Venn Diagrams and Counting Outcomes
Construct and interpret Venn diagrams with two or three sets to organise and count outcomes; use systematic listing and the product rule for counting to enumerate all possible outcomes of combined events
Lesson
Set out your lesson
“Venn Diagrams and Counting Outcomes means practising the idea at the table with counters or paper models and one clear check. We will demo once, then your child tries.”
Bring to the table
- Two overlapping circles drawn on paper
- Counter tokens or number cards
Extra for the adult
Worked example. 6 is even and a multiple of 3, so it goes in the overlap.
Optional challenge. For Venn Diagrams and Counting Outcomes, add one harder example after success.
What to notice. Keep one parent note: examples tried; results; support used. This session samples Venn Diagrams and Counting Outcomes, not mastery.
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Teaching approaches
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1 approach
Venn Diagrams and Counting Outcomes means practising the idea at the table with counters or paper models and one clear check. We will demo once, then your child tries.
Materials: Two overlapping circles drawn on paper; Counter tokens or number cards. 1. Say the goal of Venn Diagrams and Counting Outcomes in plain words once. 2. Adult sorts numbers into A, B, both, or neither for “even” and “multiple of 3”. 3. Child sorts three sets into a Venn diagram and counts each region. 4. Fresh check: one fresh item placement in the overlap. Record and stop. Done: three correctly sorted Venn diagrams with region counts. Proof: parent note of examples and results. Stop: End after the fresh check; keep optional challenge for another day.
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Practice this concept
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Learning resources
Extra practice links — they do not replace Gakuva’s teaching approach.
PhET Interactive Simulations · Practice link — not the full lesson
Plinko Probability
Before you open · source notes
Plinko Probability supports hands-on exploration for Venn Diagrams and Counting Outcomes. Not every lab worksheet.
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Source, access and review notes
Public PhET Interactive Simulations page. An anonymous GET on 2026-11-12 returned HTTP 200 with no login or payment prompt for this URL. Opening the link does not save practice or assess mastery. An adult should preview and guide the learner.
PhET Interactive Simulations. “Plinko Probability.” External page; Gakuva does not copy, host, embed, or redistribute materials.
Unknown — link only
Check understanding
- Draw a two-circle Venn diagram to sort 30 students by whether they like football, like cricket, or like both
- Shade the intersection A ∩ B and the union A ∪ B on a Venn diagram and explain what each region represents
- Use a completed Venn diagram to calculate P(A), P(B), P(A ∩ B), and P(A ∪ B)
“If your child surveys a class about which sports they play and draws a Venn diagram to show the results, can they use it to find out how many students play both sports — and calculate the probability of picking one of those students at random?”
Curriculum record
- Type
- Representational
- Subject
- Mathematics
- Domain
- Probability
- Age range
- Ages 12–13
Standards