CCSS.Math.Content.HSS-MD.B.5a
The standard
Find the expected payoff for a game of chance.
Common Core State Standards for Mathematics · Use probability to evaluate outcomes of decisions
What this standard means
Students need to calculate the expected payoff of a game by multiplying each possible outcome by its probability, then adding the results. They also need to account for the cost to play, so they can tell whether the average gain is positive, negative, or zero.
Mastery looks like a student reading a payoff table or situation, finding missing probabilities, and explaining what the expected payoff means over many plays. Students often mix up prize amount with net gain, ignore losing outcomes, or treat expected payoff as what will happen on one play.
Ways to teach it
- Have students play a simple spinner game 20 times, record gains and losses, then compare experimental average payoff to the calculated expected payoff.
- Ask students to write whether a game with a negative expected payoff can still be worth playing, and justify their answer with math and context.
- Give a three-outcome prize table with a $2 entry fee and ask students to find the expected net payoff in two minutes.
- Show a real lottery scratch-off odds table and have students calculate the expected return for one ticket.
Plan a lesson for CCSS.Math.Content.HSS-MD.B.5a
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Related standards
- CCSS.Math.Content.HSS-MD.B
Use probability to evaluate outcomes of decisions
- CCSS.Math.Content.HSS-MD.B.5
(+) Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.
- 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.