Planning tool
Year levels
Strands
Expected level of development
Australian Curriculum Mathematics V9: AC9M2N05, AC9M2N06
Numeracy Progression: Additive strategies: P7, Multiplicative strategies: P5, Understanding money: P3
At this level, students 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.
Provide novel contexts, such as story problems and challenging tasks, to apply and consolidate key understandings. Story problems involving additive and multiplicative situations can emerge from recent classroom experiences, discussions or stories read. Include opportunities to model sharing and grouping in games from a variety of cultures.
Create opportunities to model situations through roleplay, including scenarios involving money transactions using whole dollar amounts. For instance, set up a shop and engage students in buying and selling groceries where students decide whether to use addition, subtraction, multiplication or division to solve purchasing problems.
Regularly explore ‘What if…?’ scenarios, such as ‘What if we had 100 tokens to share out equally among class members? How many would we each get?’ Include financial situations like ‘What if each member of our class was sponsored $5 for the reading challenge? How much money would we make altogether as a class?’
Explore various ways to model problems including using physical and virtual materials and a think board diagram. Be explicit about the value of mathematical modelling for confidently representing and communicating thinking and ideas.
There is an opportunity to connect existing knowledge and skills in addition and subtraction (AC9M2A02, AC9M2N04) and multiplication and division (AC9M2N05).
Teaching and learning summary:
 Explore and model additive and multiplicative situations that are meaningful to students.
 Build habits of reasoning by inviting students to think about solving a problem in more than one way.
 Ensure a playful culture of learning where mistakes and time for sensemaking are seen as valuable to learning.
Students:
 decide whether to use addition, subtraction, multiplication or division in a given situation, and provide reasoning
 model and solve simple money problems involving whole dollar amounts with addition, subtraction, multiplication or division
 model and solve problems involving sharing and decide what to do when there is a remainder.
Some students may:
 not yet grasp that assigned money values don’t necessarily relate to size or colour. To help address this, hold regular conversations that build on existing knowledge of fairness. For instance, ask: Would it be fair for me to give you this $1 coin in exchange for that $2 coin? Why/why not?
 have trouble interpreting a problem due to the literacy demands involved. To help address this, use problems that are accompanied by visual representations. Another strategy is to use photos involving number, for example, a scene with countable animals and provide key language such as ‘whole group’, ‘altogether’ and ‘how many’ to invite students to generate their own story problems. This is one way of building understanding and language over time.
 have trouble interpreting exactly what a problem is asking. To address this, provide regular opportunities to ask questions that give less information than is required to solve the problem. For instance: Martin bought an apple. How much change did he get from $5? Questions like this with incomplete information provoke discussions that involve thinking deeply about the situation. Over time, these deepthinking opportunities about contexts will support general ability to solve everyday 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 solve everyday problems that involve making calculations.
Why are we learning about this?
 We use addition, subtraction, multiplication and division in everyday life.
What to do
1. Play with numbers as they come up in the environment, for example:
 'I spot a number plate with the numbers 5, 4 and 8 on it. What would those numbers make added together? (5 + 4 + 8)
 I spot the house number 39. I wonder: How many more is 50 than 39? What about 70? Or 100?'
2. Link addition and subtraction to everyday situations, for example:
 Notice and discuss situations involving addition and subtraction in storybooks.
 Discuss the scores in a game of sport and talk about the difference between scores, for instance, how much the winning team has won by.
 Provide opportunities to play with, sort and add up money. Engage in imaginary situations involving paying and working out change.
 When shopping, or when playing shops, talk about the total number of items in the basket, for example, 'There are 8 apples, 6 bananas and 5 oranges. How many pieces of fruit altogether?'
 When making money calculations, use whole dollar amounts, for example, 'The milk costs $3, the bread costs $3 and the bananas cost $4. So altogether, how much do we need to pay? If we pay with a $10 note, how much change will we get? What if we pay with a $20 note?'
3. Think about and discuss different ways of solving everyday number problems. For example, to solve 17 + 6 you might decide to:
 count up from 17 using two jumps of 3 (17… 20… 23!)
 break the 6 up into 3 and 3 to make a ‘friendly 20’, 17 + 3 = 20, then 20 + 3 = 23
 start with a known doubles fact of 6 + 6 = 12, then add 11 more to get 23.
Know that mistakes are a normal part of building mathematical understanding. Be curious about mistakes and see them as opportunities to learn. Take plenty of time to solve problems.
Success criteria
I can:
 think about what’s happening in a situation and explain how I might solve it
 use my knowledge of number and making calculations to work through everyday situations
 consider whether an answer seems correct by thinking carefully about the situation
 repeat the process of solving a problem if it doesn’t seem right.
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Teaching strategies
A collection of evidencebased 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.

Concrete, Representational, Abstract (CRA model)
The CRA model is a threephased 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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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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Feedback
It has been shown that good feedback can make a significant difference to a student’s future performance.
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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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Collaborative learning
For group work to be effective students need to be taught explicitly how to work together in different settings, such as pairs or larger groups, and they need to practise these skills.
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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.

Number books
Use various titles to explore everyday and imaginary situations involving number. Invite students to identify and pose number problems to model and solve.
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Authentic Problems: Bunches of Balloons
Use an authentic context of decorating the classroom to explore and model grouping 29 balloons.
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Understanding Australian coins
In this lesson students learn about Australian coins, their features, and their value.
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Paying It Forward Years F2
In this unit students develop understanding about the pros and cons of saving and spending and the skill of prioritising choices based on needs and wants.
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Meaning of multiplication symbols
Students use additive strategies to solve multiplication and division problems.
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Shared fruit
Use this task as a mathematical modelling opportunity to find an unknown number.
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Games on all fields
Use this challenging problem as an authentic opportunity to use counting strategies and mathematical modelling.
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