Getting Started 
Misconception/Error The student does not understand that a probability must be between zero and one. 
Examples of Student Work at this Level The student understands that a negative number cannot represent a probability but states that:
 All positive or all whole numbers can be probabilities.
 Numbers greater than one can be probabilities while numbers less than one cannot.
 States that anything that can be turned into a percent can represent a probability.
 Only probabilities related to a sixsided number cube will work.
 Only numbers less than nine and numbers that can be turned into fractions can represent probabilities.
 All of the numbers can represent probabilities because they are all between 0% and 100%.Â

Questions Eliciting Thinking How are the numbers represented (decimal or percent)? How would I represent 4.2 as a percent? How do I convert decimals into percent?
What would a probability of 4.2 mean?
What is the largest a probability can be? The smallest?
When a probability is given as a fraction, what do the numerator and denominator mean? What is the largest the numerator can be compared to the denominator?
What if numbers are not given as percents? Can they represent probabilities? 
Instructional Implications Help the student understand that the probability of an outcome or event is a number between zero and one. Larger numbers indicate greater likelihood. A probability near zero indicates an unlikely event, a probability around indicates an event that is equally likely as unlikely, and a probability near one indicates a likely event.
Provide the student with opportunities to explore and calculate the probabilities of outcomes. Using a variety of manipulatives (e.g., number cubes, coins, bags containing marbles or chips), describe outcomes and events (e.g., getting a five or getting an even number when rolling a number cube) and assist the student in calculating their theoretical probabilities. Describe some outcomes that are certain to occur (e.g., getting a number less than 10 when rolling a number cube) and some outcomes that can never occur (e.g., getting a number greater than 10 when rolling a number cube). Emphasize that examples such as these represent the extremes and have probabilities given by one and zero, respectively.
Assist the student in understanding the relationship between fractional, decimal, and percent representations of probabilities. Explain that probabilities range from zero to one when they are given by fractions and decimals but from zero to 100% when given by percents. 
Making Progress 
Misconception/Error The student cannot adequately explain why a given number can represent a probability. 
Examples of Student Work at this Level The student correctly determines which numbers can represent probabilities but:
 Explains in terms of the form of the number (whether it is a fraction or a decimal) rather than its size.
 Offers an unclear explanation such as the number is â€śexact.â€ť
 Indicates that numbers that can be converted to percents can represent probabilities.
 Explains in terms of the number representing â€śa good chanceâ€ť or not or it being a â€śgood fraction.â€ť

Questions Eliciting Thinking Does the form of the number determine whether or not it could represent a probability?
What do you mean by a â€śgood chanceâ€ť (or a â€śgood fractionâ€ť)?
What do you mean about being able to convert these numbers to a percent or not? Can any number be converted to a percent? 
Instructional Implications Model justifying whether or not a number can represent a probability by referring to its size (e.g., whether or not it is between zero and one, inclusive).
If needed, assist the student in understanding the relationship between fractional, decimal, and percent representations of probabilities. Explain that probabilities range from zero to one when they are given by fractions and decimals but from zero to 100% when given by percents.
Consider implementing the MFAS tasks Likelihood of an Event and Likely or Unlikely? (7.SP.3.5) to further assess understanding of the range of possibilities for the probability of outcomes and events. 
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 correctly identifies the numbers that can represent probabilities and explains in terms of the size of the number. For example, the student says:
 1 and 0.5 cannot represent probabilities because a probability cannot be negative.
 4.2 cannot represent a probability because it is greater than one.
 0.6, 0.888, 0, and 0.39 can represent probabilities because they are between zero and one, inclusive.
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Questions Eliciting Thinking What does a probability of zero mean?
What does a probability of one mean?
How likely is a probability of 0.6?
Why can't probability be more than one? Less than zero? More than 100%? 
Instructional Implications Consider implementing the MFAS tasks from 7.SP.3.6 to assess finding the probability of various outcomes and events. 