What students learn in AC9M8N04
This unit helps students build a clear, usable understanding of The 4 operations with integers and with rational numbers, choosing.... 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: use the 4 operations with integers and with rational numbers, choosing and using efficient strategies and digital tools where appropriate.
- Use concrete examples, pictures, oral explanation and short written responses before moving to independent practice.
- using patterns to assist in establishing the rules for the multiplication and division of integers applying and explaining efficient strategies such as using the commutative or associative property for regrouping, partitioning, place value, patterning, multiplication or division facts to solve problems involving positive and negative integers, fractions and decimals
- 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: use the 4 operations with integers and with rational numbers, choosing and using efficient strategies and digital tools where appropriate
- E1: using patterns to assist in establishing the rules for the multiplication and division of integers
- E2: applying and explaining efficient strategies such as using the commutative or associative property for regrouping, partitioning, place value, patterning, multiplication or division facts to solve problems involving positive and negative integers, fractions and decimals
- E3: recognising the effect of sign in the multiplication of integers; for example, (-1)^4\;=\;1 and (-1)^5\;= -1
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
AC9M8N04 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 | AC9M8N04 — use the 4 operations with integers and with rational numbers, choosing and using efficient strategies and digital tools where appropriate |
| Victoria | Victorian Curriculum F-10 | Year 8 Maths: closest match in Number. Use this page as a VIC-aligned practice and worksheet reference. |
| NSW | NSW Curriculum | Stage 4 Maths: closest content focus for The 4 operations with integers and with rational numbers, choosing... and related outcomes. |
| United States | Common Core / NGSS | Grade 8 Common Core Mathematics/ELA closest topic match for The 4 operations with integers and with rational numbers, choosing.... |
| England / UK | National Curriculum | Key Stage 3 / Year 8: closest programme-of-study match for The 4 operations with integers and with rational numbers, choosing.... |
| Canada | Provincial and territory curricula | Grade 8 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 4 Maths: closest achievement-objective topic for The 4 operations with integers and with rational numbers, choosing.... |
| India | NCERT / CBSE | Class 8 closest NCERT/CBSE topic match for The 4 operations with integers and with rational numbers, choosing.... |