In this activity, students analyze a set of 36 two-dimensional figures, choose an attribute for classifying the figure, and then sort them into several categories. After sorting, students have opportunities to test and refine their decisions—first by discussing their categories with another group, and then by removing the labels of their categories to see if a second group of peers could identify how the shapes are sorted. To encourage students to think beyond two categories (for example, “triangles” and “not triangles”), the task specifies 3–5 categories.

During Activity Synthesis, collect the categories that students generate. Students will likely use informal language in describing their categories (for example, “they have all the same sides” or “the sides are slanted the same way”). Encourage students to use more precise mathematical language (MP6) and support them in doing so by revoicing their ideas (for example, “all sides have the same length” for “all sides are the same”).

This activity uses MLR2 Collect and Display. Advances: Conversing, Reading, Writing

• “What were some of the categories you used to sort the figures?”
• As students share responses, update the display by adding (or revising) language, diagrams, or annotations.
• Point out to students that some categories had to do with the sides of the figures and others had to do with the angles.
• Remind students to borrow language from the display in the next activity.

In the first activity, students sorted a given set of figures based on one or more attributes. In this activity, they continue that work in groups of two. Quietly, one partner chooses a geometric attribute, defines a category (for instance, “figures with no parallel sides”), and finds several figures that fit and don’t fit the category. The other partner makes a conjecture about what the category is, first by looking for a common attribute in the given examples (or absence of a common attribute in the non-examples), and then testing a few more figures that they think belong or don’t belong. Consider playing a quick round as a class to clarify directions.

As students look for an attribute shared by one set of figures but not by another, they identify a mathematical property or structure (MP7).

• “Who used a brand new category while playing? What was it?”
• Add any new categories to the list from the first activity, again organizing by attribute.