Getting Started 
Misconception/Error The student is unable to interpret a tree diagram. 
Examples of Student Work at this Level The student calculates an incorrect probability and provides an explanation that indicates he or she does not understand the structure of the diagram.
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Questions Eliciting Thinking How many possible car outcomes are shown by the diagram? How many of the cars are black? Silver? Sedans?
How did you use the diagram to calculate your probability?
What does the diagram indicate when it shows the word black branching to the words coupe, sedan, and wagon? 
Instructional Implications Provide instruction on how to construct and interpret a tree diagram. Define a tree diagram as an organized diagram that lists of all possible outcomes in a sample space. Guide the student to identify what constitutes an outcome in the tree diagram. Ask the student to count the number of outcomes associated with particular events, such as, choosing a black car, a sedan, a car with a V6 engine, a sedan with an I4 engine, or a silver coupe with a V6 engine. Next, 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. Ask the student to revise his or her response and explain how the new probability was calculated.
Consider implementing the CPALMS Lesson Plan Chancy Candy (ID 48804) onÂ using a tree diagram to determine compound probability. Then provide additional opportunities to construct and use tree diagrams to find probabilities. 
Moving Forward 
Misconception/Error The student does not understand how to write or calculate probability. 
Examples of Student Work at this Level The student:
 Writes a probability of four instead of .
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 Calculates the denominator incorrectly.
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Questions Eliciting Thinking What is probability? How are probabilites calculated?
How can you represent probability in fraction form? Should the total number of outcomes be in the numerator or denominator? Why?
Can probability be a whole number? 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 the tree diagram in this task to demonstrate how probabilities of outcomes and events are calculated. Clearly describe each possible outcome, the total number of outcomes, and the number of outcomes favorable to the event of selecting a V6 wagon. Guide the student to calculate specific probabilities and to write the probabilities in different equivalent 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%). Provide the student with additional opportunities to write and calculate probabilities of outcomes, simple events, and compound events using tree diagrams, number cubes, and spinners. 
Almost There 
Misconception/Error The student is unable to clearly explain how a tree diagram can be used to find the probability of a compound event. 
Examples of Student Work at this Level The student provides an incomplete explanation. The student:
 Restates the probability.
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 Provides a vague or incomplete explanation such as, â€śI counted all of them.â€ť
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Questions Eliciting Thinking How did you determine your answer?
Can you show me how you knew there were only four V6 wagons? How did you determine the total number of outcomes?
Show me in the tree diagram how you could determine the probability of randomly selecting a V6 sedan.
How are probabilities calculated? 
Instructional Implications Model a clear and concise explanation for the student using the tree diagram in the task. Address both the quantities needed for the probability calculation and how to use the tree diagram to determine these quantities.
Provide the student with additional opportunities to explain how to use a tree diagram to determine probabilities. 
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 writes the correct probability,Â P(V6 wagon) = Â (or its equivalent) and explains how he or she used the tree diagram to find the answer.Â
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Questions Eliciting Thinking What is the probability of randomly selecting a silver car with a V6 engine?
Would it be more or less likely to get a silver car with a V6 engine than to get a V6 wagon? Explain. 
Instructional Implications Challenge the student to determine the total possible outcomes if there were five color options rather than four. Encourage the student to discuss how the probability of selecting a V6 wagon is affected by adding another â€ścolorâ€ť branch to the tree diagram.
Provide the student with a verbal description similar to the one in this task, and have the student draw a tree diagram to represent all possible outcomes. Then, ask the student to determine specific probabilities based on his or her diagram.
Consider implementing the MFAS tasks Number List (7.SP.3.8), Work Clothing (7.SP.3.8), and/or Coat Count (7.SP.3.8) to further assess the student. 