# Lesson 11

Polygons

### Lesson Narrative

Students have worked with polygons in earlier grades and throughout this unit. In this lesson, students write a definition that characterizes polygons. There are many different accurate definitions for a polygon. The goal of this lesson is not to find the most succinct definition possible, but to articulate the defining characteristics of a polygon that makes sense to students.

Another key takeaway for this lesson is that the area of any polygon can be found by decomposing it into triangles. The proof that all polygons are triangulable (not a word students need to know) is fairly sophisticated, but students can just take it as a fact for now. In observing and using this fact students look for and make use of structure (MP7).

### Learning Goals

Teacher Facing

• Compare and contrast (orally) different strategies for finding the area of a polygon.
• Describe (orally and in writing) the defining characteristics of polygons.
• Find the area of a polygon, by decomposing it into rectangles and triangles, and present the solution method (using words and other representations).

### Student Facing

Let’s investigate polygons and their areas.

### Required Preparation

If doing the optional Pinwheel activity, prepare one copy of the blackline master for every group of 4 students. If larger paper (and a photocopier that can accommodate it) is available, it would be helpful to have larger-format copies of this.

### Student Facing

• I can describe the characteristics of a polygon using mathematical vocabulary.
• I can reason about the area of any polygon by decomposing and rearranging it, and by using what I know about rectangles and triangles.

Building On

Building Towards

### Glossary Entries

• polygon

A polygon is a closed, two-dimensional shape with straight sides that do not cross each other.

Figure $$ABCDE$$ is an example of a polygon.