CCSS.Math.Content.HSS-MD.A.1
The standard
(+) Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.
Common Core State Standards for Mathematics
What this standard means
Students need to turn outcomes into numbers. They choose a quantity to track, list the possible events, assign each event a value, and connect each value to its probability. Then they display the distribution with a dot plot, histogram, bar graph, or table.
Mastery looks like a clear link between the real situation, the sample space, the random variable, and the graph. Students often get stuck by listing outcomes but not defining the variable, mixing up outcomes with values, or making a graph that shows raw data instead of probabilities.
Ways to teach it
- Have students roll two dice 50 times, define the variable as the sum, then make a probability bar graph from the full sample space.
- Ask students to explain why rolling a 7 and rolling doubles can be events, but only one can match their chosen variable.
- Give a three-card prize game and ask students to list outcomes, assign winnings, and sketch the probability distribution in five minutes.
- Use a simple carnival spinner with cash prizes, then have students graph the probability distribution for expected payouts.
Plan a lesson for CCSS.Math.Content.HSS-MD.A.1
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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-MD.A.3
(+) Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected ...
- CCSS.Math.Content.HSS-MD.A.4
(+) Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value...
- CCSS.Math.Content.HSS-MD.A.2
(+) Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.