Unfolding Shapes: Exploring Nets of Polyhedra

Mathematics Grades 7th Grade 6:48 Video
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Lesson Description

Discover the fascinating world of polyhedra and their nets! This lesson explores what polyhedra are, how to identify them, and how to visualize and create their nets (flattened versions).

Video Resource

Nets of polyhedra | Perimeter, area, and volume | Geometry | Khan Academy

Khan Academy

Duration: 6:48
Watch on YouTube

Key Concepts

  • Polyhedra: 3D shapes with flat faces and straight edges.
  • Nets: 2D patterns that can be folded to form a 3D polyhedron.
  • Visualization: Mentally manipulating shapes in 2D and 3D.

Learning Objectives

  • Define and identify polyhedra (e.g., cube, rectangular pyramid).
  • Explain what a net of a polyhedron is and its purpose.
  • Draw and visualize different nets for a given polyhedron.
  • Recognize that a polyhedron can have multiple different nets.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing basic 2D shapes (squares, rectangles, triangles). Then, introduce the concept of 3D shapes and ask students for examples of objects in the classroom that are 3D shapes.
  • Video Viewing (10 mins)
    Play the Khan Academy video 'Nets of polyhedra | Perimeter, area, and volume | Geometry | Khan Academy'. Instruct students to take notes on the definitions of polyhedra and nets and examples given.
  • Guided Practice (15 mins)
    Work through examples of creating nets for simple polyhedra (cube, rectangular pyramid) on the board. Emphasize different ways to 'unfold' the same shape.
  • Independent Practice (15 mins)
    Provide students with pre-cut squares, rectangles, and triangles. Have them experiment with creating different nets for a cube or rectangular pyramid. Have them draw their nets on paper.
  • Wrap-up (5 mins)
    Review the key concepts of polyhedra and nets. Address any remaining questions.

Interactive Exercises

  • Net Creation Challenge
    Divide students into small groups. Give each group a different polyhedron (e.g., triangular prism). Challenge them to find as many different nets as possible for their polyhedron within a given time limit.
  • Virtual Polyhedra
    Use online resources where students can manipulate 3D shapes and their nets virtually.

Discussion Questions

  • What are some real-world examples of polyhedra you see every day?
  • Why is understanding nets helpful in real life?
  • Can the same polyhedron have different nets? Why or why not?

Skills Developed

  • Spatial reasoning
  • Problem-solving
  • Visualizing 3D shapes from 2D representations
  • Geometric understanding

Multiple Choice Questions

Question 1:

Which of the following is NOT a characteristic of a polyhedron?

Correct Answer: Curved surfaces

Question 2:

What is a 'net' of a polyhedron?

Correct Answer: A 2D pattern that can be folded into the polyhedron

Question 3:

Which of these shapes is a polyhedron?

Correct Answer: Cube

Question 4:

How many faces does a cube have?

Correct Answer: 6

Question 5:

Which polyhedron has a rectangular base and triangular sides that meet at a point?

Correct Answer: Rectangular Pyramid

Question 6:

A cube's net is unfolded. How many squares should you see?

Correct Answer: 6

Question 7:

Can a polyhedron have more than one net?

Correct Answer: Yes

Question 8:

What characteristic defines a polyhedron?

Correct Answer: Flat Sides

Question 9:

Imagine you're folding a net into a cube. What do the lines on the net represent?

Correct Answer: Edges

Question 10:

What is the minimum number of faces a polyhedron can have?

Correct Answer: 4

Fill in the Blank Questions

Question 1:

A 3D shape with flat surfaces and straight edges is called a ________.

Correct Answer: polyhedron

Question 2:

The plural of polyhedron is ________.

Correct Answer: polyhedra

Question 3:

A ________ is a 2D pattern that can be folded to create a 3D shape.

Correct Answer: net

Question 4:

A cube has _______ faces.

Correct Answer: six

Question 5:

A rectangular pyramid has a _________ as its base.

Correct Answer: rectangle

Question 6:

The flat surfaces of a polyhedron are called ________.

Correct Answer: faces

Question 7:

The lines where the faces of a polyhedron meet are called _______.

Correct Answer: edges

Question 8:

A cube is made of six equal ______.

Correct Answer: squares

Question 9:

Creating different nets allows for better ________ of a polyhedron.

Correct Answer: visualization

Question 10:

A net is a ______ dimensional representation of a three-dimensional shape.

Correct Answer: two

Educational Standards

7.GM.1:Develop and understand the concept of surface area and volume of rectangular prisms with rational-valued edge lengths. 7.GM.1.1:Recognize that the surface area of a rectangular prism can be found by finding the area of each component of the net of that figure. Know that rectangular prisms of different dimensions can have the same surface area.

Teaching Materials

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