CCSS.Math.Content.HSS-MD.A

CCSS.Math.Content.HSS-MD.A is a cluster heading. These are the individual standards under it.

• CCSS.Math.Content.HSS-MD.A.1

  (+) 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 dist...

• CCSS.Math.Content.HSS-MD.A.2

  (+) Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.

• 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...

01

What Students Need to Do

Students connect each possible outcome with its probability and use those pairs to find a weighted average. They use that long-run average to compare games, costs, risks, or choices.

02

What Mastery Looks Like

Students build a probability distribution, multiply each outcome by its probability, and add the products. They interpret the result as a long-run average and use it to compare options or judge fairness.

03

Common Misconceptions

Students may average the possible payoffs without weighting them by probability. They may ignore ticket costs, confuse expected value with a guaranteed result, or choose the largest possible prize.

04

How to Assess It

Exit ticket: A $2 ticket pays $10 with probability 0.1 and $0 otherwise. Find the expected net gain and justify whether buying it is financially favorable.

1. 01

   Give pairs two dice and a payout table, then have them calculate the theoretical return and compare it with 30 recorded trials.

2. 02

   Ask students to write whether a negative expected return always means a person should reject an option, then defend their reasoning.

3. 03

   Run a card game where groups rank four payout rules by expected return before checking each calculation.

4. 04

   Compare the expected costs of two phone insurance plans using claim probabilities, deductibles, and annual premiums.

• 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.