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 three to calculate the values that are within one, two, and three standard deviations of the mean.
 Draws a normal curve and correctly calculates the values that are within one, two, and three standard deviations of the mean but incorrectly locates them.Â

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 the 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 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 tasks Label a Normal Curve (SID.1.4) or Range of Texting Thread (SID.1.4). 
Moving Forward 
Misconception/Error The student is unable to determine the probability that a thread is at least 13 texts. 
Examples of Student Work at this Level The student correctly graphs and labels the normal curve but:
 Finds the probability of a thread containing 13 or fewer texts.
 Finds the correct zscore but does not subtract that value from one.

Questions Eliciting Thinking What probability are you being asked to find? What is another way to say â€śat least 13â€ť?
Can you shade the area under the curve that you are being asked to find? You stated the probability as 90.8%. Does this answer make sense considering what you shaded? 
Instructional Implications 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 less than or greater than a given value. 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.
Provide the student with several examples of zscore calculations that contain mistakes and have the student identify and correct the errors. These errors may come from other Moving Forward studentsâ€™ work.
Consider using the NCTM task Should We Send Out a Certificate? (http://www.illustrativemathematics.org/illustrations/1218). 
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 and states that the probability is 9.18% but provides no supporting work or explanation. 
Questions Eliciting Thinking How did you determine the probability? 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.
Consider using the NCTM task Should We Send Out a Certificate? (http://www.illustrativemathematics.org/illustrations/1218). 
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 0, 3, 6, 9, 12, 15, and 18. The student correctly determines the probability of a randomly selected thread containing at least 13 texts by:
 Calculating the zscore for 13 and
 Using a graphing calculator (or other technology) or a standard normal distribution table to find the associated probability.

Questions Eliciting Thinking Could you have used the 689599.7 rule? Why or why not? 
Instructional Implications Consider using the NCTM lessons SAT Scores (http://www.illustrativemathematics.org/illustrations/216), Should We Send Out a Certificate? (http://www.illustrativemathematics.org/illustrations/1218) or Do You Fit In This Car? (http://www.illustrativemathematics.org/illustrations/1020).
Consider using the MFAS task Area Under the Normal Curve (SID.1.4). 