Likelihood of Familiar Events
Warm-up
I am going to say two events. Tell me which is more likely. Sunny vs. cloudy in January. Getting older vs. getting younger. Eating lunch tomorrow vs. flying to the moon for lunch. Start easy to build the language, then move to genuinely uncertain comparisons.
Explore
Comparative sorting: pairs receive 8 event cards and sort them into pairs, then for each pair determine which is more likely and justify. Is it more likely to rain on a cloudy day or a sunny day? How do you know? Groups share reasoning.
Formalize
Class probability line: place selected events from Never to Always. Debate events that different students place differently. One student says eating lunch is always and another says sometimes. Who is right? It depends: what if you are home sick? This productive ambiguity is excellent mathematical thinking.
Likelihood of Familiar Events
Seasonal cycle discussion. Which is more likely in July: hot or cold weather? Which is more likely in January in our city: rain or snow? Connect to local knowledge. What have Elders or grandparents observed about weather patterns? How did they use this to predict?
Practice
Students draw 3 pairs of events, record which is more likely for each pair, and write one sentence explaining their reasoning. Exit ticket: teacher names two weather events and students hold up hands for more likely on one side for A, other side for B.
Exit ticket
Students draw 3 pairs of events, record which is more likely for each pair, and write one sentence explaining their reasoning. Exit ticket: teacher names two weather events and students hold up hands for more likely on one side for A, other side for B.
Step 1: Read event cards aloud and sort them onto a three-zone mat: "The sun will come up tomorrow" (certain). "You will roll a 7 on this die" — check the die together: faces show only 1–6 (impossible). "It will snow on Friday" (possible).
Step 2: For every placement, require a BECAUSE: "impossible, because the die has no 7 anywhere on it." The reason is the mathematics; the placement alone is just sorting.
Step 3: Take on the hard case: "I will see a rainbow at night." Students often say impossible. Probe gently: is it truly CAN'T-happen (like rolling a 7), or just very rare? (Moonbows exist — extremely unlikely, not impossible.) The distinction between never-can and hardly-ever is the day's sharpest idea.
Step 4: Have each student write one event of their own for each zone and defend it to a partner.
The setup: Spinner A is half red, half blue. Spinner B is one-quarter red, three-quarters blue. You want RED.
Step 1: Predict by LOOKING: which spinner shows more red space? A — red owns half of it, versus only a small slice of B. More space for red → red is more likely.
Step 2: Test the prediction: spin each spinner 10 times, tally the reds. Suppose A gives 6 reds and B gives 2. The tallies lean the way the space predicted.
Step 3: Handle the surprise honestly if it comes: if B happens to beat A in ten spins, that's chance being chance — likely doesn't mean always. Spin ten MORE times and watch the totals drift back toward the prediction.
Step 4: The sentence to keep: "more space means more likely, but not guaranteed." Both halves of that sentence matter equally.
The moment: a student said rain was unlikely; it rained anyway. Another laughs: "You were WRONG!" Was the prediction bad?
Step 1: Replay a cleaner version with the marble bag: 9 yellow marbles, 1 purple. Everyone predicts a draw. "Yellow is likely" is clearly the smart prediction.
Step 2: Draw — and suppose the purple comes out. Ask: "Was 'probably yellow' a BAD prediction?" No. Unlikely things really happen; that's what unlikely MEANS. One purple draw doesn't make the bag any less yellow-heavy.
Step 3: Draw twenty more times with replacement and tally: yellow dominates, purple sneaks in once or twice. The long run matches the prediction even though single draws surprise us.
Step 4: The takeaway sentence: "a good prediction can still turn out differently — being unlikely is not the same as being impossible."