Lesson objective: Extend understanding that in addition to categories of two-dimensional figures, we can also have subcategories as well.

Students bring prior knowledge of shapes in different categories (rhombuses, rectangles, etc.) sometimes sharing attributes from 3.G.A.1. This prior knowledge is extended to classification into subcategories as students explore common attributes of quadrilaterals. A conceptual challenge students may encounter is understanding that when a new classification is identified, a prior one still applies (i.e. rectangles are still parallelograms even though they belong to a new subcategory).

The concept is developed through work with Venn diagrams, which allow students to vizualize the common attributes of each category and subcategory.

This work helps students deepen their understanding of equivalence because some two-dimensional figures have classifications based on congruency (i.e. isosceles triangles have two congruent sides).

Students engage in Mathematical Practice 7 (look for and make use of structure) as they use and create organized structures for categories of shapes, to visualize the relationships between different plane figures.

**Key vocabulary:**

- attribute
- classification
- parallel
- parallelogram
- perpendicular
- quadrilateral
- trapezoid