Unfolding Boxes: Mastering Surface Area with Nets

Mathematics Grades 7th Grade 4:43 Video
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Lesson Description

Learn how to calculate the surface area of a box by visualizing and using its net. This lesson explores the relationship between 3D shapes and their 2D representations.

Video Resource

Surface area of a box using nets

Khan Academy

Duration: 4:43
Watch on YouTube

Key Concepts

  • Surface Area
  • Nets of 3D Shapes
  • Area of Rectangles

Learning Objectives

  • Students will be able to define surface area and explain its significance.
  • Students will be able to identify and draw the net of a rectangular prism.
  • Students will be able to calculate the surface area of a rectangular prism using its net.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the concept of area and how to calculate the area of a rectangle (length x width). Briefly discuss 3D shapes and their properties. Ask students if they have ever unfolded a box and what it looked like.
  • Video Viewing (10 mins)
    Play the Khan Academy video 'Surface area of a box using nets'. Instruct students to pay attention to how the box is unfolded and how each face contributes to the total surface area.
  • Net Exploration (15 mins)
    Discuss the concept of a 'net' as a 2D representation of a 3D shape. Have students sketch their own nets of a rectangular prism (cereal box). Emphasize that there can be multiple valid nets for the same box. Provide pre-cut nets for students who struggle with spatial reasoning.
  • Surface Area Calculation (15 mins)
    Guide students through the process of calculating the surface area using the net. Assign measurements to each side of their sketched or pre-cut box nets. Have them calculate the area of each rectangle in the net and then sum those areas to find the total surface area. Work through an example problem together on the board.
  • Practice and Application (10 mins)
    Provide students with various dimensions of rectangular prisms and have them calculate the surface area using nets. Encourage them to draw the nets first to visualize the problem. Have students check answers with a partner.

Interactive Exercises

  • Net Building Challenge
    Provide students with cardstock or construction paper and rulers. Challenge them to create a net that can be folded into a rectangular prism with specific dimensions. Students exchange nets and calculate the surface area of the prism that would be formed.
  • Real-World Application
    Bring in various boxes (cereal boxes, tissue boxes, etc.). Have students measure the dimensions of the boxes and calculate the surface area using nets. Discuss how this knowledge could be useful in real-life scenarios (e.g., calculating the amount of wrapping paper needed).

Discussion Questions

  • What is the difference between area and surface area?
  • Can a rectangular prism have more than one possible net? Explain.
  • Why is understanding nets helpful when calculating surface area?

Skills Developed

  • Spatial Reasoning
  • Problem-Solving
  • Measurement and Calculation

Multiple Choice Questions

Question 1:

What is surface area?

Correct Answer: The total area of all the surfaces of a 3D shape

Question 2:

What is a 'net' in geometry?

Correct Answer: A 2D shape that can be folded into a 3D shape

Question 3:

Which of these is NOT a step in finding the surface area of a box using a net?

Correct Answer: Measure the volume of the box

Question 4:

A rectangular prism has dimensions 5cm x 3cm x 2cm. What is the area of ONE of the largest faces?

Correct Answer: 15 cm²

Question 5:

A cube has sides of 4 inches. What is the area of one face?

Correct Answer: 16 square inches

Question 6:

If you have a rectangular prism that is 6 cm long, 4 cm wide, and 2 cm high, how many rectangles are in its net?

Correct Answer: 6

Question 7:

Why is it helpful to use a net when calculating the surface area of a rectangular prism?

Correct Answer: It makes it easier to visualize all the faces

Question 8:

What unit is surface area measured in?

Correct Answer: Square Centimeters (cm²)

Question 9:

Which formula would you use to calculate the area of each face in a rectangular prism net?

Correct Answer: A = l x w

Question 10:

The net of a rectangular prism consists of six ____.

Correct Answer: Rectangles

Fill in the Blank Questions

Question 1:

The total area of all the surfaces of a 3D shape is called its _________ _________.

Correct Answer: surface area

Question 2:

A 2D pattern that can be folded to form a 3D shape is called a _________.

Correct Answer: net

Question 3:

The formula to find the area of a rectangle is Area = _________ x Width.

Correct Answer: length

Question 4:

A cereal box is an example of a rectangular _________.

Correct Answer: prism

Question 5:

To find the surface area of a box using its net, you must find the area of each rectangle and then _________ them together.

Correct Answer: add

Question 6:

Surface area is measured in _________ units, such as cm² or in².

Correct Answer: square

Question 7:

A cube has six equal _________ faces.

Correct Answer: square

Question 8:

If a rectangle is 5 cm long and 3 cm wide, its area is _________ cm².

Correct Answer: 15

Question 9:

A rectangular prism has _____ faces.

Correct Answer: six

Question 10:

The area of a rectangle is equal to Length multiplied by the _________ .

Correct Answer: width

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. 7.GM.1.2:Using a variety of tools and strategies, develop the concept that surface area of a rectangular prism can be found by wrapping the figure with same-sized square units without gaps or overlap. Use appropriate measurements (e.g., cm2).

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