Complementary events
Understand and apply the rule that probabilities of all mutually exclusive outcomes sum to one; use this to find the probability of a complementary event (P(not A) = 1 − P(A))
Lesson
Set out your lesson
“Complementary events 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 Complementary events, add one harder example after success.
What to notice. Keep one parent note: examples tried; results; support used. This session samples Complementary events, not mastery.
Share and support
Compare teaching approaches
Teaching approaches
Gakuva’s recommended starting approach is selected. You can still compare every option.
1 approach
Complementary events 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 Complementary events 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 practiceComplementary events practice
Practice key ideas from Complementary events.
Free · no login · no ads · Practice answers and completion are not saved. Parent observation remains the lesson record.
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 Complementary events. 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
- Verify that probabilities of all outcomes listed for a spinner sum to 1
- Calculate the probability of NOT rolling a 6 as 1 − 1/6 = 5/6
- Identify an error in a probability distribution where the values do not sum to 1
“If a spinner has three sections and one has a probability of 0.4 and another has 0.35, can your child work out the probability of landing on the third section without being told?”
Curriculum record
- Type
- Conceptual
- Subject
- Mathematics
- Domain
- Probability
- Age range
- Ages 11–13
Standards