AC9M5A01 • Year 5 Maths

AC9M5A01: Recognise and explain the connection between multiplication and division as inverse operations and use this to develop families of number facts

recognise and explain the connection between multiplication and division as inverse operations and use this to develop families of number facts

Topic GuideClassroom ViewWorksheetPracticeTest
What students learn in AC9M5A01

Students use one multiplicative relationship to generate related multiplication and division equations, solve unknowns and extend facts by scaling factors and products.

Multiplication combines equal factors and division undoes that relationship by finding a missing factor or number of groups.

The product is the whole and the factors are related parts of the multiplicative structure. Division checks multiplication and solves missing-factor problems.

Scaling one factor by 10 scales the product by 10. The related division facts change consistently because the relationship is preserved.

Learning routine: Represent → Reason → Calculate → Interpret → Verify

Success looks like

  • Represent accurately
  • Explain the relationship
  • Choose a suitable method or unit
  • Apply in context
  • Check and justify
Key vocabulary
inverse operations
operations that undo one another
fact family
set of related equations using the same values
factor
number multiplied to form a product
Concept models and worked thinking

Build a fact family from 8 × 14 = 112

relationshipequationmultiply8 × 14 = 112commute14 × 8 = 112divide by first factor112 ÷ 8 = 14divide by second factor112 ÷ 14 = 8

The product is the whole and the factors are related parts of the multiplicative structure. Division checks multiplication and solves missing-factor problems.

  1. Read every label and identify the quantities, parts or evidence.
  2. Explain the relationship shown—not just the final answer.
  3. Check the conclusion against the original question and units.

Scale a fact family while preserving structure

8 × 14 = 112→80 × 14 = 1 120→1 120 ÷ 80 = 14→1 120 ÷ 14 = 80

Scaling one factor by 10 scales the product by 10. The related division facts change consistently because the relationship is preserved.

Now transfer the same relationship to a new situation and justify the result with precise vocabulary.

Curriculum coverage and elaborations

Content description: recognise and explain the connection between multiplication and division as inverse operations and use this to develop families of number facts.

  • E1: using materials or diagrams to develop and explain division strategies, such as halving, using the inverse relationship to turn division into a multiplication
  • E2: using arrays, multiplication tables, and physical and virtual materials to develop families of facts; for example, 3 \times 4 = 12, 4 \times 3 = 12, 12 ÷ 3 = 4 and 12 ÷ 4 = 3
  • E3: demonstrating multiplicative partitioning using materials, diagrams or arrays and recording 2 multiplication and 2 division facts for each grouping; 4 \times 6 = 24, 6 \times 4 = 24, 24 ÷ 4 = 6 and 24 ÷ 6 = 4; explaining how each is different from and connected to groups in the materials, diagrams or arrays
  • E4: using materials, diagrams or arrays to recognise and explain the inverse relationship between multiplication and division; for example, solving 240 ÷ 20 = \square by thinking 20\times\square = 240; using the inverse to make calculations easier; for example, solving 17\times\square= 221 using division, \square = 221 ÷ 17
Guided learning activities

1. Model and annotate

Represent multiplication and division as inverse operations and label the relationship or measurement being used.

relationshipequationmultiply8 × 14 = 112commute14 × 8 = 112divide by first factor112 ÷ 8 = 14divide by second factor112 ÷ 14 = 8

2. Strategy or instrument comparison

Compare two valid methods or tools and justify which better suits the numbers, attribute or purpose.

8 × 14 = 112→80 × 14 = 1 120→1 120 ÷ 80 = 14→1 120 ÷ 14 = 80

3. Transfer and verify

Apply the concept to an unfamiliar example, state units or conditions and verify independently.

Write four facts for 8, 14 and 112.Use inverse to check 936 ÷ 8.Scale 7 × 6 = 42 by 10.Solve 15 × □ = 180.
Revision Notes

Core idea: Multiplication combines equal factors and division undoes that relationship by finding a missing factor or number of groups.

Remember

  • Represent accurately
  • Explain the relationship
  • Choose a suitable method or unit
  • Apply in context
  • Check and justify

Important questions

  • Write four facts for 8, 14 and 112. Explain using the model or evidence above.
  • Use inverse to check 936 ÷ 8. Explain using the model or evidence above.
  • Scale 7 × 6 = 42 by 10. Explain using the model or evidence above.
  • Solve 15 × □ = 180. Explain using the model or evidence above.
  • Explain why division is not commutative. Explain using the model or evidence above.
How to use this unit

Learn from the Topic Guide and fixed Teacher Slides, complete the Practice Sheet, use Practice for supported feedback, then take the Test when ready.

AC9M5A01 Teacher Slides

Project the fixed branded slide deck one slide at a time.

Open Classroom View
Common misconceptions
  • Division fact uses a different product — Related facts must preserve the same whole.
  • Every order change is allowed — Multiplication is commutative; division generally is not.
  • Scaling factor but not product — If one factor changes, the product changes proportionally.
  • Fact recalled without explanation — Connect the equation to groups, arrays or missing factors.
🎥 Optional Video Lesson

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  • Try the examples yourself.
  • Return to the SkillrHub lesson before continuing.
Recommended: Basic Division

Math Antics — Relate equal-group division to multiplication.

As you watch: How can a multiplication fact check a division answer?

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Try it: Use 7 × 8 = 56 to write two multiplication and two division facts.

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Curriculum equivalents: Victoria, NSW and international

Curriculum equivalents for And explain the connection between multiplication and division as inverse...

Mapped skill: recognise and explain the connection between multiplication and division as inverse operations and use this to develop families of number facts

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.

RegionCurriculum frameworkClosest level or code
AustraliaAustralian Curriculum v9.0AC9M5A01 · Year 5
VictoriaVictorian Curriculum F–10 Version 2.0 — MathematicsVC2M5A01 · Level 5
New South WalesNSW Mathematics K–10 Syllabus (2022)MA3-MR-02 · Stage 3
United States (USA)Common Core State Standards for MathematicsGrade 5
Canada (Ontario)Ontario Curriculum — MathematicsGrade 5
United Kingdom (England)National Curriculum in England — MathematicsYear 6, Key Stage 2
IndiaNCERT / CBSE — MathematicsClass 5

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.

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Topic reference: AC9M5A01 — AC9M5A01: Recognise and explain the connection between multiplication and division as inverse operations and use this to develop families of number facts

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Official curriculum reference

Australian Curriculum Version 9.0

Related Year 5 Maths topics

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Depth checkpoint

Use one multiplication fact to generate both related division facts. Explain which number is the total, which is the group size, and which is the number of groups; then test the family in a new context.