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.

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

Students should be comfortable reading and representing whole numbers, using place value, and explaining simple addition, subtraction or equal-group relationships from earlier years. Begin with a short concrete or visual recall task before moving to Multiplication and Division Strategies.

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

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.

• 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. What is 6 × 14?

   • 84
   • 74
   • 64
   • 90

2. Complete the partition.

   Prompt: 6 × 14 = 6 × 10 + 6 × □

3. Which division fact is related to 7 × 12 = 84?

   • 84 ÷ 7 = 12
   • 84 ÷ 12 = 8
   • 7 ÷ 84 = 12
   • 84 + 7 = 12

4. Draw or describe an array for 7 × 13 and split it into useful parts.

5. Match each calculation to its answer.

   Match: 4 × 18 • 75 ÷ 5 • 96 ÷ 8 ↔ 12 • 15 • 72

6. Complete the related fact.

   Prompt: 8 × 11 = 88, so 88 ÷ 8 = □

1. Solve 9 × 16 in two ways and explain which strategy is more efficient.

2. Create a multiplication story and two matching division stories for the fact family 6, 15 and 90.

Explain the reasoning, not only the final answer.

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.

• I can use arrays.
• I can partition multiplication.
• I can model division.
• I can use inverse facts.
• I can explain strategies.

Quick check: Solve 6 × 14 by partitioning. • What division fact matches 7 × 12 = 84? • Represent 52 ÷ 4.

Read the topic guide and use the teacher slide for instruction. Students can then use the worksheet for written work, open Practice for supported feedback, or take the Test when they are ready.

Use reliable, community-approved sources and identify the specific Nation, People or community where the source does. Do not present diverse First Nations knowledges as one generic tradition. Follow local cultural and intellectual property protocols before reproducing cultural material or inviting community participation.

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

• Australian Curriculum Version 9.0 — ACARA
• Victorian Curriculum — VCAA
• NSW Curriculum — NESA

Official curriculum sites are the source of record.

• AC9M3N03 — Add and Subtract with Place Value
• AC9M3N05 — Estimating Quantities and Answers
• All Year 3 Mathematics topics

Curriculum equivalents for Multiply and divide one- and two-digit numbers, representing problems using...

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

These references identify matching or closely related learning. Curriculum sequence, terminology and depth vary, so teachers should use the mapped skill and lesson difficulty to confirm suitability.

Australian Curriculum v9.0 is the canonical source for this SkillrHub lesson. Victoria and NSW entries name the closest published state codes or outcomes; international entries are planning references rather than claims of identical curricula.