Lesson objective: Understand that categories of shapes are based on their geometric properties.

Students bring prior knowledge of shapes in different categories (rhombuses, rectangles, etc.) may share attributes from 3.G.A.1, and triangles can be categorized based on their angle types from 4.G.A.2. This prior knowledge is extended to categorizing shapes by multiple attributes as students change classifications based on different geometric properties. A conceptual challenge students may encounter is understanding attributes don't change but classifications can.

The concept is developed through work with polygons, which represent both shared and unique attributes for students to compare.

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
- congruent (congruency)
- parallel
- perpendicular