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* *Reflection: Developing a Conceptual Understanding
What in the World is Surface Area? - Section 3: Instruction & Teacher Modeling

In this video, I address the difficulty in matching the side lengths of a polyhedron to its corresponding net.

*Developing a Conceptual Understanding: Matching Side Lengths of Polyhedron Figures to Their Net*

# What in the World is Surface Area?

Lesson 9 of 14

## Objective: SWBAT use the nets and composite figures to solve for the surface area of different polyhedrons.

*65 minutes*

#### Curriculum Reinforcer

*10 min*

The curriculum reinforcer, is a daily practice piece that is incorporated into almost every lesson to help my students to retain skills and conceptual understanding from earlier lessons. My strategy is to use Spiraled Review to help my students retain what they learned during the earlier part of the year. This will help me to keep mathematical concepts fresh in the students mind so that the knowledge of these concepts become a part of students' long term memories.

#### Resources

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#### Engagement

*10 min*

For our opening exercise, I will have my students complete a matching activity where they will have to match 3-D shapes (polyhedrons) to their nets. The manner in which I will have my students engage in this activity, is by presenting them with several polyhedron figures and several nets of polyhedron figures.

The students will be required to match the polyhedron figures to their net. They will complete this activity as a whole group activity.

Attached to this section of this lesson, I have included a worksheet that can be used for the purpose of completing this activity, I have also included a PowerPoint slide that can be used so that this activity can be done as a whole group without having to make copies for students.

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During the instructional piece, I will teach my students to use what they know about nets of solid figures to find the surface area of a solid figure using formulas for area. For example, if they are finding the surface area of a right rectangular prism, then they should know that all of the opposite faces are congruent, which means that you only have to find the area of three faces and then double those areas to get the total surface area of the rectangular prism. Or, if they are finding the area of a square pyramid, then you only need to find the area of the square and one of the triangles. Once you find the area of one of the triangles, you can multiply that area by 4 to get the total area of the triangles and then add the area of the square to get the total area of the square pyramid. Teaching my students how to use the formulas in conjunction with the characteristics of the solid figure will help them become more fluent in their ability to find surface area.

To help my students to visualize what I am saying as it pertains to the characteristics of different polyhedron figures, surface area, nets, and how this all links to the concept of finding the area of composite figures, I will present my students with 3 polyhedron structures. My students will tell me what I need to do in order to find the surface area of each of those structures.

To see the 3 polyhedron structures that I presented to my students, please click on the attached document.

#### Resources

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#### Independent Exploration

*20 min*

To explore the concept of surface area, I will have my students complete three activities. Each activity will showcase surface area in a different way.

**Activity 1:**

The students will solve a pretty simple problem involving finding the surface area of a pyramid. This particular activity presents the shape, provides the dimensions of the shape, and then asks the students to find the total surface area of the shape. It is a straightforward problem that is not grounded in the real-world.

**Activity 2:**

The students will have to find the surface area of one of three structures that I created. They will do this by first finding the necessary measurements of each structure to the nearest inch and then solving for surface area. This activity gives the students a little more immersion into this concept of surface area in a more abstract way.

**Activity 3:**

I will present my students with a multi-stepped word problem that requires my students to use the concept of surface area in a real-world context.

The students will complete these activities in groups. They will broken up into groups with no more than 5 students. Each group will complete activities 1 and 3. Each group will also complete Activity 2 however, they will only be assigned one of the three structures.

Attached to this section are some student samples, as well as pictures of the structures used during activity 2.

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#### Closing Summary

*15 min*

To close out this lesson, selected students will display their solution to the problems that they completed during the independent practice and explain how they arrived at their solution step by step.

The manner in which these groups will present will be by which structure they measured and found the surface area of in Activity 2. The groups that did the same structure will present simultaneously so that their solutions can be compared and any discrepancies between the two solutions can be analyzed, critiqued, and discussed.

All groups should have the same answer for Activity 1 and Activity 3. Once again, any discrepancies in answers will be analyzed, critiqued, and discussed, which will be done in a whole group setting.

TOTD:

To provide students with an opportunity to reflect on what they have learned concerning surface area, I will have them answer the following question as a ticket out the door:

- What do you find difficult about the concept of surface area? How will you overcome that difficulty?

#### Resources

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- LESSON 1: Unit 5 Pre-Assessment
- LESSON 2: Finding the Area of Rectangles, Triangles, and Squares
- LESSON 3: Finding the Area of Parallelograms and Trapezoids
- LESSON 4: Area of Regular Plane Figures
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- LESSON 6: Area of Composite Plane Figures in Real Life
- LESSON 7: Unit 5 Quiz 1: Area
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- LESSON 9: What in the World is Surface Area?
- LESSON 10: What is This Thing Called Volume?
- LESSON 11: Unit 5 Quiz 2: Area & Volume
- LESSON 12: Area & Volume: Addressing Lingering Misconceptions
- LESSON 13: Unit 5 Assessment: Area & Volume
- LESSON 14: Student Self-Assessment: Area & Volume