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# Surface Area of Composite Shapes

Lesson 26 of 37

## Objective: SWBAT find the surface area of composite shapes

#### Introduction

*10 min*

I’ll start the lesson by holding up a model of a rectangular prism. I’ll ask several questions and **cold call **students to respond. The questions will include: What is this shape? How many faces are there? What shapes are the faces? How can I find the surface area of this shape? I will then hold up a rectangular pyramid followed by a cylinder and ask the same questions. The purpose of this is to warm students’ brains up and refresh their memories about the work we’ve already done.

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Next I will place the base of the pyramid on top of the corresponding base of the prism. My models have congruent bases. I’ll ask my students what the shape is called. I don’t know the name for it so I suspect they won’t either – we’ll just agree to call it a composite shape. We will define composite shapes as an object made up of at least two basic shapes. I’ll then ask (**think-pair-share**) the students how we can find the surface area of this shape. Students will be putting two mathematical practices to use during this part of the discussion: **MP1** as students work to make sense of the problem by applying what they already know about surface area to an unfamiliar shape; **MP7** as students switch views between seeing the composite shape as one whole object that is composed of several faces of common polygons. I will take notes on the SmartBoard to record various answers about how we could find the surface area of the shape. These notes will serve as a reference for students when they begin finding surface area in later sections of this lesson.

Next I’ll place the cylinder on the rectangular prism. I’ll again ask for the name of the shape and how to find its surface area. This one is a bit more challenging due to the placement of the cylinder. I’ll be looking for student answers to be very precise (**MP6**) especially when discussing the surfaces of the shape. I will again take notes of the answers.

My hope is that by the end of this introduction, students will be prepared to solve any of the problems in the later parts of the lesson. If students get “stuck” later in the lesson, I will point them to the list that they took part in creating.

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#### Problem Solving

*15 min*

Now it’s time to actually find the surface area of some composite shapes. I included the first question to assess whether students understand that they cannot simply find the sum of the surface areas of the two solids that make up the composite solid. It also gives students a chance to practice critiquing the reasoning of others and constructing a viable argument (**MP3**). Problems 2 and 3 area shapes look like the shapes we spent the last two parts of the lesson discussing. If time is an issue, I would suggest having everyone work on problems 1-3 and then given them a choice of either 4 or 5. Before beginning, I’ll remind my students to list their steps in a neat and organized fashion. I will ask them to label the parts of their work so that I (and anyone) can understand how they came across their answers.

Students may use any notes or their neighbors as a reference during this part of the work. I will be walking around with my own solutions to check in to see how work is going. If I see anything amiss I will stop and ask students to explain their work. If I ask any questions, they will be similar to those in section 2 of the lesson.

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#### Exit Ticket

*5 min*

The two items on the exit ticket are very similar to the two composite shapes that we spent the most time discussing throughout the lesson. As I assess the exit ticket, I will not be as concerned with a final number. I want to see how students “take apart” the shape in order to find the areas of each surface.

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- LESSON 1: Explore Perimeter and Area of Composite Shapes
- LESSON 2: Perimeter of Irregular Rectilinear Shapes
- LESSON 3: Area of Composite Shapes Using a Grid
- LESSON 4: Area of Composite Shapes
- LESSON 5: Area of Regions Formed by Inscribed Shapes
- LESSON 6: CORNERSTONE:Circle Ratios: Diameter to Radius; Circumference to Diameter
- LESSON 7: CORNERSTONE: Circumference Formula
- LESSON 8: Area of a Circle
- LESSON 9: Circumference & Area Fluency Practice
- LESSON 10: Finding the Radius From a Given Circumference or Area
- LESSON 11: Circumference from Area / Area from Circumference
- LESSON 12: Circle Designs: Finding the Area and Perimeter of Shapes Composed of Arcs and Line Segments
- LESSON 13: Assessment_Area and Perimeter (Circumference) of Composite Shapes and Circles
- LESSON 14: Drawing Prisms & Pyramids
- LESSON 15: Describe Prisms and Pyramids Using Algebra
- LESSON 16: Using Nets to Find the Surface Area of Prisms
- LESSON 17: Using a Formula to Find the Surface Area of Prisms
- LESSON 18: Finding the surface area of triangular prisms using a net
- LESSON 19: Finding the Surface Area of a Triangular Prism Using A Formula
- LESSON 20: Discovering the Formula for the Surface Area of A Cylinder
- LESSON 21: Finding the Surface Area of Cylinders Using a Formula
- LESSON 22: Practice Day: Surface Area of Prisms & Cylinders
- LESSON 23: Surface Area of Prisms and Cylinders Assessment
- LESSON 24: Finding the Surface Area of Pyramids Using Nets
- LESSON 25: Finding the Surface Area of Pyramids Using a Formula
- LESSON 26: Surface Area of Composite Shapes
- LESSON 27: Surface Area of Composite Shapes With Holes
- LESSON 28: Surface Area Assessment
- LESSON 29: 3-D Models from 2-D Views
- LESSON 30: Exploring Volume and Surface Area with Unifix Cubes
- LESSON 31: Explore Volume of Rectangular Prisms
- LESSON 32: Find the Volume of Prisms Using a Formula
- LESSON 33: Volume Of Cylinders Using a Formula
- LESSON 34: Volume of Composite Shapes
- LESSON 35: Volume and Surface Area - Accelerated Math Fluency Day
- LESSON 36: Volume of Pyramids
- LESSON 37: Surface Area and Volume Final Assessment