Getting Started 
Misconception/Error The student is unable to correctly draw and label the normal curve. 
Examples of Student Work at this Level The student:
 Draws a curve that does not appear normal.
 Draws a normal curve and correctly labels it with the mean but does not label values within one, two, and three standard deviations of the mean.
 Draws a normal curve and correctly labels it with the mean but uses increments of one instead of the standard deviation of two to calculate the values that are within one, two, and three standard deviations of the mean.
 Draws a normal curve and correctly calculates values within one, two, and three standard deviations of the mean but incorrectly locates them.

Questions Eliciting Thinking What is the shape of a normal curve? How would you describe it? Is it symmetric?
Where should the mean be located on a normal curve?
How can you determine the values that are within one, two, and three standard deviations of the mean?
How did you determine where to locate values that are within one, two, and three standard deviations of the mean? 
Instructional Implications If needed, review how to use the mean and standard deviation of a distribution to calculate values at multiples of a standard deviation from the mean. Review the basic properties of a density curve and the specific properties of the normal curve. Show the student how to locate the mean, as well as points within one, two, and three standard deviations of the mean on the normal curve. Model graphing and labeling a normal curve given the mean and standard deviation of a set of normally distributed data. Then provide the student with additional opportunities to draw and label a normal curve given its mean and standard deviation.
Review the 689599.7 rule and demonstrate how to use it. For example, explain to the student that 0.68 of the area under the curve is located within one standard deviation of the mean. Guide the student to use proportions of area under the normal curve as a guide to locating points within one, two, or three standard deviations of the mean.
Review with the student how to use the technology available to graph a normal curve with a given mean and standard deviation.
Consider using the MFAS task Label a Normal Curve (SID.1.4). 
Moving Forward 
Misconception/Error The student is unable to determine the probability that a thread is between 13 and 17 texts. 
Examples of Student Work at this Level The student correctly graphs and labels the normal curve but:
 States the probability is 50% because 13 and 17 are each one standard deviation away from the mean.
 Incorrectly uses the standard normal distribution table and calculates the probability as 84.1%.Â

Questions Eliciting Thinking Can you shade the area under the curve associated with the probability that you are asked to find? Do you know what percent of the values in a normal distribution are in this area?
What do you know about the 689599.7 rule?
How do you calculate a zscore? If you knew the zscores, would you be able to calculate the probability? 
Instructional Implications Make sure the student understands the 689599.7 rule and how it can be used to determine the percentage of data within a given number of standard deviations of the mean. Provide the student with the mean and standard deviation of another set of normally distributed data such as N(72, 12), and ask the student to use the 689599.7 rule to find the percentage of data less than a given value (e.g., less than 72, 60, 48, or 36), greater than a given value (e.g., greater than 72, 84, 96 or 108), and between given values (e.g., between 60 and 84, 48 and 96, or 36 and 108). Eventually, challenge the student to determine the percentage of data between pairs of values that lie between different numbers of standard deviations from the mean (e.g., 48 and 108 or 60 and 96).
Make sure the student understands how to find the zscore associated with a particular value and what it represents in terms of distance from the mean. Then review how to use the zscore and a standard normal distribution table or graphing technology to find the percentage of data within a given number of standard deviations of the mean. Provide the student with the mean and standard deviation of another set of normally distributed data, such as N(35.6, 2.7), and ask the student to find the percentage of data that is not an integer multiple of standard deviations from the mean. For example, ask the student to find the percentage of data that is less than a score of 40. 
Almost There 
Misconception/Error The student provides a correct response but with insufficient reasoning or imprecise language. 
Examples of Student Work at this Level The student correctly sketches and labels a normal curve. However, the student:
 States that the probability is 0.68 or 68% without any supporting work or explanation.
 Shows calculations of zscores and states the probability is 0.68 or 68% without any explanation.

Questions Eliciting Thinking How did you determine that the probability is 68%? What method did you use? 
Instructional Implications Model providing supporting work with a written explanation. Provide clear and consistent expectations for the student with regard to supporting work. Provide the student with the mean and standard deviation of another set of normally distributed data such as N(35.6, 2.7), and ask the student to find the percentage of data that is not an integer multiple of standard deviations from the mean. For example, ask the student to find the percentage of data that is less than a score of 40 with adequate supporting work and explanation. 
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 draws and labels a normal curve with the values 9, 11, 13, 15, 17, 19 and 21. The student correctly determines the probability that a randomly selected thread is between 13 and 17 texts by:
 Calculating the zscores for 13 and 17,
 Determining the associated probabilities, and
 Using these probabilities to calculate the probability that a randomly selected thread is between 13 and 17 texts.
or
 Using the 689599.7 rule to state the probability that a randomly selected thread is within one standard deviation of the mean.
or
 Using a graphing calculator or other technology to determine the probability that a randomly selected thread is between 13 and 17 text is approximately 68.27%.Â

Questions Eliciting Thinking Does the 689599.7 rule apply to all distributions?
When must you use the standard normal distribution table or technology instead of the 689599.7 rule? 
Instructional Implications Challenge the student to find the probability that a randomly selected thread is between 11 and 15 texts or between 13 and 19 texts.
Consider using the MFAS tasks Probability of Your Next Texting Thread (SID.1.4) or Area Under the Normal Curve (SID.1.4). 