What students learn in AC9M8P02
This unit helps students build a clear, usable understanding of Determine all possible combinations for 2 events, using two-way tables.... 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: determine all possible combinations for 2 events, using two-way tables, tree diagrams and Venn diagrams, and use these to determine probabilities of specific outcomes in practical situations.
- Use concrete examples, pictures, oral explanation and short written responses before moving to independent practice.
- describing events using language of “at least”, exclusive “or” (A or B but not both), inclusive “or” (A or B or both) and “and” using the relation Pr(A\;and\;B)+Pr(A\;and\;not\;B)+Pr(not\;A\;and\;B)+Pr(not\;A\;and\;not\;B)=\;1 to calculate probabilities, including the special case of mutually exclusive events where Pr(A\;and\;B)\;=\;0
- 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: determine all possible combinations for 2 events, using two-way tables, tree diagrams and Venn diagrams, and use these to determine probabilities of specific outcomes in practical situations
- E1: describing events using language of “at least”, exclusive “or” (A or B but not both), inclusive “or” (A or B or both) and “and”
- E2: using the relation Pr(A\;and\;B)+Pr(A\;and\;not\;B)+Pr(not\;A\;and\;B)+Pr(not\;A\;and\;not\;B)=\;1 to calculate probabilities, including the special case of mutually exclusive events where Pr(A\;and\;B)\;=\;0
- E3: using Venn diagrams or two-way tables to demonstrate the difference between events that are mutually exclusive, such as whether a coin toss will land on a head or a tail, or those that are not mutually exclusive, such as people who have blonde hair and people who have blue eyes
- E4: exploring First Nations Australian children’s instructive games; for example, Battendi from the Ngarrindjeri Peoples of Lake Murray and Lake Albert in southern Australia, applying possible combinations and relationships and calculating probabilities using two-way tables and Venn diagrams (teaching context)
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
AC9M8P02 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 | AC9M8P02 — determine all possible combinations for 2 events, using two-way tables, tree diagrams and Venn diagrams, and use these to determine probabilities of specific outcomes in practical situations |
| Victoria | Victorian Curriculum F-10 | Year 8 Maths: closest match in Probability. Use this page as a VIC-aligned practice and worksheet reference. |
| NSW | NSW Curriculum | Stage 4 Maths: closest content focus for Determine all possible combinations for 2 events, using two-way tables... and related outcomes. |
| United States | Common Core / NGSS | Grade 8 Common Core Mathematics/ELA closest topic match for Determine all possible combinations for 2 events, using two-way tables.... |
| England / UK | National Curriculum | Key Stage 3 / Year 8: closest programme-of-study match for Determine all possible combinations for 2 events, using two-way tables.... |
| 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 Determine all possible combinations for 2 events, using two-way tables.... |
| India | NCERT / CBSE | Class 8 closest NCERT/CBSE topic match for Determine all possible combinations for 2 events, using two-way tables.... |