What students learn in AC9M5A01
This unit helps students build a clear, usable understanding of And explain the connection between multiplication and division as inverse.... The goal is not to memorise one answer pattern. Students should be able to explain the idea, recognise it in a new example and apply it in a short practice or worksheet task.
- Start with the main idea: recognise and explain the connection between multiplication and division as inverse operations and use this to develop families of number facts.
- Use concrete examples, pictures, oral explanation and short written responses before moving to independent practice.
- using materials or diagrams to develop and explain division strategies, such as halving, using the inverse relationship to turn division into a multiplication 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
- Finish with mixed questions so students must choose the correct strategy rather than copy the last example.
Curriculum coverage and elaborations
The content description and elaborations below show the curriculum ideas taught in this unit. Items marked as teaching context support lesson planning but may not appear in the initial eight-question activity.
- 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
How to use this unit
Read the topic guide, use the teacher slide for instruction, then complete the Worksheet, Practice and Test. These three activities use the same eight-question unit bank.
Teacher resource
AC9M5A01 teacher slide
Use this one-page PDF to introduce the key idea, vocabulary and teaching sequence before students begin the activities.
Open teacher slide (PDF)Common mistakes to watch for
- Rushing to a rule before checking the concrete model, drawing or number sentence.
- Using the correct answer once but not being able to explain why it works.
- Mixing up similar vocabulary such as more/less, before/after, longer/shorter or equal groups/sharing.
International curriculum mapping
This table gives closest-topic mapping for search and planning. The Australian Curriculum code is exact; overseas entries are broad equivalents because each jurisdiction structures outcomes differently.
| Region | Curriculum | Closest mapping |
|---|---|---|
| Australia | Australian Curriculum v9.0 | AC9M5A01 — recognise and explain the connection between multiplication and division as inverse operations and use this to develop families of number facts |
| Victoria | Victorian Curriculum F-10 | Year 5 Maths: closest match in Algebra. Use this page as a VIC-aligned practice and worksheet reference. |
| NSW | NSW Curriculum | Stage 3 Maths: closest content focus for And explain the connection between multiplication and division as inverse... and related outcomes. |
| United States | Common Core / NGSS | Grade 5 Common Core Mathematics/ELA closest topic match for And explain the connection between multiplication and division as inverse.... |
| England / UK | National Curriculum | Key Stage 2 / Year 5: closest programme-of-study match for And explain the connection between multiplication and division as inverse.... |
| Canada | Provincial and territory curricula | Grade 5 closest topic match. Canada varies by province, so use this as a broad Ontario/BC-style learning outcome reference. |
| New Zealand | New Zealand Curriculum | Level 3 Maths: closest achievement-objective topic for And explain the connection between multiplication and division as inverse.... |
| India | NCERT / CBSE | Class 5 closest NCERT/CBSE topic match for And explain the connection between multiplication and division as inverse.... |