Planning tool
Year levels
Strands
Expected level of development
Australian Curriculum Mathematics V9: AC9M5A01
Numeracy Progression: Multiplicative strategies: P7
At this level, students recognise and explain the connection between multiplication and division as inverse operations and use this and other multiplicative properties to develop families of number facts. They apply this knowledge to solve multiplicative numerical equations.
Make explicit that multiplication and division are closely related, that they are inverse operations. Demonstrate that understanding this connection can help students learn division facts. Use arrays to help students with multiplication facts, multiplicative properties and strengthen the connection between multiplication and division. Develop fact families for the different arrays.
Build arrays by connecting tens frames and use different counters to show ways to partition problems to illustrate the distributive property. For example, an array for 63 is 9 rows by 7 rows. The nine rows can be split into 7 and 2 using two differentcoloured counters before the multiplying begins. With the partition line in place, the array is the same as
(7 × 7) + (7 × 2).
Provide opportunities for students to apply multiplicative strategies to solve numerical equations that require them to multiply large numbers by onedigit and twodigit numbers and divide by singledigit numbers.
Teaching and learning summary:
 Make explicit that multiplication and division are closely related.
 Use arrays to help students with multiplication facts and multiplicative properties.
 Provide opportunities for students to apply multiplicative strategies to solve numerical equations.
Students:
 understand that multiplication and division are inverse operations
 describe and use the properties of multiplicative operations
 develop fact families
 solve multiplicative numerical equations.
Some students may:
 not be proficient at recalling multiplication facts. Arrays can be used for building multiplication facts in a meaningful way. Before drilling and memorising tables, it is helpful for students to understand how these facts are developed. Some students do not yet make connections between number facts in the same table and instead rely on memorising each of the facts. Supporting students to understand and apply the commutative property of multiplication may help these students.
 find division is the most challenging of the four operations to master. Typically, full understanding of division tends to occur much later than the other operations. Often students have fewer opportunities to use physical materials to develop their conceptual knowledge and instead jump into solving formal equations too early. These students typically have problems with explaining the inverse relationship between division and multiplication. To address this, use arrays to show the relationship using multiple examples. Use arrays as part of a number talk. For example, 3 × 5 = 15, or that 3 rows of 5 make 15, as can be represented by an array. Prompt students to look at the array in different ways to reveal the inverse, that is 15 ÷ 3 = 5 or 15 put into 3 rows makes 5 columns, or 5 in each row. Be mindful of the language used to describe arrays. Language plays an important role in being able to express the mathematical relationships. As students develop their conceptual knowledge, extend to large numbers and explore calculations such as 13 x 5 where the array can be split into useful chunks such as 10 and 3. This encourages students to use their known number facts to work out calculations. For example, 13 x 5 = (10 x 5) + (3 x 5). Use blank arrays for students to explore and represent calculations. The blank array helps students use other strategies, such as compensating, when carrying out multiplication. For example, 37 x 9, the student could choose to do 37 x 10 and then subtract the 37 x 1.
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 recognise the connection between multiplication and division.
Why are we learning about this?
 Knowing this relationship helps us to solve larger number problems.
What to do
Use your knowledge of fact families to complete the multiplication and division facts, filling in the missing numbers.
Success criteria
I can:
 develop fact families
 describe the relationship between multiplication and division.
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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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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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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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Spaced, interleaved and retrieval practice
These are three strategies that can be used to increase student retention and recall of their learning.
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Number Talks
An illustration of a teacher running a number talk with a lower primary class
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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.

Remainders game
Use this video to find out how to play a game which uses multiplication and division as inverse operations to solve problems.
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Factors fun
Use this video to find out how to play a game which reinforces division number facts.
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Compare the calculations
In this task, students put four multiplication problems and four division problems in order, from easiest to hardest, then justify their response.
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How do you do it?
In this task, students explain their mental calculation strategies and discuss the efficiency and effectiveness of using different strategies in different contexts.
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Productive thinking
This unit explores situations that involve solving numerical problems that draw on multiplicative thinking.
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Arrays, multiplication and division
This article explores how the array can be used as a thinking tool to help students develop an indepth understanding of multiplication and division.
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Multiplication and division: Content background
This guide provides background and context to help develop content knowledge for teaching students multiplication and division.
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Trying times
This activity focuses on using mental strategies to work out 15 times table.
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