CCSS.Math.Content.HSS-CP.B.9
The standard
(+) Use permutations and combinations to compute probabilities of compound events and solve problems.
Common Core State Standards for Mathematics
What this standard means
Students need to count outcomes without listing every case. They should know when order matters, use permutations, and when order does not matter, use combinations. Then they use those counts to find probabilities for compound events.
Mastery looks like choosing the right counting method, setting up the numerator and denominator correctly, and explaining the reasoning. Students often mix up permutations and combinations, count the same outcome twice, or forget restrictions like “without replacement” or “at least one.”
Ways to teach it
- Give pairs 5 colored tiles and ask how many 3-tile arrangements versus 3-tile groups they can make, then compare counts.
- Ask students to explain: Does choosing a class president, vice president, and treasurer use combinations or permutations, and why?
- Use an exit ticket with one card-hand probability and one race-order probability, requiring students to label P or C.
- Connect to lottery odds by having students compute the chance of matching 5 numbers chosen from 40, ignoring order.
Plan a lesson for CCSS.Math.Content.HSS-CP.B.9
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Related standards
- CCSS.Math.Content.HSS-MD.B.6
(+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).
- CCSS.Math.Content.HSS-CP.B
Use the rules of probability to compute probabilities of compound events in a uniform probability model
- CCSS.Math.Content.HSS-MD.B.7
(+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).
- CCSS.Math.Content.7.SP.C.8
Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.