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# Discovering the Formula for the Surface Area of A Cylinder

Lesson 20 of 37

## Objective: SWBAT use a cylinder net to discover the formula for the surface area of a circle

## Big Idea: A mysterious & hieroglyphic looking formula quickly becomes familiar and student friendly.

*30 minutes*

#### Lesson Beginning

*5 min*

I will make this a very brief introduction. I will tell my students there are two very important questions to be answered today: 1) What shapes make up the net of a cylinder? 2) What is a formula for the surface area of a cylinder?

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#### Lesson Middle

*15 min*

One thing I love about this lesson is how a simple piece of paper becomes such a powerful tool (**MP5**) for students to understand the surface area formula of a cylinder. I will first guide students through a series of questions that should help students answer everything they’ll need to know about the surface area of a cylinder (See video). I won’t require students to write anything. They just need to be prepared to listen to and discuss each question. I want to give students a chance to discuss and make sense of the task (**MP1**) before I require them to write anything. I find that doing the discussion first opens the way to understanding for the majority of my students. They will not feel constrained by the need to get everything right.

After the discussion, students will work through a similar set of questions with their partners. Once we debrief those questions, students will be asked to label the parts of their net to find the surface area. In other words, they’ll put the formula for the area of a circle on each of the bases, they label the length of the lateral surface (rectangle) using the circumference formula and the height of the lateral surface using the height of the prism. At this point I will show students the formula for the surface area of a cylinder . I will ask students to explain what the parts of the formula mean. If they are stuck I may ask: “What part of the formula finds the area of the bases? Which part finds the area of the lateral faces?”. As students construct and deconstruct the formula they are developing their ability to look for and make use of structure **(MP7)**.

After this (and if time permits), students will find the surface area of a few shapes.

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#### Lesson End

*10 min*

We finish by summarizing our findings. I will pose the question: "We found that the surface area of all prisms is the sum of the area of the bases plus the areas of the lateral faces. Does this apply to cylinders too?" This is another turn and talk. Hopefully students conclude that yes, the generalization applies. Some students might suggest that instead of lateral faces we say lateral surface. Students then take an exit ticket.

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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