Planning tool
Year levels
Strands
Expected level of development
Australian Curriculum Mathematics V9: AC9M2N05, AC9M2N06
Numeracy Progression: Multiplicative strategies: P5, Additive strategies: P7, Understanding money: P3
At this level, students begin to explore multiplication and realise that it can be represented in many ways.
Provide opportunities for students to explore multiplication and multiplicative thinking using physical and virtual materials. Make explicit that there are three distinct ways students can look at multiplication. One way is as repeated addition, another is as a collection of groups and it also can be viewed as an array – a collection arranged in rows and columns.
Provide opportunities for students to explore and solve divisionrelated problems. Use number talks to demonstrate that a set can be divided into equal groups using partitive division (shared between) and quotative division (how many sets of). Discuss situations where there can sometimes be a remainder, for example, when dividing the class into different sized groups.
Use different forms of representation such as arrays, bar models, number lines and thinkboards to record multiplication and division problems.
Teaching and learning summary:
 Represent multiplication and division problems using physical and virtual materials.
 Make explicit various strategies to solve multiplication and division problems.
 Encourage use of different forms of representation.
Students:
 recall addition facts
 arrange a collection into equal groups
 use increasingly sophisticated skip counting and other multiplicative strategies to find the total number represented in an array
 represent multiplication as repeated addition
 link multiplication to groups of a collection.
Some students may:
 be able to say the answer to a mathematical equation such as 5 x 4 = 20, but not be able to explain what it means or represent the equation. Most difficulties occur when students learn procedures and rules by rote and/or by using abstract symbols without understanding their meaning. To overcome this, give students opportunities to use physical or representative models such as arrays to help them recognise the structure of the problem and promote the use of mathematical language such as ‘groups of’ or ‘shared between’.
For further information refer to Emphasise the usefulness of multiplication.
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 arrange a collection into an array to make it easier to count.
 We are learning to skip count by twos, fives and tens.
Why are we learning about this?
 We build number sense when we learn to count the same number of items in different ways.
What to do
 Make a pile of 20 buttons. Find some different ways to organise the collection to make it easy to count, for example, try putting them in pairs.
 Draw some of the different ways you arranged your collection. Can you write a number sentence to go with each drawing?
Success criteria
I can:
 rearrange a collection to make it easy to count.
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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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Classroom talks
Classroom talks enable students to develop language, build mathematical thinking skills and create mathematical meaning through collaborative conversations.
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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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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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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 array
Use an arraybuilding tool to help solve multiplications by exploring strategies to break up multiplications.
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Multiplication: reSolve fruit shop
Students use strategies such as skip counting, repeated addition and partitioning the array into smaller parts. They investigate how some numbers can be represented as an array in different ways.
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reSolve fruit shop 2
This video supports students to explore and record different ways that lemons could be arranged in arrays for the fruit shop.
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reSolve: Multiplication – Making robots
Students explore the total number of different robots that can be made using three heads, three bodies and three feet. The students represent the different combinations for the robots as an array.
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Arrays hooray
In this unit students are given the opportunity to explore multiplication concepts using arrays.
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reSolve: Authentic Problems: Bunches of Balloons
In this lesson sequence students use a variety of processes associated with multiplication and division.
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How many clumps?
Use this lesson to connect division and multiplication using partpartwhole terms.
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Multiplication stories
In this unit students explore the different situation types to which multiplication can be applied.
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Table time
Students look for patterns in a table and apply multiplicative thinking to solve simple problems.
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Related divisors
Support students to derive new division facts from known facts in a measurement situation.
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Assessment

Assessment task: Year 2 Thinkboard Multiplication
Use this task to assess a student’s understanding of properties of multiplication and writing a related number story to match an equation.
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Difficulty relating a times table fact to a model
Arrays give students a visual representation that can be used to explore multiplication concepts.
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Multiplication as a binary operation
The following diagnostic questions indicate students’ understanding of, and ability to apply, multiplication and division to situations that involve equal sets.
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