What students learn in AC9M5N02
This unit helps students build a clear, usable understanding of Express natural numbers as products of their factors, recognise multiples.... 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: express natural numbers as products of their factors, recognise multiples and determine if one number is divisible by another.
- Use concrete examples, pictures, oral explanation and short written responses before moving to independent practice.
- using a certain number of blocks to form different rectangles and using these to list all possible factors for that number; for example, 12 blocks can form the following rectangles: 1 \times 12, 2 \times 6, and 3 \times 4 researching divisibility tests and explaining each rule using materials; for example, using base-10 blocks to test if numbers are divisible by 2, 5 and 10
- 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: express natural numbers as products of their factors, recognise multiples and determine if one number is divisible by another
- E1: using a certain number of blocks to form different rectangles and using these to list all possible factors for that number; for example, 12 blocks can form the following rectangles: 1 \times 12, 2 \times 6, and 3 \times 4
- E2: researching divisibility tests and explaining each rule using materials; for example, using base-10 blocks to test if numbers are divisible by 2, 5 and 10
- E3: using divisibility tests to determine if larger numbers are multiples of one-digit numbers; for example, testing if 89 472 is divisible by 3 using 8 + 9 + 4 + 7 + 2=30 as 30 is divisible by 3 then 89 472 is a multiple of 3
- E4: demonstrating and reasoning that all multiples can be formed by combining or regrouping; for example, multiples of 7 can be formed by combining a multiple of 2 with the corresponding multiple of 5; 3 \times 7 = 3 \times 2 + 3 \times 5, and 4 \times 7 = 4 \times 2 + 4 \times 5
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
AC9M5N02 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 | AC9M5N02 — express natural numbers as products of their factors, recognise multiples and determine if one number is divisible by another |
| Victoria | Victorian Curriculum F-10 | Year 5 Maths: closest match in Number. Use this page as a VIC-aligned practice and worksheet reference. |
| NSW | NSW Curriculum | Stage 3 Maths: closest content focus for Express natural numbers as products of their factors, recognise multiples... and related outcomes. |
| United States | Common Core / NGSS | Grade 5 Common Core Mathematics/ELA closest topic match for Express natural numbers as products of their factors, recognise multiples.... |
| England / UK | National Curriculum | Key Stage 2 / Year 5: closest programme-of-study match for Express natural numbers as products of their factors, recognise multiples.... |
| 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 Express natural numbers as products of their factors, recognise multiples.... |
| India | NCERT / CBSE | Class 5 closest NCERT/CBSE topic match for Express natural numbers as products of their factors, recognise multiples.... |