In this activity, students individually sort cards of different scatter plots then discuss with a partner. Students sort different scatter plots during this activity. A sorting task gives students opportunities to analyze representations, statements, and structures closely and make connections (MP2, MP7).

Select groups to share their initial categories and how they sorted their scatter plots into the given categories. Attend to the language that students use to describe their categories and scatter plots, giving them opportunities to describe their scatter plots more precisely. Highlight the use of terms like “linear,” “non-linear,” and “positive or negative association.” 
To help clarify the meaning of non-linear association, consider asking:

• “How did you determine if an association is non-linear?” (if the data looks like it’s curving or not in a line)
• “Can a non-linear association show a positive association? What might that look like in a scatter plot?” (Yes, the scatter plot on card F is an example.)
• “If a scatter plot has no association at all (neither linear nor non-linear), what might its scatter plot look like?” (a lot of random dots scattered all around the plot with no obvious trend)

In addition to the type of model appropriate for the data represented in a scatter plot and the positive or negative association, there are other patterns that can be worth noticing before performing a more in-depth analysis. In this activity, students compare scatter plots that have more than one pattern embedded in them. In the discussion following the activity, this feature is identified as clustering.

As students compare the scatter plots in this activity, monitor for students who notice clustering of the data and name it in their own words.

The purpose of this discussion is for students to understand what it means for data to appear in clusters and recognize when they might appear.

Direct students’ attention to the reference created using Collect and Display. Ask previously identified students to share their observations about the scatter plots. Invite students to borrow language from the display as needed and update the reference to include additional phrases as they respond.

Tell students that when data seems to have more than one pattern, it is called ”clustering.“ Clustering of the data like in graphs B, C, and D can reveal hidden patterns. Usually, clustering means there are subgroups within our data that may represent different trends.

For example, in Plot B, the data may represent body measurements of a certain species of bird. Although the data originally came from a group that made sense (a single species), there appear to be subgroups that have a large influence on the data as well. The lower half of the data may represent females and the upper half may represent males, so we can see that there are different patterns within the different subgroups.

When clustering is present, it may be helpful to investigate the cause of the separation and analyze the data within the subgroups rather than as a whole.