Mathematical modelling for practical problems

Students use mathematics to make sense of practical situations. The important skill is not simply completing a calculation: students decide what the problem is asking, choose a representation and operation, solve it, then explain what the answer means in the original situation.

• Identify the quantities that are known and the quantity that is unknown.
• Represent the situation using materials, drawings, bar models, arrays, number lines, tables or number sentences.
• Choose addition, subtraction, multiplication or division because it matches the structure of the problem.
• Use an efficient Year 2 calculation strategy.
• Check whether the answer is reasonable and whether a remainder needs to be interpreted.
• State the answer with the correct unit and in terms of the real situation.

The curriculum includes modelling equal grouping and sharing through First Nations Australian children’s instructive games, including Yangamini from the Tiwi Island Peoples. When using this elaboration, use curriculum-authorised or community-appropriate source material and avoid inventing cultural details. Keep the mathematical focus on the equal-group relationships, the number sentence and the interpretation of the solution within the source context.

Content description: use mathematical modelling to solve practical problems involving additive and multiplicative situations, including money transactions; represent situations and choose calculation strategies; interpret and communicate solutions in terms of the situation.

• E1: interpret everyday additive or multiplicative situations, choose an operation and justify why it matches the relationship.
• E2: model and solve simple whole-dollar money problems using addition, subtraction, multiplication or division.
• E3: model practical grouping and sharing problems, including deciding what to do when there is a remainder.
• E4: model “How many days are there left in this year?” using a calendar.
• E5: use First Nations Australian children’s instructive games as a teaching context for equal grouping and sharing, representing relationships with number sentences and communicating solutions in context.

Key idea: Modelling turns a real situation into a drawing, number sentence, table or materials model, then checks whether the answer makes sense in context.

Remember

• Represent situations
• Choose calculation strategy
• Use money contexts
• Interpret the answer
• Communicate solutions

Quick questions

• Model a $6 + $4 purchase.
• What operation fits 4 bags of 5?
• Write a context sentence for 18 ÷ 3 = 6.
• Check if 100 pencils is reasonable for 3 boxes of 4.

If an answer is uncertain, return to the model and explain what each part represents before calculating or drawing a conclusion.

• Choosing an operation from one keyword: ask students to describe the relationship between the quantities first.
• Calculating before representing: a quick diagram or bar model often reveals what the problem is actually asking.
• Ignoring the unit: a correct numerical result can still be an incomplete answer.
• Forcing a remainder to disappear: practical division sometimes needs a decision about leftover people or objects.
• Not checking reasonableness: compare the answer with the original quantities before accepting it.

Teach the modelling cycle explicitly, then mix additive, multiplicative, money, grouping and calendar problems. Require students to show a representation and a final context sentence so the task remains about modelling rather than calculation alone.

Students use mathematics to make sense of practical situations. The important skill is not simply completing a calculation: students decide what the problem is asking, choose a representation and operation, solve it, then explain what the answer means in the original situation.

• Identify the quantities that are known and the quantity that is unknown.
• Represent the situation using materials, drawings, bar models, arrays, number lines, tables or number sentences.
• Choose addition, subtraction, multiplication or division because it matches the structure of the problem.
• Use an efficient Year 2 calculation strategy.
• Check whether the answer is reasonable and whether a remainder needs to be interpreted.
• State the answer with the correct unit and in terms of the real situation.

• Australian Curriculum Version 9.0
• Victorian Curriculum F–10
• NSW Curriculum

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