Getting Started 
Misconception/Error The student is unable to approximate the probability of a chance event based on the observed frequencies. 
Examples of Student Work at this Level The student is unable to determine the probabilities of one or both of the questions. The student:
 Determines the average number of eggs. The student interprets â€śapproximateâ€ť to mean â€śfind the average or the mean.â€ť
 Provides a â€śyesâ€ť or â€śnoâ€ť answer. The student investigates a pattern.
 Confuses the number of eggs with the number of times.
 Accounts for â€śnext weekâ€ť by adding a week, making the denominator 13.

Questions Eliciting Thinking What is probability? How can the probability of an event be determined?
What do the numbers in the list represent?
How many times did the hen lay exactly five eggs? How many times were the number of eggs recorded? Can you express that as a fraction, decimal, and percent? Show me.
Is it likely for the hen to lay exactly five eggs? Explain. 
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%). Consider implementing CPALMS Lesson Plans A Roll of the Dice (ID 34343) or Marble Mania (ID 4732), to help students understand probability of simple events.
Explain to the student that the probability of an event in the future can be based on the frequency of its occurrence in the past. Guide the student to understand that the observed frequencies given in the problem can be used to calculate the requested probabilities. Ask the student to organize the given data in a frequency table. Then assist the student in identifying the total number of outcomes as well as the number of outcomes favorable to each event. Ask the student to use these values to express the probability of each event.
Provide additional opportunities to estimate the probability of an event based on observed frequencies. 
Making Progress 
Misconception/Error The student does not provide a clear explanation. 
Examples of Student Work at this Level The student:
 Does not provide an adequate explanation.
 Does not provide any explanation.

Questions Eliciting Thinking How did you determine your answer?
What do the 12 numbers represent? What do you mean by â€śthree of them are fivesâ€ť?
Is it likely for the hen to lay exactly five eggs? Explain.
Is it likely for the hen to lay four or fewer eggs? Explain.
Is it possible for the hen to lay only two eggs? Is it likely for the hen to lay only two eggs? Explain. 
Instructional Implications Encourage the student to explain using mathematically correct terminology. Have the student identify how many numbers are listed and what they represent. Model an adequate explanation using appropriate terminology [e.g., â€śSince the hen laid exactly five eggs three of the 12 weeks, then the probability of that event (laying five eggs) is â€ť]. Have the student convert the fraction to a decimal and percent. Encourage the student to verbalize the probability as a percent (e.g., â€śThere is a 25% chance that the hen will lay exactly five eggs the next week.â€ť).
Provide additional opportunities to estimate the probability of an event based on observed frequencies. 
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 uses the observed frequencies to estimate the probabilities, and explains using appropriate terminology:
 There is a or or 25% chance of the hen laying exactly five eggs next week.
 There is a or or 50% chance of the hen laying four or fewer eggs next week.
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Questions Eliciting Thinking What number of eggs is the hen most likely to lay?
Based on the observed frequencies, what is the probability that the hen will lay only one egg? Suppose the hen laid one egg next week? Why might an outcome differ from a probability based on observed frequencies?
Do you think the probabilities will be different if you recorded the number of eggs the hen laid for six months instead of three months? Why or why not? 
Instructional Implications Demonstrate the difference between theoretical probability and experimental probability, using a number cube, coin, or spinner. Explain why the outcomes of an experiment may differ from the expected outcomes. Discuss how the number of trials might account for the differences in the experimental and theoretical probabilities. Explain probability in terms of what is expected to occur in the long run.
Consider implementing the MFAS tasksÂ Game of Chance andÂ Probabilities Cubed (7.SP.3.6). 