Getting Started 
Misconception/Error The student makes significant errors in scaling the horizontal axis. 
Examples of Student Work at this Level The student:
 Does not provide a number line or any number references on the box plot.
 Uses the incorrect unit to scale the axis (e.g., “years” rather than “number of attacks”).
 Scales the axis disproportionately.

Questions Eliciting Thinking What is a box plot (or box and whisker plot)? What elements are required to construct one?
What does a number line look like? Are the numbers you used for your axis represented as they would be on a number line? How can you include the needed numbers without using only those numbers?
Can you explain how you scaled the number line? Can the intervals be any width? Does it matter if they are not all the same width?
What is actually graphed on your horizontal axis? Can you provide a scale for this axis? 
Instructional Implications Review the concept of a box plot and explain the important features including minimum, maximum, median, and quartiles which represent the data on an appropriately scaled horizontal axis. Guide the student to construct a box plot of the data in this task. Assist the student in identifying an appropriate range and scale for the horizontal axis. Ask the student to draw and scale the axis. Assist the student in calculating the median and upper and lower quartiles and graphing the data. Then ask the student to label the axis and title the graph. Provide feedback as needed.
Emphasize that the horizontal axis of a box plot is just a portion of a number line that captures the range of data from least to greatest. The horizontal axis should be scaled so the locations of the data points can be readily identified. On the other hand, the scale should allow for the data to be displayed on one line. Guide the student to observe the maximum and minimum values and to select an appropriate scale. Discuss with the student the importance of keeping a consistent scale on the number line.
Show the student a variety of examples of box plots including some generated by technology. Describe features of the scale that make it appropriate to the data.
Provide additional opportunities to create box plots for sets of data. 
Moving Forward 
Misconception/Error The student does not accurately or appropriately represent the data. 
Examples of Student Work at this Level The student makes significant errors when calculating and/or graphing the fivenumber summary (e.g., minimum, first quartile, median, third quartile, and maximum). The student:
 Makes errors calculating the median and/or quartiles.
 Calculates and graphs other measures (e.g., mean, range) not needed for a box plot.
 Graphs the measures incorrectly on the number line.
 Marks and labels the five key numbers on the number line without drawing the “box and whiskers.”

Questions Eliciting Thinking What are the key numbers you need in order to summarize data in a box plot? How do you find each one?
How must you organize the data in order to find the median?
Can you check the accuracy of the location of the points you graphed?
Now that you have labeled your five key numbers, can you draw the “box” and “whiskers” to relate the values? 
Instructional Implications Review relevant vocabulary including minimum, maximum, quartiles and median, the method for determining each measure, and how the summary is used to construct a box plot. Be sure the student understands that the median is the same as the second quartile and should be found first. 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 given data set along with the other quartiles and to create the box plot.
Explain that the quartiles divide the data into four groups each containing 25% of the data. Then show the student how to calculate the interquartile range (IQR). Emphasize that the IQR describes the range of the middle 50% of the data. Explain that a small IQR indicates little variability (spread) in the middle portion of the data and a large IQR indicates great variability (spread) in the middle portion of the data. Remind the student that the IQR is a good measure of spread when the median is used as a measure of center and when there are outliers in the data.
Provide a checklist of features the box plot must contain:
 An appropriately scaled number line,
 Vertical segments at the quartiles including the median,
 A box encompassing the interquartile range,
 Points locating the extremes (maximum and minimum),
 Horizontal lines (“whiskers”) from the box to the extremes,
 An axis label, and
 A title.
Provide additional data sets and ask the student to calculate the fivenumber summary and construct box plots.

Almost There 
Misconception/Error The student makes a minor error in some component of the box plot. 
Examples of Student Work at this Level The student scales the axis correctly and constructs a box plot but makes one or more of the following errors:
 Makes an error calculating a quartile.
 Graphs a number inaccurately on the number line.
 Does not include a title and/or label the axis.
 Omits a number inadvertently from the data, but has a correct box plot for the data used.
 Graphs the fivenumber summary correctly but does not name/label them.

Questions Eliciting Thinking Can you verify your calculations for each of your five key numbers?
Can you verify where you placed each value on the number line?
What title and label should your box plot have?
How many data points should you have recorded when you reordered your data? Can you verify which one(s) is missing?
What are each of these numbers called that you graphed? What does each mean? 
Instructional Implications Provide feedback regarding any errors made and ask the student to revise his or her work. Provide a checklist of features the box plot must contain:
 An appropriately scaled number line,
 Vertical segments at the quartiles including the median,
 A box encompassing the interquartile range,
 Points locating the extremes (maximum and minimum),
 Horizontal lines (“whiskers”) from the box to the extremes,
 An axis label, and
 A title.
Pair the student with a classmate to verify work and offer suggestions for improvement.
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 correctly scales the axis using reasonable limits, finds and graphs the fivenumber summary (minimum = 11, = 15.5, median = 23, = 29, and maximum = 34), draws the box and whiskers, and includes an axis label and title.

Questions Eliciting Thinking Are you able to calculate the mean using the box plot? Explain.
Would you be able to reconstruct the original list of data by looking at the box plot? Explain.
If one new value of 40 were added to the data, how would that change the look of the box plot you drew? 
Instructional Implications Challenge the student to explain how each statistical measure represented in the box plot summarizes the data set. Ask the student to calculate and interpret the interquartile range.
Provide the student with additional opportunities to summarize statistical data using a variety of graphs by implementing the MFAS tasks Basketball Histogram and Chores Data (6.SP.2.4). 