In this lesson, students explore the defining characteristics of polygons. Then they find the areas of polygons by decomposing the regions into triangles or parallelograms.

Students have worked with polygons in earlier grades and throughout this unit without having a formal term for this category of shapes. This lesson prompts them to examine examples and non-examples of polygons and write a definition for a polygon. There are many different accurate definitions for a polygon. The goal is not to find the most succinct definition possible, but to articulate the defining characteristics of a polygon in a way that makes sense to students.

Then students reason about the areas of quadrilaterals on a grid. The lesson also includes an optional activity that involves finding the area of a polygon in the shape of a pinwheel. The activity is an opportunity for students to apply familiar reasoning strategies to find the area of a more complex figure—a polygon with 8 sides.

The work here allows students to see that the area of a polygon can be found by decomposing it into triangles. In observing and using this fact, students look for and make use of structure (MP7).

Today’s math community building time has two goals. The first is for students to make a personal connection to the math actions chart and to share on their Cool-down the math action that is most important to them. The second is to introduce the idea that the math actions that students have identified will be used to create norms for their mathematical community in upcoming lessons.