A Gallery of Data

5 min

Narrative

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.

Launch

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.

Student Task

The dot plots represent the distribution of the amount of tips, in dollars, left at 2 different restaurants on the same night.

What do you notice? What do you wonder?

<p>Dot plot from 0 to 11 by 1’s. tip amount (dollars). Beginning at 0, number of dots above each increment is 0, 1, 2, 3, 4, 2, 1, 1, 2, 1, 1, 0.</p>

<p>Dot plot from 7 to 18 by 1’s. tip amount (dollars). Beginning at 7, number of dots above each increment is 0, 1, 2, 3, 4, 2, 1, 1, 2, 1, 1, 0.</p>

Sample Response

Things students may notice:

  • The shape of the distribution is the same.
  • The second dot plot is the same data shifted up $7.

Things students may wonder:

  • What would a box plot of the data look like?
  • What would a dinner cost that had a $17 tip?

Synthesis

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.

Standards
Addressing
  • HSS-ID.A.1·Represent data with plots on the real number line (dot plots, histograms, and box plots).
  • S-ID.1·Represent data with plots on the real number line (dot plots, histograms, and box plots).
  • S-ID.1·Represent data with plots on the real number line (dot plots, histograms, and box plots).
  • S-ID.1·Represent data with plots on the real number line (dot plots, histograms, and box plots).
Building Toward
  • HSS-ID.A.2·Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.
  • S-ID.2·Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.
  • S-ID.2·Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.
  • S-ID.2·Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.

25 min