Getting Started 
Misconception/Error The student is unable to draw a box plot. 
Examples of Student Work at this Level The student constructs a dot plot, a line graph, or a bar graph with each tree corresponding to a point or bar.

Questions Eliciting Thinking What does a box plot look like? How is it constructed?
What kind of data is graphed on a box plot?
Do you know how to find the median of a set of data? Do you know how to find the other quartiles? 
Instructional Implications If needed, review how to find the median and the quartiles of a set of data. Be sure the student understands the median is the same as the second quartile and should be found first. To find the other quartiles, the student need only find the median of the lower half of the data and the median of the upper half of the data. Include an example in which there are six distinct data points.
Explain the distinction between categorical and quantitative data and be sure the student understands that box plots are used to display quantitative data. Review the five number summary (which includes the lowest value, the three quartiles, and the highest value) and emphasize that box plots are used to display these values in relation to each other. Indicate that box plots always contain an axis with a scale, so the values can be interpreted. Ask the student to find the median of the data set along with the other two quartiles and to write the five number summary on his or her paper. Assist the student in constructing an appropriately scaled number line near which the boxplot will be constructed. Show the student how to construct the box and its â€śwhiskersâ€ť emphasizing the relationship between the five number summary and the parts of the box and whiskers. Ask the student to give the plot a title.
Show the student a variety of examples of box plots including some generated by technology. Pose questions that address various aspects of the box plot [e.g., overall shape, the values of the quartiles, the range of the data, and values between which a portion of the data (such as the middle 50%) falls].
Provide the student with a new set of data and ask the student to construct a box plot that includes all of the necessary components. 
Moving Forward 
Misconception/Error The student produces a graph that is difficult to read or interpret or contains multiple significant errors. 
Examples of Student Work at this Level The student uses a nonlinear scale on the number line.
The box plot is drawn carelessly with precise values of Â difficult to determine.
The value of more than one of the numbers in the five number summary is incorrect. 
Questions Eliciting Thinking In general, what is the five number summary of a data set? How is the five number summary used to construct a box plot? If someone read your box plot, would they be able to accurately read the five number summary?
What was your reason for scaling the axis as you did? Does your axis look like a number line? Is anything missing? Are the coordinates equally spaced? 
Instructional Implications Guide the student to find the five number summary before constructing a box plot. Show the student how to consider the range of values in the data set when scaling the axis. Remind the student that the axis is just a number line (or a portion of it) and should be constructed with a linear scale. Explain that the box plot should be drawn so precisely that a reader could easily identify the five number summary.
Be sure the student understands how to determine the median (or quartiles) when there are an even number of values in the data set. Ask the student to revise his or her graph and provide feedback as needed.
Provide the student with additional opportunities to construct box plots. 
Almost There 
Misconception/Error The student makes an error in calculating or displaying the five number summary. 
Examples of Student Work at this Level The student:
 Places the median line at either 161 or 162.
 Chooses Â to be either the third smallest value or the fourth smallest value.
 Chooses Â to be either the third largest value or the fourth largest value.
 Indicates that Â (or ) is an interval, rather than a number.Â

Questions Eliciting Thinking How should you find the median when there is an even number of values in the data set?
Is Â a number or an interval?
Do , the median, and Â need to be actual data values? 
Instructional Implications Review how to determine the median (or quartiles) when there are an even number of values in the data set. Be sure that the student understands that the quartiles (like the median) are values not intervals. Ask the student to revise his or her graph and provide feedback as needed.
Provide the student with additional opportunities to construct box plots. 
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:
 Indicates that the following constitutes the five number summary: Min = 15, Â = 132, median = 161.5, = 171, Max = 194.
 Includes an appropriately scaled number line.
 Draws and precisely locates the box and whiskers.
 Titles the graph.

Questions Eliciting Thinking Why are Â and Â located where you put them?
Will the shape of the box plot change if you convert the data values to inches?
Can one determine the mean of a data set given only the box plot?
How would the box plot change if each data value were increased by five? 
Instructional Implications Show the student a test for identifying outliers and have the student apply it to the value 15 in the data set. Then show the student how to modify a box plot so that it shows the outliers. Have the student modify his or her box plot to show that 15 is an outlier. 