Planning tool
Year levels
Strands
Expected level of development
Australian Curriculum Mathematics V9: AC9M6A02
Numeracy Progression: Additive strategies: P9, Multiplicative strategies: P9, Number patterns and algebraic thinking: P5
At this level, students find unknown quantities in numerical equations involving a combination of operations.
Provide examples of number sentences that include the use of brackets and the four operations. Invite students to work out possible answers to discuss and establish the need for an agreed set of rules.
Use worked examples to make explicit the correct order of operations. Provide opportunities to find unknown values in numerical equations that involve combinations of mathematical operations and numbers. Include number sentences for students to create their own equations.
Teaching and learning summary:
 Investigate the use of brackets and the order of operations to solve number sentences.
 Make explicit the need for an agreed set of rules to complete multiple operations within the same number sentence.
 Construct equivalent number sentences involving brackets and the combination of four operations.
Students:
 solve numerical equations involving one or more operations following conventions of order of operations
 use equivalence in number sentences to solve problems involving numerical equations.
Some students may simply answer the equation starting from left to right.
To avoid confusion and to ensure that everyone gets the same result, a set of rules has been developed:
 First, work out calculations in brackets.
 Second, calculate any multiplication or division (left to right).
 Third, calculate any addition or subtraction (left to right).
Use worked examples to demonstrate the possible variations in answers compared with using the order of operations.
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 about using the order of operations.
Why are we learning about this?
 To solve number sentences that involve all the operations and brackets, we need to have an agreed order to solve the problem.
What to do
 Open this web page, Whole numbers with all four operations. Use your knowledge of the order of operations and the use of brackets to answer the questions and check your answers.
 In this activity, there are four groups of numbers. Each group has four digits and a target number. The aim is to make the target using all four digits only once, and any of the operations or brackets. You can change the order of the digits.
Success criteria
I can:
 describe patterns in arrangements of numbers
 write a rule to describe a repeating pattern to solve problems.
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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.

Structuring lessons
A welldeveloped lesson structure is important for both teacher and students.
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Worked examples
A worked example is not just a preworked question that is given to the students. There are several types of worked examples and ways of using them.
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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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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.

The order of operations
In this unit, students develop an understanding of number operations and recognise that there is a need for rules to guide us in the order in which we carry out these operations.
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Whole numbers with all four operations
Find student resources and content information about the order of operations.
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Which wheels where?
This is a level 4 algebra link activity from the Figure It Out series. It is focused on using a table to find a linear relationship. A PDF of the student activity is included.
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Solving multistep equations
In this unit, students read, write, and solve multistep equations that include variables that stand for fixed values. Importantly, students also come to see that a variable can be interpreted in other ways, including representing a quantity that varies in relation to another quantity.
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Four fours challenge
This unit provides an opportunity for students to use all the arithmetic operations, investigate the effect of combinations of arithmetic operations, communicate mathematical thinking using brackets and other mathematical signs and symbols correctly, and use their calculators correctly.
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