CCSS.Math.Content.HSS-MD.A
The standard
Calculate expected values and use them to solve problems
Common Core State Standards for Mathematics · High School — Statistics and Probability
What this standard means
Students need to find the long-run average outcome of a chance situation. They multiply each possible outcome by its probability, then add the products. They also need to use that value to compare choices, games, insurance plans, warranties, or risks.
Mastery looks like setting up a probability table, calculating accurately, and explaining what the expected value means in context. Students often think the expected value is the most likely outcome, or that it must be a possible outcome. They also get stuck when probabilities are written as percents, fractions, or odds.
Ways to teach it
- Have students play a simple dice game 20 times, record wins and losses, then calculate the expected value from the game rules.
- Ask students to write which carnival game is the better deal and justify their choice using expected value.
- Give a three-outcome prize table and ask students to compute expected value and interpret it in one sentence.
- Compare a phone insurance plan to repair costs, using given probabilities to decide whether the plan is worth buying.
Plan a lesson for CCSS.Math.Content.HSS-MD.A
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Related standards
- CCSS.Math.Content.7.EE.B
Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
- CCSS.Math.Content.HSA-SSE.B
Write expressions in equivalent forms to solve problems
- CCSS.Math.Content.HSS-MD.B.5b
Evaluate and compare strategies on the basis of expected values.
- CCSS.Math.Content.HSS-MD.A.2
(+) Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.