Studio Aletheia · The Center for Quantitative Studies
6.DPSR.2.2SC 6th Grade Math
Practice Calculating Probability
Lesson 19 · Guided Practice, Find the Probability of Simple Events
Yesterday you learned to calculate a probability from outcome counts. Today you'll get faster and more flexible, working with larger totals and starting from a probability to figure out matching outcomes.
Learning Targets and Success Criteria
Today's mini-lesson recaps yesterday's calculation and stretches it in two new directions.
What I will learn
- I can calculate the probability of a simple event from a data set with up to 200 outcomes.
- I can move flexibly between fraction, decimal, and percent forms of a probability.
- I can work backward from a probability to figure out possible outcome counts.
- I can compare the probabilities of two different simple events.
What success looks like
- I can calculate at least four probabilities correctly as simplified fractions.
- I can convert any probability fraction to a decimal and percent for common denominators.
- I can find a possible set of outcomes that matches a given probability.
- I can state which of two events has the greater probability and explain why.
Build fluency calculating and comparing the probability of simple events.
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.
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.
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.
Practice Makes the Numbers Trustworthy
Actuaries run the same probability calculation thousands of times a year until it becomes second nature, because a single mistake can mean a company charges the wrong price for real people. The fluency you're building today with fractions, decimals, and percents is exactly what makes that trust possible.
Getting Faster and More Flexible
Today's mini-lesson recaps yesterday's calculation and stretches it in two new directions.
Yesterday you found the 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. of a simple eventAn event made up of a single outcome, or a small set of favorable outcomes, from all the possible outcomes in a situation. by counting favorable outcomes over total outcomes. Today the total outcomes get bigger, up to 200, which means your fraction skills matter more than ever. A bag of 200 marbles with 50 red ones gives a probability of 50/200, which simplifies all the way down to 1/4, exactly the same probability as a bag of just 4 marbles with 1 red one. The size of the group changes, but the probability, and the story it tells, stays the same.
Today you'll also practice working backward. If you're told an event has a probability of 1/5, you can build a scenario that matches: a spinner with 5 equal sections and 1 favorable one, or a bag of 20 marbles with 4 favorable ones, since 4/20 also simplifies to 1/5. Being able to move in both directions, from outcomes to probability and from probability to outcomes, is what lets you compare two events fairly, even when they come from very different-sized data sets.
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 spinner divided into 10 equal sections
- B. A bag of 20 or 50 marbles
- C. Fraction/decimal/percent conversion chart
- D. Your Data Journal
- E. A calculator (optional)
Before comparing two probabilities, convert both to the same form — fraction, decimal, or percent — so the comparison is fair.
Probability Lab: Round Two
Today's lab mixes forward calculations with backward ones, so you build true flexibility.
Match the Probability
You'll design your own spinner or bag to match a target probability, then check it against a partner's.
Data Journal Entry
Accountability Checklist
Build the Match
Design a bag of 25 marbles where the probability of pulling a green marble is exactly 20%. State how many green marbles and how many total marbles are in your bag.
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