Geometry

Lesson 5

Math

Unit 7

6th Grade

Lesson 5 of 17

Objective


Find the area of polygons using composition and decomposition.

Common Core Standards


Core Standards

  • 6.G.A.1 — Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

Foundational Standards

  • 3.MD.C.7.D
  • 4.MD.A.3

Criteria for Success


  1. Understand that polygons can be decomposed into different shapes in order to find the total area, or polygons can be built around the shape and the extra area can be subtracted to find the area of the original polygon. 
  2. Use multiple strategies to find the area of polygons using composition and decomposition.
  3. Find the area of a trapezoid using composition and decomposition.

Tips for Teachers


Students will have further opportunities to find the area of irregular polygons using composition and decomposition in Lessons 7–9; in these lessons, the polygons will be located in the coordinate plane.

Fishtank Plus

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

Anchor Problems


Problem 1

Jung's teacher drew a shape on the board (shown below), and asked the students to find the area of the shape. Describe a method Jung could use to find the area and then determine the area. 

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Problem 2

Find the area of the trapezoid below in three different ways by:

a.   Drawing a rectangle around the trapezoid and subtracting the additional area around it

b.   Dividing the trapezoid into two triangles using a diagonal line across the trapezoid

c.   Dividing the trapezoid into two right triangles and a rectangle

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Problem 3

Find the area of the triangle in the grid below.

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

Problem Set

Fishtank Plus Content

Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task


Find the area that is shaded in each figure.

a.   

b.   

c.   

d.   

Student Response

Create a free account or sign in to view Student Response

References

Illustrative Mathematics Finding Areas of Polygons

Finding Areas of Polygons, accessed on July 1, 2016, 9:08 a.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by Fishtank Learning, Inc.

Additional Practice


The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

icon/arrow/right/large copy

Lesson 4

icon/arrow/right/large

Lesson 6

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Area of Triangles, Quadrilaterals, and Polygons

Topic B: Polygons in the Coordinate Plane

Topic C: Volume of Rectangular Prisms

Topic D: Nets and Surface Area

Request a Demo

See all of the features of Fishtank in action and begin the conversation about adoption.

Learn more about Fishtank Learning School Adoption.

Contact Information

School Information

What courses are you interested in?

ELA

Math

Are you interested in onboarding professional learning for your teachers and instructional leaders?

Yes

No

Any other information you would like to provide about your school?

Effective Instruction Made Easy

Effective Instruction Made Easy

Access rigorous, relevant, and adaptable math lesson plans for free