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Keep students in groups of 2. Allow 2 minutes quiet think time followed by partner and whole-class discussion.
Use Collect and Display to create a shared reference that captures students’ developing mathematical language. Collect the language students use to describe the scatter plots. Display words and phrases, such as “groups,” “subgroups,” “clusters,” “trends,” and “associations.”
Find groups of 2 or 3 scatter plots that share something in common that the others do not. What do they have in common?
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.