Getting Started 
Misconception/Error The student does not describe a statistical simulation. 
Examples of Student Work at this Level The student:
 Attempts to calculate the probability that none of the next four cats will have orange coats.
 Describes a simulation that will not generate frequencies of chance events.Â

Questions Eliciting Thinking What does it mean to design a simulation?
Can you think of a way to use this probability to simulate the event of getting an orange cat or a nonorange cat? 
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. Review the process of finding probabilities experimentally by counting the number of outcomes favorable to an event and comparing this number to the total number of outcomes. Use a variety of manipulatives (e.g., coins, number cubes, and spinners) to find the probabilities of specific events. Include simple events (e.g., the probability of rolling one or two on a number cube) as well as compound events (e.g., the probability of flipping a coin three times and getting heads at least twice). Guide the student to organize results in a frequency table and use the table to assist in calculating probabilities.
Define a simulation as an imitation of chance behavior based on a probability model. Guide the student through the steps of a simulation:
 Identify the question to be answered: What is the probability that none of the next four cats the shelter takes in will have orange coats?
 State assumptions: of the cats the shelter takes in have orange coats.
 Assign digits or symbols to represent outcomes that reflect assumptions: 1 represents a cat with an orange coat; 2 through 6 represent all other cats.
 Describe a single simulation of the event: To simulate one event of taking in four cats, roll a die four times. Each outcome represents one of the next four cats taken in.
 Repeat the simulation many times and record the outcomes: The results of six simulations might be {6,3,2,5}, {5,4,6,1}, {4,4,6,5}, {5,3,2,4}, {1,5,5,6}, {2,5,6,3}.
 Use the results to calculate a probability that answers the question: P (none of the next four cats the shelter takes in will have orange coats) = or .
Provide additional examples of questions that can be answered by simulations. Ask the student to design a simulation and provide feedback. Then have the student conduct the simulation to answer the question. 
Moving Forward 
Misconception/Error The studentâ€™s digit assignment does not represent the assumptions. 
Examples of Student Work at this Level The studentâ€™s digit assignment does not reflect that of the cats the shelter takes in have orange coats (e.g., the student assigns 1 to a cat with an orange coat and 6 to a cat without an orange coat). 
Questions Eliciting Thinking Suppose you assign 1 to a cat with an orange coat and 6 to a cat without an orange coat. What assumption are you making about the proportion of cats that have orange coats?
In your simulation, how did you use the fact that of the cats taken in by the shelter, have orange coats?
Can you assign digits that reflect this fact? 
Instructional Implications Assist the student in understanding that if the shelter estimates that of the cats it takes in have orange coats, then the probability of any one cat coming in with an orange coat is . Guide the student to assign digits in a way that reflects this probability (e.g., 1 represents a cat with an orange coat; 2 through 6 represent all other cats). Ask the student to describe another way to assign digits that reflects this probability.
Provide other probabilities of outcomes (e.g., , , or ) and ask the student to assign digits to represent the probabilities. Provide feedback. 
Almost There 
Misconception/Error The student does not describe a simulation that can represent the single event of taking in the next four cats. 
Examples of Student Work at this Level The student describes a single simulation of the event of taking in four cats as:
 Rolling a die one time. If a 1 is rolled, then an orange cat is taken in; if any other number is rolled, an orange cat was not taken in.
 The student rolls the die many times (e.g., 50 times) without regard to what constitutes a single event.Â

Questions Eliciting Thinking Your method looks like it will work if the question is about the probability of the next cat having an orange coat. But what if the question is about the probability of none of the next four cats having an orange coat?
How can you represent the event of taking in the next four cats? 
Instructional Implications Review the question that the simulation is intended to answer and guide the student to understand what constitutes a single event. Explain that each roll of the die represents taking in one cat, so four rolls are required to represent the event of taking in the next four cats.
Provide additional examples of questions that can be answered by simulations. Ask the student to describe what constitutes a single event in the simulation. Provide feedback. 
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 describes a simulation that will generate frequencies for the events of â€śno cats with an orange coatâ€ť and â€śat least one cat with an orange coatâ€ť (e.g., rolling four number cubes with the number one representing a cat with an orange coat). 
Questions Eliciting Thinking What is the theoretical probability that the next cat taken in does not have an orange coat?
How could you calculate the theoretical probability that none of the next four cats taken in has an orange coat? 
Instructional Implications Guide the student to calculate the theoretical probability that none of the next four cats taken in has an orange coat. Have the student compare the probability that he or she calculated as part of the simulation to the theoretical probability.
Ask the student to design a simulation to answer the question: â€śWhat is the probability that exactly two of the next five cats will have orange coats?â€ť
Challenge the student to use technology (e.g., a graphing calculator or a spreadsheet) to generate a large number of simulated events to answer the question in the Coat Count worksheet. Then, ask the student to approximate the probability.
Consider administering other MFAS tasks for standard 7.SP.3.8. 