Lesson 3

The purpose of this warm-up is to elicit the idea that distributions can be discussed in terms of shape, which will be useful when students describe data displays in a later activity. While students may notice and wonder many things about these images, shape and the values on the horizontal axis are the important discussion points. This prompt gives students opportunities to see and make use of structure (MP7). The specific structure they might notice is that data sets with different values can have distributions with the same shape if all of the values in the data set are increased or decreased by the same value.

Display the dot plots for all to see. Ask students to think of at least one thing they notice and at least one thing they wonder. Give students 1 minute of quiet think time, and then 1 minute to discuss the things they notice with their partner, followed by a whole-class discussion.

Ask students to share the things they noticed and wondered. Record and display their responses for all to see. If possible, record the relevant reasoning on or near the image. After all responses have been recorded without commentary or editing, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to respectfully disagree, ask for clarification, or point out contradicting information. If the shape of the distribution and the values on the horizontal axis of each dot plot do not come up during the conversation, ask students to discuss these ideas using these questions.

• “What do you notice about the shape of each distribution?” (The data is distributed in exactly the same way in each dot plot.)
• “What is the most frequent value in each dot plot?” ($4 and $11)
• “What is the value of the highest tip in each dot plot?” ($10 and $17)
• “What is the value of the lowest tip in each dot plot?” ($1 and $8)
• “What happens if $7 is added to each of the tips in the first dot plot?” (You get the data distribution in the second dot plot.)

In this lesson, students create and display a dot plot and a box plot using numerical data 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 family (last) 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, what is the furthest, in miles, that each student in this class has ever been from home? {50, 50, 50, 100, 200, 200, 250, 250, 300, 300, 300, 500, 500, 500, 500, 500, 500, 800, 1000, 2000}
• 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. Provide an example display and ask the class to give answers for the questions in the task about the example to help students understand the types of responses expected.

Arrange students in groups of 2–4 and assign each group one of the statistical questions for which students already collected numerical data. Provide each group with tools for creating a graphical display. Ask students to pause after the second question for the gallery walk.

Students may neglect including 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 they refer back to their work in the previous lesson.

The goal is to make sure students understand how to represent a distribution of data data using a dot plot, histogram, and a box plot, and to interpret each distribution in the context of the data. The purpose of the discussion is to elicit evidence of student thinking about the distributions. Here are some questions for discussion.

• “What are some ways you summarized the information in the display?” (The data were clustered around one value. The dot plot showed this but the box plot did not. The box plot shows the median as a typical value.)
• “If you collected data from all the students in the school, instead of just your classmates, which would you rather create, a dot plot or a box plot? Why?” (A box plot because all you have to do is find the five number summary. In a dot plot, you would 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 were very spread apart.)
• “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 displayed the quartiles and the median.)