Expected level of development
Australian Curriculum Mathematics V9: AC9M3A01
Numeracy Progression: Additive strategies: P6, Multiplicative strategies: P4
At this level, students recognise and explain the connection between addition and subtraction. They use partitioning of numbers to find unknown values in number sentences involving addition and subtraction.
Provide multiple opportunities to partition numbers, developing part-part-whole relationships. This allows students to think of a number as a composition of other numbers. For addition and subtraction, this includes knowing the parts and being able to find the whole, knowing the whole and finding the parts, knowing a part and a whole and finding the missing part. Students who develop a deep understanding of numbers will be able to partition numbers in flexible ways.
Develop students’ algebraic thinking using number sentences of addition and subtraction problems. Use part-part-whole diagrams or bar models to identify the known numbers. Discuss what is ‘unknown’ and ways to calculate the unknown. Discuss different ways of seeing a problem, for example: There are 12 T-shirts, 5 are red, the rest are white. How many white T-shirts are there? This problem can be written as 12 − 5 = ? or
5 + ? =14. Make explicit that we can think of it as subtraction or unknown addend addition.
Use maths games that draw on additive thinking and use of number facts including strategy games to reach a target number or continue a pattern.
Teaching and learning summary:
- Partition numbers using materials, part-part-whole diagrams or bar models, recording addition and subtraction facts for each representation.
- Explain how each fact is connected to the materials, diagrams or models.
- Model how to use the inverse relationship between addition and subtraction to find unknown values with representations as well as a calculator.
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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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Explicit teaching
Explicit teaching is about making the learning intentions and success criteria clear, with the teacher using examples and working though problems, setting relevant learning tasks and checking student understanding and providing feedback.
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Concrete, Representational, Abstract (CRA)
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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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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Using games and storybooks
Games and storybooks are great resources to use in the classroom and are engaging for students.
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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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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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Strike it out
This game offers an engaging context for students to recall addition and subtraction facts and use strategic thinking.
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Are you well balanced?
This problem can be used to introduce the notion of balancing an equation using additive thinking.
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Number balance
Students use their knowledge of number bonds to develop their algebraic reasoning skills.
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Equivalent pairs
Use this task to develop students’ understanding of equivalence and to practise number bonds.
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Interactive balance
Use this task to explore equivalence using an interactive balance and online calculator.
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One big triangle
This problem is useful for consolidating number bonds to 10 and the corresponding subtraction facts.
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What was in the box?
Use this task to practise addition and subtraction using a type of number machine.
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Find the difference
This problem is a challenging way of practising subtraction at the same time as being logical about arranging the numbers.
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Number families and relationships
Use this unit to develop an understanding of the operations of addition and subtraction and how they relate to one another.
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Missing addends to ten
Students apply their knowledge of addition facts to ten by recalling the missing addend in a sum to ten.
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Easy nines
Students solve nine time tables problems.
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