The purpose of this Warm-up is to elicit the idea that the same data can be displayed in different ways, which will be useful when students create different data displays in a later activity. While students may notice and wonder many things about these images, the comparison of the three representations and interpreting the information in each representation are the important discussion points.

This prompt gives students opportunities to see and make use of structure (MP7). Specifically, they might use the structure of the three representations, particularly the structure of the horizontal number line, to find mathematically important similarities in how the same set of data is represented.

Ask students to share the things they noticed and wondered. Record and display their responses without editing or commentary for all to see. If possible, record the relevant reasoning on or near the images. Next, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to observe what is on display and to respectfully ask for clarification, point out contradicting information, or voice any disagreement.

The goal is to help students recall different ways to represent distributions of data. Highlight the similarities between the dot plot and the histogram. Tell students that the tallest bar in the histogram is created from the two data values at 5 and the six data values at 5.5 in the dot plot, and that the final bar is created from the two data values at 6 and the two data values at 6.5 in the dot plot. If time permits, discuss questions such as

• “Which representation(s) shows all the data values?” (The dot plot shows all the data values.)
• “How do you create a box plot?” (You calculate the values for the five-number summary and then graph them on a number line. The first quartile, the median, and the third quartile are used for the box, and the minimum value and maximum value are used for the whiskers.)

The mathematical purpose of this activity is to represent and analyze data with histograms. Students will create two different histograms from the same data set by organizing data into different intervals.

The mathematical purpose of this activity is to represent the distribution of data on the real number line with a box plot and to help students think informally about the median as a measure of center. Students calculate the values for the five-number summary and create a box plot. The median, quartiles, and extreme values split the data set into four intervals, with approximately the same number of data values in each. Students interpret these values in the given context (MP2). Although these intervals are often called “quartiles,” the term “quarters” is used in these materials to avoid confusion with the quartile values Q1 and Q3.