What students learn in AC9M6A02
This unit helps students build a clear, usable understanding of Find unknown values in numerical equations involving brackets and combinations.... 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: find unknown values in numerical equations involving brackets and combinations of arithmetic operations, using the properties of numbers and operations.
- Use concrete examples, pictures, oral explanation and short written responses before moving to independent practice.
- using brackets and the order of operations to write number sentences and appreciating the need for an agreed set of rules to complete multiple operations within the same number sentence; for example, for 40 ÷ 2 \times (4 + 6) = \square, you solve what is in the brackets first then complete the number sentence from left to right as there is no hierarchy between division and multiplication constructing equivalent number sentences involving brackets and combinations of the 4 operations; explaining the need to have shared agreement on the order of operations when solving problems involving more than one operation to have unique solutions
- 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: find unknown values in numerical equations involving brackets and combinations of arithmetic operations, using the properties of numbers and operations
- E1: using brackets and the order of operations to write number sentences and appreciating the need for an agreed set of rules to complete multiple operations within the same number sentence; for example, for 40 ÷ 2 \times (4 + 6) = \square, you solve what is in the brackets first then complete the number sentence from left to right as there is no hierarchy between division and multiplication
- E2: constructing equivalent number sentences involving brackets and combinations of the 4 operations; explaining the need to have shared agreement on the order of operations when solving problems involving more than one operation to have unique solutions
- E3: finding pairs of unknown values in numerical equations that make the equation hold true; for example, listing possible combinations of natural numbers that make this statement true: 6+4\times8\;=\;6\times\bigtriangleup+\square
- E4: applying knowledge of inverse operations and number properties to create equivalent number sentences; removing one of the numbers and replacing it with a symbol, then swapping with a classmate to find the unknown values
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
AC9M6A02 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 | AC9M6A02 — find unknown values in numerical equations involving brackets and combinations of arithmetic operations, using the properties of numbers and operations |
| Victoria | Victorian Curriculum F-10 | Year 6 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 Find unknown values in numerical equations involving brackets and combinations... and related outcomes. |
| United States | Common Core / NGSS | Grade 6 Common Core Mathematics/ELA closest topic match for Find unknown values in numerical equations involving brackets and combinations.... |
| England / UK | National Curriculum | Key Stage 2 / Year 6: closest programme-of-study match for Find unknown values in numerical equations involving brackets and combinations.... |
| Canada | Provincial and territory curricula | Grade 6 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 Find unknown values in numerical equations involving brackets and combinations.... |
| India | NCERT / CBSE | Class 6 closest NCERT/CBSE topic match for Find unknown values in numerical equations involving brackets and combinations.... |