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* *Reflection: Developing a Conceptual Understanding
Nets vs. Composite Figures - Section 3: Instruction & Teacher Modeling

This reflection discusses the similarities between nets and composite figures.

*Developing a Conceptual Understanding: The Similarity Between Nets & Composite Figures*

# Nets vs. Composite Figures

Lesson 8 of 14

## Objective: SWBAT recognize the nets of different polyhedrons and see them as a composite figure.

*70 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' minds so that the knowledge of these concepts become a part of students' long-term memories.

#### Resources

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#### Engagement

*10 min*

In today’s opening exercise, I will show my students several 3-D shapes. When I show them a shape, I will ask them, “What 2-D shapes are used to create this 3-D shape?” The 3-D shapes that I will show them are:

- Rectangular prism
- Square pyramid
- Triangular prism
- Hexagonal pyramid

Once I have received an answer as to what 2-D shapes create the 3-D shaped listed above, I will then show the students the all of the nets of those 3-D shapes. After showing them the nets, I will ask them which net belongs to which 3-D shape and how do you know.

For the Rectangular Prism, students should tell me (6 rectangles or 4 rectangles and 2 squares... Depending upon the prism's base shape). They should tell me that the square pyramid is made up of one square and four triangles. The triangular prism is created with two triangles and three rectangles. And the Hexagonal pyramid is comprised of one hexagon and 6 triangles.

#### Resources

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Today, during instruction, I will focus on teaching my students how to see the nets of solid figures as composite plane figures. They should be able to take a solid figure and see the regular plane figures that are used to create that solid figure. The ability to do this is an essential skill that is necessary to being able to find the surface area of a solid figure.

I will also teach my students the characteristics of different 3-D figures. For example, they will not only know that a square pyramid is made up of a square base and 4 triangles, but they will also know that those 4 triangles are congruent. Knowing things like this will help them when they learn how to find surface area by using formulas for area.

Furthermore, during this instructional piece, we will explore how polyhedron fold out into irregular polygons. I will present my students with the four polyhedron listed below:

- Rectangular Prism
- Square Pyramid
- Triangular Prism
- Triangular Pyramid

In this presentation, I will demonstrate to my students, how to draw the net of a polyhedron, that is presented with measurements, on grid paper. Each square on the grid paper will represent one unit of measure.

For further explanation pertaining to this portion of this lesson, please see the video attached.

#### Resources

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#### Try It Out

*5 min*

To practice finding the regular plane figures that are used to create a solid figure, I will present my students with two different solid figures, one being rectangular prism and the other being a square pyramid. Each of the figures will be labeled with their dimensions. Using grid paper, I will guide my students through drawing the nets of these solid figures ensuring that we use one square on the grid paper to represent one unit of measurement.

#### Resources

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#### Independent Practice

*20 min*

For today’s independent practice. Students will show that they are able to determine what the net of a 3-D figure should look like. They will demonstrate this ability by drawing the net of several 3-D figures to scale. To do this, the students will be given 8 different 3-D figures with whole number dimensions. The students will draw the nets of these 3-D figures on grid paper using the given the dimensions ensuring that one square represents one unit.

#### Resources

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#### Closing Summary

*15 min*

To close out this lesson, I will chose one student per 3-D figure to present how they drew the net of the figure and how they estimated the area using the grid paper. The presenting students need to also be prepared to answer questions asked by me and their peers. They need to be ready to defend their work.

The rest of the students need to be ready to ask questions, provide critique, and make comments pertaining to what is being presented.

During this closing, I am looking for my students to demonstrate that they can visually see each polygon within a polyhedron, while also determining which sides of the polygons join in order to create the polyhedron.

Being able to visualize polyhedron figures in such a way, will help students to master the concept of surface area.

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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
- LESSON 5: Finding the Area of Composite Plane Figures
- LESSON 6: Area of Composite Plane Figures in Real Life
- LESSON 7: Unit 5 Quiz 1: Area
- LESSON 8: Nets vs. Composite Figures
- 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