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# Teaching and Learning SequenceMultiplicative Thinking (1 - 6) Key Ideas

Students are first introduced to multiplication at the year 2 level as repeated addition and equal groups. This is usually done through skip counting where students learn to add multiples of the same number either through a repeated sequence or along a number line.

When explicitly linking skip counting to multiplication however, we want to focus on a particular number of groups rather than continuing the sequence indefinitely. This gets the students to focus on the product of the repeated addition as well as the two factors required to acquire that product. For example, if we are skip counting or repeatedly addition the number 2, five times. This can be expressed as: Activity Ideas

Activity Ideas

• Division as partition

• Division as quotition

• Sharing with remainders

• Multiplication as ‘groups of’

*See Instructions for full details

Instructions

CRA Board

## Arrays

Key Ideas

Multiplication and division using arrays should be consolidated by year 3 and once students have had practise with multiplication using repeated addition and division using sharing.

Arrays are a visual model used to represent multiplication and division using rows and columns. Their use in multiplication and division is extremely important because they move students from thinking additively to thinking multiplicatively.

To make this additive to multiplicative process easier, arrays should be introduced in three different ways:

1. As discrete arrays

2. As grid arrays

3. As open arrays 1. Discrete Arrays

When first learning to multiply and divide using arrays, the discrete array should always be practised first. This is because it provides a good scaffold between students' additive reasoning of multiplication or the groups of model and the factor-factor-product model.

With the discrete arrays, students can use counters to create their groups, as rows, and repeat those groups as their columns (and vice versa). They can then draw a representation of their array using dots to reinforce their thinking. The whole premise behind discrete arrays is to allow the students to practise moving their thinking from an additive model of multiplication to a multiplicative model.

2. Grid Arrays

Once students have had practice with multiplication using discrete arrays, they can then move to a grid array.

The grid array still provides the visualisation of the total product in the multiplication, however, it allows students to begin seeing multiplication as an area model. This is because students can still count or skip count to find the product of the multiplication using the squares in the grid, in order to check their methods or solutions.

3. Open Arrays

Open arrays should be introduced to students once they have shown proficiency in multiplying and dividing using the discrete arrays and then the grid arrays. This is because the open array relies on a student's knowledge of multiplication facts as the scaffold of the counters and grid is no longer available to them.

The open array is the preferred model of multiplication and division due to its efficiency and versatility, particularly with larger numbers. It is also a great way of representing both multiplication and division and linking them directly to their various abstract methods.

Activity Ideas

Activity Ideas

• Multiplication facts

• Division facts

• Inverse operations

• Strategy

Year 3

AC9M3N04

Year 4

AC9M4N06

Year 5

Instructions

Empty game boards

## Activity Videos

#### This video looks at the various strategies involved with the multiplication table and how these can be used to help students better understand, and remember, their multiplication facts.

Games and Activities

### Five Sweets Per Packet

Year 1

AC9MFA01

recognise, copy and continue repeating patterns represented in different ways

AC9M1A02

recognise, continue and create repeating patterns with numbers, symbols, shapes and objects, identifying the repeating unit

Year 2

AC9M2N05

multiply and divide by one-digit numbers using repeated addition, equal grouping, arrays, and partitioning to support a variety of calculation strategies

### Number Trails

• Multiplication

• Division

• Division using repeated subtraction

Year 2

AC9M2N05

multiply and divide by one-digit numbers using repeated addition, equal grouping, arrays, and partitioning to support a variety of calculation strategies

*NOTE: This activity can be differentiated to include similar Number and Algebra content descriptors from

F - 6

### Multiplication Toss

• Multiplication using arrays

• Multiplying using the commutative property

• Multiplying using the distributive property

Year 2

AC9M2N05

multiply and divide by one-digit numbers using repeated addition, equal grouping, arrays, and partitioning to support a variety of calculation strategies

Year 3

AC9M3N04

multiply and divide one- and two-digit numbers, representing problems using number sentences, diagrams, and arrays, and using a variety of calculation strategies

• Multiplication using efficient strategies

• Multiplying using the commutative property

• Multiplying using the distributive property

Year 2

AC9M2N05

multiply and divide by one-digit numbers using repeated addition, equal grouping, arrays, and partitioning to support a variety of calculation strategies

Year 3

AC9M3N04

multiply and divide one- and two-digit numbers, representing problems using number sentences, diagrams, and arrays, and using a variety of calculation strategies

*NOTE: This activity can be differentiated to include similar Number and Algebra content descriptors from

F - 6.

### Partially Covered Arrays

• Multiplication using arrays

• Multiplying using the commutative property

Year 2

AC9M2N05

multiply and divide by one-digit numbers using repeated addition, equal grouping, arrays, and partitioning to support a variety of calculation strategies

Year 3

AC9M3N04

multiply and divide one- and two-digit numbers, representing problems using number sentences, diagrams, and arrays, and using a variety of calculation strategies

Year 4

AC9M4A02

recall and demonstrate proficiency with multiplication facts up to 10 x 10 and related division facts; extend and apply facts to develop efficient mental strategies for computation with larger numbers without a calculator

*NOTE: This activity can be differentiated to include similar Number and Algebra content descriptors from

F - 6.

### Multo

• Multiplication facts

• Factors

Year 2

AC9M2N05

multiply and divide by one-digit numbers using repeated addition, equal grouping, arrays, and partitioning to support a variety of calculation strategies

Year 3

AC9M3N04

multiply and divide one- and two-digit numbers, representing problems using number sentences, diagrams, and arrays, and using a variety of calculation strategies

Year 4

AC9M4A02

recall and demonstrate proficiency with multiplication facts up to 10 x 10 and related division facts; extend and apply facts to develop efficient mental strategies for computation with larger numbers without a calculator

Year 5

AC9M5N010

create and use algorithms involving a sequence of steps and decisions and digital tools to experiment with factors, multiples, and divisibility; identify, interpret, and describe emerging patterns

*NOTE: This activity can be differentiated to include similar Number and Algebra content descriptors from

F - 6.

### Factor 24

• Multiplication Facts

• Multiplying using the distributive strategy

• Factors

• Order of operations

Year 2

AC9M2N05

multiply and divide by one-digit numbers using repeated addition, equal grouping, arrays, and partitioning to support a variety of calculation strategies

Year 3

AC9M3N04

multiply and divide one- and two-digit numbers, representing problems using number sentences, diagrams, and arrays, and using a variety of calculation strategies

Year 4

AC9M4A02

recall and demonstrate proficiency with multiplication facts up to 10 x 10 and related division facts; extend and apply facts to develop efficient mental strategies for computation with larger numbers without a calculator

Year 5

AC9M5N02

express natural numbers as products of their factors, recognise multiples and determine if one number is divisible by another

Year 6

AC9M6A02

find unknown values in numerical equations involving brackets and combinations of arithmetic operations, using the properties of numbers and operations

### Multiply it up

• Recalling multiplication facts to 10 x 10

Year 4

AC9M4A02

recall and demonstrate proficiency with multiplication facts up to 10 x 10 and related division facts; extend and apply facts to develop efficient mental strategies for computation with larger numbers without a calculator

*NOTE: This activity can be differentiated to include similar Number and Algebra content descriptors from

F - 6.

### Four in a Row

• Multiplication Facts

• Multiplying using the distributive strategy

• Factors

• Order of operations

Year 3

AC9M3N04

multiply and divide one- and two-digit numbers, representing problems using number sentences, diagrams, and arrays, and using a variety of calculation strategies

Year 4

AC9M4A02

recall and demonstrate proficiency with multiplication facts up to 10 x 10 and related division facts; extend and apply facts to develop efficient mental strategies for computation with larger numbers without a calculator

Year 5

AC9M5N010

create and use algorithms involving a sequence of steps and decisions and digital tools to experiment with factors, multiples and divisibility; identify, interpret and describe emerging patterns

Year 6

AC9M6A02

find unknown values in numerical equations involving brackets and combinations of arithmetic operations, using the properties of numbers and operations

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