What students learn in AC9M5A02
This unit helps students build a clear, usable understanding of Find unknown values in numerical equations involving multiplication and division.... 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 multiplication and division using the properties of numbers and operations.
- Use concrete examples, pictures, oral explanation and short written responses before moving to independent practice.
- using knowledge of equivalent number sentences to form and find unknown values in numerical equations; for example, given that 3\times5=15 and 30\div2=15 then 3\times5=30\div2 therefore the solution to 3\times5=30\div\square is 2 using relational thinking, an understanding of equivalence and number properties to determine and reason about numerical equations; for example, explaining whether an equation involving equivalent multiplication number sentences is true, such as 15 ÷ 3 = 30 ÷ 6
- 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 multiplication and division using the properties of numbers and operations
- E1: using knowledge of equivalent number sentences to form and find unknown values in numerical equations; for example, given that 3\times5=15 and 30\div2=15 then 3\times5=30\div2 therefore the solution to 3\times5=30\div\square is 2
- E2: using relational thinking, an understanding of equivalence and number properties to determine and reason about numerical equations; for example, explaining whether an equation involving equivalent multiplication number sentences is true, such as 15 ÷ 3 = 30 ÷ 6
- E3: using materials, diagrams and arrays to demonstrate that multiplication is associative and commutative but division is not; for example, using arrays to demonstrate that 2 \times 3 = 3 \times 2 but 6 ÷ 3 does not equal 3 ÷ 6; demonstrating that 2 \times 2 \times 3 = 12 and 2 \times3 \times2 = 12 and 3 \times 2 \times 2 = 12; understanding that 8 ÷ 2 ÷ 2 = (8 ÷ 2) ÷ 2 = 2 but 8 ÷ (2 ÷ 2) = 8 ÷ 1 = 8
- E4: using materials, diagrams or arrays to recognise and explain the distributive property; for example, where 4 \times 13 = 4 \times 10 + 4 \times 3
- E5: constructing equivalent number sentences involving multiplication to form a numerical equation, and applying knowledge of factors, multiples and the associative property to find unknown values in numerical equations; for example, considering 3 \times 4 = 12 and knowing 2 \times 2 = 4 then 3 \times 4 can be written as 3\times (2 \times 2) and using the associative property (3 \times 2) \times 2 so 3 \times 4 = 6 \times 2 and so 6 is the solution to 3 \times 4 = \square\times 2
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
AC9M5A02 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 | AC9M5A02 — find unknown values in numerical equations involving multiplication and division using the properties of numbers and operations |
| 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 Find unknown values in numerical equations involving multiplication and division... and related outcomes. |
| United States | Common Core / NGSS | Grade 5 Common Core Mathematics/ELA closest topic match for Find unknown values in numerical equations involving multiplication and division.... |
| England / UK | National Curriculum | Key Stage 2 / Year 5: closest programme-of-study match for Find unknown values in numerical equations involving multiplication and division.... |
| 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 Find unknown values in numerical equations involving multiplication and division.... |
| India | NCERT / CBSE | Class 5 closest NCERT/CBSE topic match for Find unknown values in numerical equations involving multiplication and division.... |