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, the shape of the images and the values on the horizontal axis of each 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.

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, use these questions to prompt students to discuss those ideas.

• “What do you notice about the shape of each distribution?” (The data are 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.)

Math Community

After the Warm-up, display the class Math Community Chart for all to see and explain that the listed “Doing Math” actions come from the sticky notes students wrote in the first exercise. Give students 1 minute to review the chart. Then invite students to identify something on the chart they agree with and hope for the class or something they feel is missing from the chart and would like to add. Record any additions on the chart. Tell students that the chart will continue to grow and that they can suggest other additions that they think of throughout today’s lesson during the Cool-down.

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.