Getting Started 
Misconception/Error The student is unable to determine the probability of either event. 
Examples of Student Work at this Level The student:
 Does not know how to represent or calculate probabilities.
 Provides an incorrect probability to question one and/or question two.

Questions Eliciting Thinking How is probability determined?
How many favorable outcomes are there? How many possible outcomes are there?
How can you represent probability in fraction form? Should the total number of outcomes be the numerator or denominator? Why?
What does observed frequency mean? 
Instructional Implications Review the meaning of probability and how it is calculated. Explain that the probability of an event is the number of outcomes favorable to that event compared to the total number of outcomes. Use a variety of manipulatives (e.g., coins, number cubes, and spinners) to demonstrate how probabilities are calculated. Clearly describe each possible outcome, the total number of outcomes, outcomes favorable to a particular event, and the number of outcomes favorable to that event. Guide the student to calculate specific probabilities and to write the probabilities in multiple forms: fraction, decimal, and percent. Remind the student that the probability of an event is a number between zero and one (or 0% and 100%), inclusive. Consider implementing CPALMS Lesson Plan A Roll of the Dice (ID 34343) or Marble Mania (ID 4732), to help students understand probability of simple events. 
Making Progress 
Misconception/Error The student is unable to explain why the probabilities differ. 
Examples of Student Work at this Level The student correctly calculates the two probabilities but is unable to explain why the probabilities might differ. The student:
 Writes an irrelevant or incorrect statement.
 Only explains that one is theoretical and the other is experimental.

Questions Eliciting Thinking If a boy has a 50% or chance of being selected, why do you think a boy was selected 80% of the time (in a 20 week time period)?
Was a boy selected more often or less often than you expected? Explain.
Why might the theoretical and experimental probabilities differ in this case? Can you think of a plausible reason? 
Instructional Implications Guide the student to compare the theoretical probabilities of getting tails (selecting a boy) on a â€śfairâ€ť coin to the experimental probabilities and to determine if they are reasonably close. Explain to the student that some deviation from the theoretical probabilities will occur even when the coin is fair; in the long run, however, the frequency of each outcome should be nearly the same. Significant departures from the theoretical probability suggest that getting tails (selecting a boy) is not equally likely. Further explain that the observed pattern suggests the coin may not be fair because the observed frequency, tails 80% of the time, significantly deviates from the expected outcome of tails 50% of the time. Consider implementing CPALMS Lesson Plan M & M Candy: I Want Green (ID 7021), a lesson in which theoretical and experimental probabilities are compared. 
Got It 
Misconception/Error The student provides complete and correct responses to all components of the task. 
Examples of Student Work at this Level The student determines the probability of each event and explains how the probability was calculated. The student is able to explain why the two probabilities differ:
 The probability of selecting a boy is or 50% (or equivalent) because there is one favorable outcome out of two possible outcomes.
 The probability is (based on the observed frequency) or 80% (or equivalent) because tails was tossed 16 out of 20 times.
 The probabilities may differ because the coin is not fair or is being tossed in an unfair manner. The student may suggest that the coin is fair and that this pattern of events, although possible, is highly unlikely.Â

Questions Eliciting Thinking Suppose the coin is fair. What would you expect to happen in the long run? 
Instructional Implications Ask the student to consider how different the probabilities would need to be for the student to confidently conclude that the coin is not â€śfair.â€ť
Consider implementing MFAS tasks Marble Probability and Number Cube (7.SP.3.7) to further assess the studentâ€™s understanding. 