The purpose of this activity is for students to sort two-dimensional shapes into categories that make sense to them. Students may have leftover shapes, depending on how they sort.

Monitor for and select students with the following approaches to share in the Activity Synthesis:

• Sort by nondefining attributes (color, orientation, size).
• Sort by defining attributes (straight sides and curved sides, number of sides, number of corners).
• Sort by shape names (triangle, square, rectangle), with or without describing the defining attributes.

The sorting approaches are sequenced, from ways students may use nondefining attributes to ways they may use defining attributes to describe the shapes in different ways. They will learn more about the attributes that define shapes in future activities. Aim to elicit both key mathematical ideas and a variety of student voices, especially students who haven't shared recently. As students work, encourage them to refine their descriptions of the shapes, using more precise language and mathematical terms (MP6).

• Invite previously selected students to share in the given order. Record or display their work for all to see.
• Connect students’ approaches by asking:
  • “What is the same about the way they sorted their shape cards? What is different?” (They all found cards that were the same and put them in a group.  They all sorted the cards into different groups. They all have leftover shapes.)
• Connect students’ approaches to the learning goal by asking:
  • “What do you think they named this group?” (gray shapes, shapes with 4 sides, triangles)
  • “Why do you think they named it that?” (All shapes in that group are gray and no shapes in the other groups are gray. All shapes in the group have no corners and all other shapes have corners.)
• Repeat for one group in each sort.

The purpose of this activity is for students to practice using language to describe two-dimensional shapes. Students sort shape cards into groups of the same shape and share what they notice with their partner. This sorting task gives students opportunities to closely analyze triangles, squares, and rectangles and make connections (MP7). As students work, encourage them to refine their descriptions of the shapes, using more precise language and mathematical terms (MP6).

Before beginning this activity, be sure to remove the student sorts that were displayed in the previous activity.

• Display a group of rectangles, a group of squares, and a group of triangles.
• Display a square that has not been sorted.
• “Tell your partner what group you would put this shape into and why.” (I would put it with the squares, because it has 4 straight sides. I would put it with the squares, because it has square corners.)
• “How did you explain to your partner the group in which this shape would fit?” (I told them how many sides I saw. I explained that it is a square because all sides are the same length.)
• As students share, highlight language such as “triangle,” “square,” “rectangle,” “corners,” and “sides.”
• If needed, ask: “Why didn’t you put this shape with the rectangles?” (Squares have all sides the same length, but rectangles have 2 sides that are longer than the other 2 sides. Squares have four sides, but triangles have three sides.)