Identifying Nets For Cubes

Identifying Nets For Cubes

Introduction to Nets

Opening

Introduction to Nets

Watch the video. Then, discuss the following concepts.

  • The 2-D version of a cube is called a net.
  • The surface area of a prism is the area of its net.
  • You can find the surface area of a 3-D figure by adding together the areas of each surface.
  • The surface area of a cube with side lengths of 1 unit is 6 square units.

VIDEO: Cube

Math Mission

Opening

Create and analyze 2-D nets of 3-D figures to determine the surface areas of the figures.

Explore Nets

Work Time

Explore Nets

  • Which of the nets in the diagram are nets of cubes?
  • Explain your thinking.

Make Nets

Work Time

Make Nets

  • Draw a net for each rectangular prism.

Hint:

There are many possible nets. Try sketching the bottom face of the prism in the center of a grid. Look at the prism and determine which surfaces share a common side with this bottom face. Then draw these surfaces, connecting them to the bottom face at the shared side. Where would you draw the top of the prism?

Explore Nets and Surface Area

Work Time

Explore Nets and Surface Area

  • Find the surface area of each rectangular prism. Use the nets you drew.

Prepare a Presentation

Work Time

Prepare a Presentation

  • Show one of the prism nets you drew and explain why it represents the prism. (You might want to print your drawing, cut it out, and then assemble it to prove that your net represents the prism.)
  • Explain how you determined the surface area of the prism.

Challenge Problem

  • Several different rectangular prisms are each made up of 24 cubes. Will their nets all look the same? Provide examples to support your answer.

Make Connections

Performance Task

Ways of Thinking: Make Connections

  • Take notes about your classmates’ explanations of their net drawings and how they calculated surface area.

Hint:

As your classmates present, ask questions such as:

  • Explain your strategy for creating a net.
  • Do you think it’s easier to determine the surface area from the net or from the three-dimensional figure?
  • How could you check whether you found the correct surface area?
  • How do you know that your net accurately represents the prism?

Surface Area and Nets of Rectangular Prisms

Formative Assessment

Summary of the Math: Surface Area and Nets of Rectangular Prisms

Read and Discuss

  • A rectangular prism is a prism in which all faces are rectangles. There are many ways to “cut” along the edges of the prism in order to lay it flat (and thus make a net of the prism). Figures 2 and 3 show two different ways to make a net of the rectangular prism in Figure 1.
  • The surface area is the total area of the six rectangles that form the six faces of the prism. Regardless of which net you use, you will find that the surface area is 176 ft2.

Hint:

Can you:

  • Explain what a net is?
  • Give at least one strategy for sketching the net of a rectangular prism?
  • Define surface area?
  • Describe how to use the net of a three-dimensional object to find its surface area?
  • Explain why the surface area that you calculate from two different nets of the same three-dimensional object will be the same?

Reflect On Your Work

Work Time

Reflection

Write a reflection about the ideas discussed in class today. Use the sentence starter below if you find it to be helpful.

I can find the surface area of three-dimensional figures using nets by …