the conclusion answers the original question.

Example 4

Choose operations from the situation 4 boxes × 6 → 24 items → share among 3 → 8 each Some situations require more than one operation. Apply the same relationship to the new context, then justify the answer using the labels and evidence shown.

Curriculum examplesCopied content

The content description and elaborations below show the curriculum ideas taught in this unit. Items marked as teaching context support lesson planning.

  • Content description: use mathematical modelling to solve practical problems involving additive and multiplicative situations including financial contexts; formulate problems using number sentences and choose calculation strategies, using digital tools where appropriate; interpret and communicate solutions in terms of the situation
  • E1: modelling practical additive situations, choosing whether to use an addition, subtraction or both when representing the problem as a number sentence, and explaining how each number in their number sentence is connected to the situation
  • E2: modelling additive problems using a bar model to represent the problem; for example, “I had 75 tomatoes and then picked some more, now I have 138. How many did I pick?”
  • E3: modelling practical multiplicative situations using materials or a diagram to represent the problem; for example, if 4 tomato plants each have 6 tomatoes, deciding whether to use an addition or multiplication number sentence, explaining how each number in their number sentence is connected to the situation
  • E4: modelling and solving practical division problems involving unknown numbers of groups or finding how much is in each group by representing the problem with both division and multiplication number sentences; explaining how the 2 number sentences are connected to the problem
  • E5: modelling the problem of deciding how to share an amount equally; for example, 48 horses into 2, 4, 6 or 8 paddocks, representing the shares with a division and a multiplication number sentence, and counting the number in each share to check the solutions

Australian, Victorian and NSW alignment retained from the previous page

RegionCurriculumClosest mapping
AustraliaAustralian Curriculum v9.0AC9M3N06 — use mathematical modelling to solve practical problems involving additive and multiplicative situations including financial contexts; formulate problems using number sentences and choose calculation strategies, using digital tools where appropriate; interpret and communicate solutions in terms of the situation
VictoriaVictorian Curriculum F-10Year 3 Maths: closest match in Number. Use this page as a VIC-aligned practice and worksheet reference.
NSWNSW CurriculumStage 2 Maths: closest content focus for Use mathematical modelling to solve practical problems involving additive and multiplicative situations including financial contexts; formulate problems using number sentences and choose calculation strategies, using digital tools where appropriate; interpret and communicate solutions in terms of the situation and related outcomes.
Questions and answersWith answers
What is the big idea in this topic?
Mathematical modelling turns a practical situation into a diagram, table or number sentence, then connects the solution back to the context.
What routine should I use?
Understand context → Choose representation → Formulate → Solve → Check → Interpret
How do I know I am ready to move on?
You can represent situations, formulate number sentences, use multiple operations, use financial contexts, interpret solutions and explain how your model or calculation supports the answer.
Practice and reviewReady for practice
  • Using every number — Choose numbers and operations that match the question.
  • Stopping at a number — Interpret what the result means in context.
  • No check — Use estimation, inverse operations or a second representation.

  1. Explain how a diagram or table can help choose an operation.

  2. A student adds all the numbers in every word problem. Give an example where this fails and correct it.

Review hint: Follow the routine “Understand context → Choose representation → Formulate → Solve → Check → Interpret” and use the worked model to check whether your answer is reasonable.

Curriculum alignmentStart here

Mathematical modelling turns a practical situation into a diagram, table or number sentence, then connects the solution back to the context.

Learning routine: Understand context → Choose representation → Formulate → Solve → Check → Interpret

Success looks like

  • Represent situations
  • Formulate number sentences
  • Use multiple operations
  • Use financial contexts
  • Interpret solutions

Success criteria:

  • Represent situations
  • Formulate number sentences
  • Use multiple operations
  • Use financial contexts
  • Interpret solutions
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