In this activity, students analyze the sides and angles of quadrilaterals with attention to the presence of parallel and perpendicular lines. Students are given a set of shapes (a subset of the cards used in previous lessons) and prompted to look for quadrilaterals that have certain attributes. They also have an opportunity to propose an attribute for their partner to find, and make some general observations about the sides and angles of quadrilaterals.

In the Activity Synthesis, when discussing quadrilaterals with two pairs of parallel sides, introduce the term parallelogram. Students are not required to know the definition of this term at this point, and should not be assessed on it.

• “Let’s use our arms to show what parallel lines look like.” (Students hold up two arms parallel to each other.)
• “How did you decide if the sides of a figure are parallel?” (Check if the distance between them is always the same. Extend the sides to see if the lines would eventually meet.)
• As needed, place a ruler between the extended arms of a student to illustrate checking for parallelism.
• “How did you know if any sides are perpendicular?” (Check if the sides make a right angle.)
• Ask students to share their completed sentences for the last question. Record their responses and invite the class to agree or disagree.
  • Some quadrilaterals . . .
  • All quadrilaterals . . .
  • No quadrilaterals . . .
• Explain to students that quadrilaterals with two pairs of parallel sides are called parallelograms.
• Ask students to identify all the parallelograms in the set of cards. (D, K, N, U, Z, AA, EE, JJ)
• “We may know some of these figures by other names like rectangle or rhombus, but as long as the quadrilaterals have two pairs of parallel sides, they are also parallelograms.”

In this activity, students begin to formalize their understanding of the attributes of some shapes they have worked with since IM Grades 2 and 3. Students use their observations from the previous activity to draw general conclusions about rectangles, squares, parallelograms, and rhombuses. The conclusions may be incomplete at this point.

Students are not expected to recognize that the attributes of one shape may make it a subset of another shape (for example, that squares are rectangles, or that rectangles are parallelograms). They may begin to question these ideas, but the work to understand the hierarchy of shapes will take place formally in IM Grade 5. During the Activity Synthesis, highlight how sides and angles can help us define and distinguish various two-dimensional shapes.

When students describe the sides and angles in the shapes they use language precisely (MP6) and observe common structure in the different sets of quadrilaterals (MP7).

• For each set of quadrilaterals, select one group to share their poster of statements. Invite other students to suggest amendments or corrections if they disagree.
• “Rectangles and parallelograms share many attributes. What makes them different?” (To be a rectangle, all angles must be equal or must be right angles.)
• “Rectangles and squares share many attributes. What makes them different?” (To be a square, all sides must have the same length.)
• “Rhombuses and squares share many attributes. What makes them different?” (To be a square, all angles must be equal or must be right angles.)

In this optional activity, students work with a partner to practice naming and looking for certain attributes in quadrilaterals. Each partner has a chance to select a particular attribute that a quadrilateral might have and to find examples and non-examples. Their partner must deduce the attribute they chose based on the examples and non-examples.

Students may choose familiar attributes—lengths of sides, presence of certain types of angles, parallelism, or perpendicularity—or pick a one that is much narrower or broader. In the Activity Synthesis, consider discussing how the specificity of an attribute affects the guessing process.

• Invite students to share the attributes they chose. Ask them to reflect on the process of deducing the attributes from examples and non-examples.
• “Was there an attribute that was particularly tricky to figure out? What about the examples and non-examples might have made it hard to guess?” (The examples and non-examples had many attributes in common. There are not enough examples in the set. The attribute is very specific—for example, one angle that is greater than but less than .)