Lesson 26

Surface Area of Composite Shapes

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SWBAT find the surface area of composite shapes

Big Idea

If a student can find the area of a basic polygon, they can find the surface area of a composite shape.


10 minutes

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. 


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.

Introduction Part 2

5 minutes

Problem Solving

15 minutes

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.   

Exit Ticket

5 minutes

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.