Expected level of development
Australian Curriculum Mathematics V9: AC9M4N07, AC9M4N08
Numeracy Progression: Number and place value: P7, Additive strategies: P8, Number patterns and algebraic thinking: P6, Understanding money: P7
At this level, students use mathematical modelling processes to solve practical problems involving additive and multiplicative situations including financial contexts. They formulate problems using number sentences and choose efficient calculation strategies.
Use classroom talks to show how to use additive strategies to solve problems, choosing addition, subtraction, or both, and make explicit how each number is connected to the number sentence. A bar model or cherry diagram may be used to represent these additive problems. At various stages let students select a model they think would be used to represent the problem, opening up choice and asking them to justify their selection. The aim here is to move from giving them the mathematical operation to use to students suggesting the relevant mathematical operation.
Use contexts that require multiplicative thinking to encourage students to see the link between repeated addition and multiplication and how these can be used to solve problems. Discuss which is more efficient, with respect to the context, and why. Use mathematical modelling processes to collaboratively solve division problems working out an unknown number of groups and other problems that ask how much is in each group. Make explicit the related division and multiplication number sentences.
There is an opportunity to incorporate estimation strategies to determine the reasonableness of calculations and detect errors when solving problems involving additive or multiplicative thinking. Choose and use estimation and rounding to check and explain the reasonableness of calculations including the results of financial transactions (AC9M4N07).
Teaching and learning summary:
- Provide guidance on using mathematical modelling processes to solve number problems.
- Give students problems to solve that encourage them to choose a number operation.
- Explicitly teach and provide meaningful contexts in which to apply rounding up and down when making estimations about the answer to number problems.
The Learning from home activities are designed to be used flexibly by teachers, parents and carers, as well as the students themselves. They can be used in a number of ways including to consolidate and extend learning done at school or for home schooling.
Learning intention:
- We are learning to use our number knowledge to make estimates.
Why are we learning about this?
- Estimation is used in everyday life and work.
What to do
The school canteen staff is looking at the menu.
1. Each week they have bread left over. Some weeks when they buy less bread they don’t have enough.
- What can they do to make sure they don’t waste bread but still have enough to make sandwiches?
- Think about your school canteen. How much bread would they need to buy to make sandwiches?
- How would they ensure they don’t have too much or not enough?
2. Draw a plan to describe how you would solve the problem.
Success criteria:
I can:
- make estimates that are reasonable
- use what is known together with rounding to convenient numbers (for example, to multiples of 10) to make reasonable estimates to addition and multiplication problems
- solve addition and multiplication problems.
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Teaching strategies
A collection of evidence-based teaching strategies applicable to this topic. Note we have not included an exhaustive list and acknowledge that some strategies such as differentiation apply to all topics. The selected teaching strategies are suggested as particularly relevant, however you may decide to include other strategies as well.
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Classroom talks
Classroom talks enable students to develop language, build mathematical thinking skills and create mathematical meaning through collaborative conversations.
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Concrete, Representational, Abstract (CRA model)
The CRA model is a three-phased approach where students move from concrete or virtual manipulatives, to making visual representations and on to using symbolic notation.
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Culturally responsive pedagogy
Mathematics is not an exclusive western construct. Therefore, it is important to acknowledge and demonstrate the mathematics to be found in all cultures.
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Multiple exposures
Providing students with multiple opportunities within different contexts to practise skills and apply concepts allows them to consolidate and deepen their understanding.
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Questioning
A culture of questioning should be encouraged and students should be comfortable to ask for clarification when they do not understand.
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Teaching resources
A range of resources to support you to build your student's understanding of these concepts, their skills and procedures. The resources incorporate a variety of teaching strategies.
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Buying presents
In this lesson, students will use mathematical modelling to make decisions based on the purchasing of gifts.
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Pocket money: Mathematical modelling
In this lesson, students use mathematical modelling to solve problems that involve financial decisions.
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The netball tournament
Use this task to explore, discuss and model strategies to solve a problem choosing relevant number operation to perform the calculations.
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Mathematical modelling buying presents
Use the context of purchasing presents to investigate and problem-solve using mathematical modelling.
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Mathematical modelling pocket money
Use the context of pocket money to investigate and problem-solve using mathematical modelling.
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Estimate and match the number sentence
Use this slide deck as a prompt to develop estimation skills when making calculations and also discuss relevant mathematical models.
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Let's party!
Students learn about needs and wants, while budgeting for a birthday party.
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Paying It Forward Years 3-4
In this unit students develop financial literacy skills including the costs and benefits of saving and spending and strategies that can be used to reach financial goals.
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