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# Surface Area and Area Differentiation

Lesson 6 of 14

## Objective: Students will be able to apply their understanding of area formulas to solve problems.

## Big Idea: In a differentiated task that gets students moving around the room, students work on problems targeted to their level of understanding.

*80 minutes*

#### Notes: Surface Area

*20 min*

At this point in my unit on Geometric Measurement and Dimensionality, I want to activate students' prior knowledge of surface area so they can focus on visualizing all of the faces of a three dimensional figure and make sense of the surface area formulas.

I give students the answer key for the Surface Area Notes. Then, I give them time to explain in their own words as they did with the area formulas throughout the unit. While students take notes and work on the practice problems, I circulate the room, answering students' individual questions. They know the content here, the resources provided spark and scaffold the use of their prior knowledge.

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#### Practice: Surface Area

*20 min*

Next, I give my students a worksheet with several surface area problems. Since these are multistep problems, I think it is important for students to gain as much practice as possible before moving on.3 I tell students they must attend to precision, drawing each type of face when working through these problems. I expect my students' thinking to be clearly evident in their work—that is, their work should truly reflect their thought process and correspond to the unique faces they have drawn (**MP6**).

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This is one of the last area lessons in my course, which is why it is important to differentiate students’ practice. Today, I post “foundational” and “extension” problems all around the classroom, which have been photocopied onto green and pink cardstock to help students differentiate between the two levels. The foundational problems provide basic understanding of areas of triangles, trapezoids, parallelograms, kites, regular polygons, and circles. The extension problems require students to extend their thinking and apply their understanding in novel ways.

Students can choose to work individually or quietly with a partner, choose whichever problems they want to work on based on their perception of how well they are doing with area, and choose to work standing up on the whiteboard (which encourages them to also write out their ideas while discussing with others) or sitting at a student desk. I give students the goal of trying to do at least ten problems. I circulate the room to get a sense of how my students are working; this gives me time to check in with those who struggle more in the class in a safe way while allowing me the chance to encourage others to take risks by tackling the non-routine extension problems (**MP1**).

I pass answer keys towards the end of class so students can self-assess their understanding of how they did on each of the problems they attempted.

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- UNIT 1: Creating Classroom Culture to Develop the Math Practices
- UNIT 2: Introducing Geometry
- UNIT 3: Transformations
- UNIT 4: Discovering and Proving Angle Relationships
- UNIT 5: Constructions
- UNIT 6: Midterm Exam Review
- UNIT 7: Discovering and Proving Triangle Properties
- UNIT 8: Discovering and Proving Polygon Properties
- UNIT 9: Discovering and Proving Circles Properties
- UNIT 10: Geometric Measurement and Dimension
- UNIT 11: The Pythagorean Theorem
- UNIT 12: Triangle Similarity and Trigonometric Ratios
- UNIT 13: Final Exam Review

- LESSON 1: Sectors of Circles
- LESSON 2: Making Sense of Area Formulas for Triangles, Parallelograms, Trapezoids, and Kites
- LESSON 3: Making Sense of Area Formulas for Regular Polygons and Circles
- LESSON 4: Strategies for Decomposing 2-D Figures
- LESSON 5: Sector Area Application: The Grazing Goat
- LESSON 6: Surface Area and Area Differentiation
- LESSON 7: Extreme Couponing: Pizza Edition
- LESSON 8: Area "Quest"
- LESSON 9: Introduction to Volume: Origami Boxes
- LESSON 10: Origami Boxes Gallery Walk
- LESSON 11: Volume Formulas, Cavalieri's Principle, and 2-D Cross-Sections
- LESSON 12: Real World Volume Context Problems
- LESSON 13: Ratios of Similarity and 3D Solids Generated by Revolving 2D Figures
- LESSON 14: Volume "Quest"