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

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

Students should be comfortable reading and representing whole numbers, using place value, and explaining simple addition, subtraction or equal-group relationships from earlier years. Begin with a short concrete or visual recall task before moving to Mathematical Modelling in Practical Problems.

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

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.

• 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. Three notebooks cost $4 each. What is the notebook cost?

   • $12
   • $7
   • $34
   • $1

2. Complete the two-step model.

   Prompt: 4 boxes of 6 items gives □ items; shared among 3 groups gives □ each.

3. Which operation matches five $3 tickets?

   • 5 × 3
   • 5 + 3 only
   • 5 − 3
   • 5 ÷ 3

4. A class buys 3 packs of 8 markers and shares them equally among 4 tables. Model and solve the problem.

5. Match the situation to the operation.

   Match: four bags of 7 • $30 minus $12 • 24 shared by 6 ↔ division • multiplication • subtraction

6. Complete the context sentence.

   Prompt: 36 ÷ 4 = 9, so each team receives □ cones.

1. Create and solve a two-step financial problem that uses multiplication and subtraction.

2. Solve one practical problem using both a diagram and a number sentence, then compare the representations.

Explain the reasoning, not only the final answer.

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.

• I can represent situations.
• I can formulate number sentences.
• I can use multiple operations.
• I can use financial contexts.
• I can interpret solutions.

Quick check: Model 4 packs of 6 shared among 3 children. • What operation fits three $7 items? • Write a context sentence for 36 ÷ 4 = 9.

Read the topic guide and use the teacher slide for instruction. Students can then use the worksheet for written work, open Practice for supported feedback, or take the Test when they are ready.

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

• Australian Curriculum Version 9.0 — ACARA
• Victorian Curriculum — VCAA
• NSW Curriculum — NESA

Official curriculum sites are the source of record.

• AC9M3N05 — Estimating Quantities and Answers
• AC9M3N07 — Number Algorithms and Patterns
• All Year 3 Mathematics topics

Curriculum equivalents for Mathematical modelling to solve practical problems involving additive and multiplicative...

Mapped skill: 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

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.