In this lesson, students create and display a dot plot and a box plot using numerical data that they collected from a survey question in a previous lesson. The focus of the lesson is on creating graphical displays of data, so appropriate data sets take precedence over the class’s actual data. Here are sample data sets for each of the four questions from the previous lesson.

• On average, how many letters are in the preferred names for students in this class? {4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 9, 10}
• On average, how many speed limit signs do students in our class see on the way to school? {2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 7, 7}
• About how long did it take students in this class to get to school this morning? {5, 5, 5, 5, 10, 10, 12, 15, 15, 15, 15, 25, 25, 25, 25, 30, 35, 40, 45, 55}
• On average, how many movies in the theater did each student in the class watch this summer?  {0, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 3, 4, 6, 6, 7, 7, 8, 10, 12}
• After groups have had a chance to complete their displays, pause the class to discuss how to do a gallery walk. To help students understand the types of responses expected, provide an example display. Ask the class to refer to the example and to answer the questions in the task.

This is the first time Math Language Routine 7: Compare and Connect is suggested in this course. In this routine, students are given a problem that can be approached using multiple strategies or representations, and they record their methods for all to see. They then compare and identify correspondences across strategies by means of a teacher-led gallery walk with commentary or teacher think-aloud (such as "I notice . . . .” or I wonder . . . ."). As they compare their own strategy to that of others, a typical discussion prompt is “What is the same and what is different?”. The purpose of this routine is to allow students to make sense of mathematical strategies and, through constructive conversations, develop awareness of the language used as they compare, contrast, and connect other ways of thinking to their own.

Students may neglect to include titles for axes and may forget the importance of building their plots on a number line with equally spaced intervals. Monitor for groups that do not recall the details of making the different types of displays, and suggest that they refer back to their work in the previous lesson.

The purpose of the discussion is to elicit evidence of the students’ thinking about the data in the displays and interpretation of the distributions in context.

Invite groups to share their displays. After all strategies have been presented, use Compare and Connect to help students compare, contrast, and connect the different representations. Ask,

• “What is the same and what is different about each display?”
• “How did the comments help you understand the displays?”
• “Are there any benefits or drawbacks to one representation compared to another?”
• “What are some ways you summarized the information in the display?” (The data are clustered around one value. The dot plot shows this but the box plot does not. The box plot shows the median as a typical value.)
• “If you had collected data from all of the students in the school, instead of just from your classmates, would you rather create a dot plot or a box plot? Why?” (A box plot because all I’d have to do is find the five-number summary. In a dot plot, I’d have to plot every point, and that might be hard to do with the tools that I have).
• “What is the shape of the distribution in your dot plot?” (The data are very spread apart, but mostly evenly distributed.)
• “What information is displayed by the dot plot that is not displayed by the box plot?” (The dot plot displays all the values in the data set.)
• “What information is displayed by the box plot that is not displayed by the dot plot?” (The box plot displays the quartiles and the median.)