Getting Started 
Misconception/Error The student does not understand the meaning of numerical representations of a probability. 
Examples of Student Work at this Level The student cannot distinguish between events that are unlikely, nearly as likely as unlikely, or likely based on a given numerical probability. The student misinterprets all or most of the given probabilities.

Questions Eliciting Thinking What does it mean that an event is unlikely (neither likely nor unlikely or likely)? What (numerical) probability would indicate this?
If you focus on the numerical value, rather than the scenario itself, would you reconsider your responses?
What does a probability of 40% mean? How would you describe the likelihood of that event?
What is the relationship between a decimal, fraction, and percent? Can you change the percent to a decimal or fraction? 
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. Assist the student in assigning numerical probabilities to realworld events that are easily understood. Describe an event that could never occur (e.g., the probability of snow in Miami in July), that is certain to occur (the probability that there will be no school on Saturday), and that is as likely to occur as not (e.g., the probability the next person to walk into the room is a male). Assign numerical probabilities to these events to assist the student in developing an intuitive understanding of numerical representations of probability. Ask the student to describe events with given probabilities and to assign numerical probabilities to events that are described.
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 interpret probabilities close to 50%. 
Examples of Student Work at this Level The student says that a 40% probability is:
 Unlikely because it is less than half.
 Likely because of some feature of the scenario.

Questions Eliciting Thinking What is the meaning of a probability close to ?
Is 40% closer to onehalf or zero? 
Instructional Implications Model describing probabilities as unlikely, equally likely as unlikely or likely based on comparisons to zero, onehalf, and one. Explain that 40% is closest to 50% so it indicates an event that is just a little less likely to occur than equally likely. So, of the three choices given, â€śneither likely nor unlikelyâ€ť best describes this event. Provide the student with opportunities to explore and calculate the probabilities of outcomes that vary in terms of the likelihood of their occurring. Then ask the student to describe in words the likelihood of events.
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 task Likelihood of an Event (7.SP.3.5) for further practice with understanding the range of possibilities for the probability of 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 gives correct descriptions of each probability. For example, the student responds:
 Neither likely nor unlikely since 40% is close to 50%.
 Likely, since 9/10 is close to one.
 Unlikely, since .08 is close to zero.

Questions Eliciting Thinking Can you give another example of an event for each of these probabilities?
Is it possible for a probability to be greater than one or less than zero? Explain. 
Instructional Implications Consider implementing the MFAS tasks from 7.SP.3.6 to assess finding the probability of various events. 