Studio Aletheia · The Center for Quantitative Studies
6.DPSR.2SC 6th Grade Math
Probability: Putting It All Together
Lesson 24 · Consolidation, 6.DPSR.2 Wrap-Up
Over the last nine lessons you've described likelihood, calculated probability, and found complements. Today you'll pull all three skills together and show that you can move between them without missing a step.
Learning Targets and Success Criteria
Today's mini-lesson connects everything you've learned about probability into one toolkit.
What I will learn
- I can describe the likelihood of an event using certain, likely, unlikely, impossible, or equally likely.
- I can calculate the probability of a simple event as a fraction, decimal, or percent.
- I can calculate the complement of an event using P(not A) = 1 − P(A).
- I can choose the right probability tool for a new problem without being told which one to use.
What success looks like
- I can correctly describe the likelihood of at least three new events.
- I can correctly calculate at least three new simple-event probabilities.
- I can correctly calculate at least three complements and verify each with addition.
- I can solve a mixed review problem that requires more than one of these skills.
Review and connect likelihood, probability, and complement across the whole standard.
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.
Probability
A number from 0 to 1 (or 0% to 100%) that tells how likely an event is to happen, found as favorable outcomes over total outcomes.
Simple Event
An event made up of a single outcome, or a small set of favorable outcomes, from all the possible outcomes in a situation.
Complementary Event
The event that everything that is NOT the original event happens instead; P(not A) = 1 − P(A).
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.
One Job, Three Tools
Every calculation an actuary runs uses some combination of the three skills you've just reviewed: judging likelihood, calculating a probability, and finding a complement. Reflect on which of the three felt most natural to you today, because that instinct is exactly the kind of thinking actuaries rely on.
Three Skills, One Standard
Today's mini-lesson connects everything you've learned about probability into one toolkit.
This standard began with language. You learned to call an event certainAn event that will always happen. Its probability is 1, or 100%., impossibleAn event that can never happen. Its probability is 0, or 0%., likelyAn event that has a good chance of happening — more likely than not, though not guaranteed., unlikelyAn event that has a small chance of happening — less likely than not, though still possible., or equally likelyTwo or more outcomes that have the exact same chance of happening. just by comparing outcome counts. That language turned out to be a preview of an exact number.
From there, you learned to calculate a probabilityA number from 0 to 1 (or 0% to 100%) that tells how likely an event is to happen, found as favorable outcomes over total outcomes. for any simple eventAn event made up of a single outcome, or a small set of favorable outcomes, from all the possible outcomes in a situation., as a fraction, decimal, or percent, and finally you learned the complement rule, which finds the probability of a complementary eventThe event that everything that is NOT the original event happens instead; P(not A) = 1 − P(A). with a single subtraction. All three skills describe the same underlying idea: how much of the total space of outcomes belongs to the event you care about. Today's job is to move between the three without hesitating over which one to use.
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. A bag of 20 or 25 marbles
- B. A spinner divided into equal sections
- C. Fraction/decimal/percent conversion chart
- D. Your Data Journal
- E. A calculator (optional)
For any new probability problem, first describe the likelihood in words, then calculate the number, then check the complement.
Probability Review Lab
Today's lab mixes all three skills from the standard into one set of scenarios.
Full Probability Challenge
You'll work all four scenarios through all three skills from the standard, start to finish.
Data Journal Entry
Accountability Checklist
Show What You Know
A spinner has 4 equal sections, 1 of which is purple. Describe the likelihood of landing on purple, calculate its probability, and find the probability of its complementary event.
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