CCSS.Math.Content.HSS-MD.A.2
The standard
(+) Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.
Common Core State Standards for Mathematics
What this standard means
Students need to multiply each possible outcome by its probability, then add those products to find the long-run average outcome. They should connect a probability table, spinner, game, or payout situation to one number that represents the average result over many trials.
Mastery looks like setting up the distribution correctly, including zero or negative outcomes, and explaining the answer in context. Students often get stuck by averaging outcomes without using probabilities, mixing up probability and outcome columns, or thinking the expected value must be a possible result.
Ways to teach it
- Hands-on activity: Have pairs roll two dice 50 times, track a payout rule, then compare their average winnings to the calculated expected value.
- Prompt: Explain why an expected value of 2.4 points per turn can make sense even though no single turn earns 2.4 points.
- Quick assessment: Give a three-row probability table and ask students to compute expected value and write one sentence interpreting it.
- Real-world connection: Analyze a simple raffle with ticket cost, prize value, and chance of winning to decide if it is favorable.
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