Planning tool
Year levels
Strands
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 partpartwhole 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 partpartwhole 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 Tshirts, 5 are red, the rest are white. How many white Tshirts 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, partpartwhole 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.
Students:
 partition numbers as a composition of other numbers
 use models to solve addition and subtraction problems
 interpret number problems to identify known and unknown parts
 recognise and explain the relationship between addition and subtraction using materials and representations.
Some students may:
 have difficulty in identifying the known and unknown numbers in a number story that involves addition and subtraction. Provide multiple exposures to number stories, using questioning and feedback to guide learning. Support learning through use of models.
 find it a challenge to read the questions written using the format 4 + ? = 10. Use materials and model how to read the equation. Use number talks to discuss approaches and develop student thinking.
 be able to solve addition or subtraction problems written as an expression such as 15 − 8 = or 3 + 12 = but not be able to provide the related addition or subtraction number facts. Provide models that show the numbers partitioned and make explicit the associated number facts.
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 figure out the missing number.
 We are learning that fact families can help to find missing numbers.
Why are we learning about this?
 An important area of maths learning is about finding missing or 'unknown' values.
What to do
1. Find the unknown value in this equation.
? – 7 = 14
 What is the missing or unknown number?
 Draw a picture to help find the missing value.
 Write the fact family from these clues.
 Write or tell a number story that uses these numbers to match the equation.
2. Can you write the equation as an addition problem?
 How are addition and subtraction similar?
3. Try writing your own problem for a family member to solve.
Success criteria
I can:
 solve addition and subtraction problems
 use number facts to work out the missing or unknown number
 explain how addition and subtraction are similar.
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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.

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 threephased 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.

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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The missing ones and tens
Solve addition and subtraction problems using groups of ten.
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Using one hand
Use this task for students to solve addition and subtraction problems to 20 by counting all the objects in their head.
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