In IM Grade 3, students understand that different shapes may share attributes. They learn that shapes with four sides are part of a larger category of shapes, called quadrilaterals. In IM Grade 4, students classify two-dimensional shapes by attributes, such as angle sizes, and the presence of perpendicular or parallel lines containing the sides.

In this lesson, students sort quadrilaterals into categories in a way that makes sense to them, with an emphasis on side lengths, angles, perpendicular sides, and parallel sides. Students may begin to notice some relationships between categories of quadrilaterals. For example, they might notice that squares have 4 right angles like rectangles and their opposite sides are parallel like parallelograms. These relationships will be brought out more fully in the next several lessons. Students should have access to straight edges, protractors, and patty paper throughout this lesson.

In the next lesson, students consider subcategories within the hierarchy of quadrilaterals. Did students discuss subcategories or a hierarchy during today’s lesson? What questions can you ask tomorrow to encourage students to think about a hierarchy?