Studio Aletheia · The Center for Quantitative Studies
6.DPSR.2.1SC 6th Grade Math
Comparing Likelihood Across Events
Lesson 16 · Guided Practice, State the Likelihood of an Event
Yesterday you learned the five likelihood words. Today you'll dig deeper, comparing events side by side and defending your reasoning when someone might disagree.
Learning Targets and Success Criteria
Today you'll recap yesterday's likelihood words, then stretch further by comparing events and defending your reasoning.
What I will learn
- I can compare the likelihood of two or more events using outcome counts.
- I can defend my choice of likelihood word when another student disagrees.
- I can identify events that are equally likely and explain why.
- I can connect likelihood language to an approximate probability value.
What success looks like
- I can rank at least three events from least likely to most likely.
- I can write a justification that another student could use to check my reasoning.
- I can identify at least one pair of equally likely events in a new scenario.
- I can estimate a probability value (close to 0, about 1/2, or close to 1) for an event I've described in words.
Compare and justify the likelihood of events using precise probability language.
The words we'll use in today's lesson.
These terms will carry through today's mini-lesson, Data Lab, hands-on activity, journal, and exit challenge, and they'll keep coming back all year.
Certain
An event that will always happen. Its probability is 1, or 100%.
Impossible
An event that can never happen. Its probability is 0, or 0%.
Likely
An event that has a good chance of happening — more likely than not, though not guaranteed.
Unlikely
An event that has a small chance of happening — less likely than not, though still possible.
Equally Likely
Two or more outcomes that have the exact same chance of happening.
Where this shows up in the real world.
Thinking like a mathematician is not just a school skill. It's what people get paid to do every day, in jobs you may not have heard of yet.
Ranking Risk Before Pricing It
Before an actuary ever calculates an exact probability, they start by ranking risks the same way you will today, deciding which events are more or less likely to happen. Getting that ranking right the informal way is what makes the precise calculations later actually mean something.
Defending Your Word Choice
Today you'll recap yesterday's likelihood words, then stretch further by comparing events and defending your reasoning.
Yesterday you placed events on a scale from impossibleAn event that can never happen. Its probability is 0, or 0%. to certainAn event that will always happen. Its probability is 1, or 100%.. Today the challenge gets harder: instead of describing one event at a time, you'll compare two events and decide which one is more likely, then defend that decision the way a mathematician would, with the actual outcome counts, not just a hunch.
Comparing gets especially interesting when events are close. If a bag has 4 green counters and 4 orange counters, pulling green and pulling orange are equally likelyTwo or more outcomes that have the exact same chance of happening., and no amount of arguing changes that; the counts settle it. But if one bag is mostly green and another bag is mostly orange, you have to compare across two different situations, and that's where students often disagree at first. The fix is always the same: go back to favorable outcomes over total outcomes for each event, decide whether each is likelyAn event that has a good chance of happening — more likely than not, though not guaranteed. or unlikelyAn event that has a small chance of happening — less likely than not, though still possible., and only then compare. A clear argument beats a confident guess every time.
Adapted from Studio Aletheia's The Center for Quantitative Studies curriculum library, drawing on mathematical resources and the SC CCR Mathematics Standards.
Materials for the Data Lab.
- A. Two small bags of colored counters
- B. A spinner divided into equal sections
- C. Sticky notes for ranking events
- D. Your Data Journal
- E. A calculator (optional)
Whenever you compare two events, write both favorable-over-total ratios side by side before choosing a likelihood word.
Likelihood Lab: Round Two
Today's lab pushes you to rank and defend, not just label.
Rank the Risks
You'll rank a set of events from least likely to most likely and defend your order to a partner.
Data Journal Entry
Accountability Checklist
Which Event Wins?
Bag X has 3 red and 5 blue marbles. Bag Y has 4 red and 4 blue marbles. In which bag is pulling red closer to being equally likely with pulling blue? Explain.
The Center for Quantitative Studies · Course Navigation
Move between lessons or return to the larger Studio Aletheia ecosystem.