Year 3 Mathematics · 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 combines equal groups and division shares or groups equally. Arrays and partitioning make the structure of a problem visible

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Learning goalsSay it simply

Multiplication combines equal groups and division shares or groups equally. Arrays and partitioning make the structure of a problem visible.

Learning routine: Represent → Partition → Calculate → Connect inverse → Explain

Success looks like

  • Use arrays
  • Partition multiplication
  • Model division
  • Use inverse facts
  • Explain strategies

Success criteria:

  • Use arrays
  • Partition multiplication
  • Model division
  • Use inverse facts
  • Explain strategies
Key conceptTeach from the board

Key idea: Multiplication combines equal groups and division shares or groups equally. Arrays and partitioning make the structure of a problem visible.

Learning routine: Represent → Partition → Calculate → Connect inverse → Explain

array
objects arranged in equal rows and columns
factor
a number multiplied by another number
quotient
the result of a division
Clean visual examplesOne-page board

Clean one-page examples

AC9M3N04 - Multiply and divide one- and two-digit numbers, representing problems using number sentences, diagrams and arrays, and using a variety of calculation strategies
Example 1

6 × 14 = 84 84 ÷ 6 = 14 84 ÷ 14 = 6

Example 2

4 × 18 75 ÷ 5 9 × 10 48 ÷ 4

Example 3

Partition 6 × 14 6 × 14 = 6 × 10 + 6 × 4 Partition 14 into 10 and 4, then combine 60 and 24. Read every label and identify what each quantity or feature represents. Describe the relationship shown by the model. Check that the conclusion answers the original question.

Example 4

Connect multiplication and division 84 6 14 6 × 14 = 84 84 ÷ 6 = 14 84 ÷ 14 = 6 The same array represents related multiplication and division facts. Apply the same relationship to the new context, then justify the answer using the labels and evidence shown.

Curriculum examplesCopied content

The content description and elaborations below show the curriculum ideas taught in this unit. Items marked as teaching context support lesson planning.

  • Content description: multiply and divide one- and two-digit numbers, representing problems using number sentences, diagrams and arrays, and using a variety of calculation strategies
  • E1: applying knowledge of numbers and the properties of operations using a variety of ways to represent multiplication or division number sentences; for example, using a Think Board to show different ways of visualising 8 \times 4, such as an array, a diagram and as a worded problem
  • E2: using part-part-whole and comparative models to visually represent multiplicative relationships and choosing whether to use multiplication or division to solve problems
  • E3: matching or creating a problem scenario or story that can be represented by a given number sentence involving multiplication and division; for example, using given number sentences to create worded problems for others to solve
  • E4: formulating connected multiplication and division expressions by representing situations from First Nations Australians’ cultural stories and dances about how they care for Country/Place such as turtle egg gathering using number sentences (teaching context)

Australian, Victorian and NSW alignment retained from the previous page

RegionCurriculumClosest mapping
AustraliaAustralian Curriculum v9.0AC9M3N04 — multiply and divide one- and two-digit numbers, representing problems using number sentences, diagrams and arrays, and using a variety of calculation strategies
VictoriaVictorian Curriculum F-10Year 3 Maths: closest match in Number. Use this page as a VIC-aligned practice and worksheet reference.
NSWNSW CurriculumStage 2 Maths: closest content focus for Multiply and divide one- and two-digit numbers, representing problems using number sentences, diagrams and arrays, and using a variety of calculation strategies and related outcomes.
Questions and answersWith answers
What is the big idea in this topic?
Multiplication combines equal groups and division shares or groups equally. Arrays and partitioning make the structure of a problem visible.
What routine should I use?
Represent → Partition → Calculate → Connect inverse → Explain
How do I know I am ready to move on?
You can use arrays, partition multiplication, model division, use inverse facts, explain strategies and explain how your model or calculation supports the answer.
Practice and reviewReady for practice
  • Unequal groups — Multiplication and equal sharing require equal groups.
  • Partitioning only one factor incorrectly — Keep one factor fixed and split the other into useful parts.
  • Multiplication and division disconnected — Use related facts to check answers.

  1. Solve 52 ÷ 4 using a diagram, sharing model or known facts.

  2. A student says 3 groups of 14 is 17 because 3 + 14 = 17. Explain the operation error.

Review hint: Follow the routine “Represent → Partition → Calculate → Connect inverse → Explain” and use the worked model to check whether your answer is reasonable.

Curriculum alignmentStart here

Multiplication combines equal groups and division shares or groups equally. Arrays and partitioning make the structure of a problem visible.

Learning routine: Represent → Partition → Calculate → Connect inverse → Explain

Success looks like

  • Use arrays
  • Partition multiplication
  • Model division
  • Use inverse facts
  • Explain strategies

Success criteria:

  • Use arrays
  • Partition multiplication
  • Model division
  • Use inverse facts
  • Explain strategies
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