Florida B.E.S.T. MA.912.DP.6.7
The Standard
Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values and standard deviations. Evaluate and compare strategies on the basis of the calculated expected values and standard deviations.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students create a probability table for each choice, including every payoff and its chance. They calculate the long term average payoff and how widely results vary, then use both measures to compare choices.
What Mastery Looks Like
- Students organize each choice in a complete probability and payoff table. They correctly calculate the expected payoff and standard deviation. They explain why choices with similar averages can carry different levels of risk.
Common Misconceptions
- Students may assume all payoffs are equally likely. They may treat standard deviation as profit rather than variability. Some choose the largest possible payoff without considering its probability or risk.
How to Assess It
- Exit ticket: Strategy A pays $4 every time. Strategy B pays $0 or $10 with equal probability. Calculate both means and standard deviations, then recommend one strategy for higher average payoff and one for lower risk.
Lesson moves
Ways to Teach It
Pairs roll a die 30 times using a posted payoff table, then compare the sample mean and spread with calculated values.
Ask, "Would you choose a guaranteed $40 or a 50 percent chance at $100, and what calculations support your choice?"
Use a card sort matching payoff tables with their expected values, standard deviations, and descriptions of risk.
Give students two mock phone warranty plans, failure probabilities, and repair costs, then have them compare expected cost and variability.
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Related Standards
- MA.7.DP.2.2
Given the probability of a chance event, interpret the likelihood of it occurring. Compare the probabilities of chance events.
- MA.912.DP.6.4
Given a binomial distribution, calculate and interpret the expected value. Solve real-world problems involving binomial distributions.
- MA.912.DP.6.8
Apply probabilities to make fair decisions, such as drawing from lots or using a random number generator.
- MA.7.DP.2
Develop an understanding of probability. Find and compare experimental and theoretical probabilities.
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