Lesson plan

# Lesson 11: Polygons

teaches Arizona State Standards 6.G.A.1
teaches Common Core State Standards MP1 http://corestandards.org/Math/Practice/MP1
teaches Common Core State Standards MP7 http://corestandards.org/Math/Practice/MP7
teaches Common Core State Standards MP6 http://corestandards.org/Math/Practice/MP6
teaches Common Core State Standards 6.G.A.1 http://corestandards.org/Math/Content/6/G/A/1
teaches Georgia State Standards MGSE6.G.1.
teaches Kansas State Standards 6.G.1.
teaches New York State Standards NY-6.G.1.
teaches Ohio State Standards 6.G.1.
teaches Pennsylvania State Standards CC.2.3.6.A.1.

# Lesson 11: Polygons

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).

Lesson overview

• 11.1 Warm-up: Which One Doesn’t Belong: Bases and Heights (5 minutes)
• 11.2 Activity: What Are Polygons? (20 minutes)
• 11.3 Activity: Quadrilateral Strategies (15 minutes)
• Includes "Are you Ready for More?" extension problem
• 11.4 Optional Activity: Pinwheel (30 minutes)
• Lesson Synthesis
• 11.5 Cool-down: Triangulation (5 minutes)

Learning goals:

• 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).

Learning goals (student facing):

• Let’s investigate polygons and their areas.

Learning targets (student facing):

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

Required materials:

• geometry toolkits

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.

Glossary:

• 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.

• Access the complete Grade 6 glossary.

Standards

• This lesson builds on the standards:CCSS.4.G.A.2MS.4.G.2MO.4.GM.A.2 CCSS.5.G.BMO.5.GM.A
• This lesson builds towards the standard:CCSS.6.G.A.1MS.6.G.1MO.6.GM.A.1

IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 2017-2019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/math-curriculum/.