Tree diagrams
Generate theoretical sample spaces for single and combined events using listing, tables, and tree diagrams, and calculate theoretical probabilities as the number of favourable outcomes divided by the total number of equally likely outcomes
Lesson
Set out your lesson
“Tree diagrams 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
- Tally sheet or simple bar/dot sketch
- A short set of category counts
Extra for the adult
Worked example. Cats 4, dogs 2 — cats have more. The tally and comparison are the proof.
Optional challenge. For Tree diagrams, add one harder example after success.
What to notice. Keep one parent note: examples tried; results; support used. This session samples Tree diagrams, not mastery.
Share and support
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Teaching approaches
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1 approach
Tree diagrams 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: Tally sheet or simple bar/dot sketch; A short set of category counts. 1. Say the goal of Tree diagrams in plain words once. 2. Adult tallies one category and sketches a bar or dot plot. 3. Child tallies three small data sets and compares the tallest category. 4. Fresh check: one fresh tally comparison. Record and stop. Done: three correct tallies with a comparison sentence each. Proof: parent note of examples and results. Stop: End after the fresh check; keep optional challenge for another day.
Family records and proof options
Keep a record of your learning
Save photos, notes, and attendance. Export a proof packet for compliance or portfolio reviews.
Practice this concept
Start practiceTree diagrams practice
Practice key ideas from Tree diagrams.
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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 Tree diagrams. Not every lab worksheet.
Free interactive page, no sign-in required for the tested path.
Before you openAsk the learner what they changed in the sim or page and what they observed.
Opening this link does not save learning or assess mastery.
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
- List all 36 outcomes when rolling two dice and find P(total = 7)
- Draw a tree diagram for two successive events and multiply along branches for combined probabilities
- Calculate the probability of a combined event using a sample space diagram and simplify the fraction
“Can your child draw a tree diagram to map out all possible outcomes of a two-step probability situation — like flipping a coin and then rolling a die — and calculate the probability of any particular combination?”
Curriculum record
- Type
- Procedural
- Subject
- Mathematics
- Domain
- Probability
- Age range
- Ages 12–14
Standards