Unfolding Surface Area: Cracking the Net Code!

Mathematics Grades 7th Grade 4:19 Video
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Lesson Description

Learn how to calculate the surface area of 3D shapes by understanding and using their 2D nets. We'll explore rectangular prisms and their unfolded forms to master this geometric skill!

Video Resource

Finding surface area: nets of polyhedra | Perimeter, area, and volume | Geometry | Khan Academy

Khan Academy

Duration: 4:19
Watch on YouTube

Key Concepts

  • Surface Area
  • Nets of Polyhedra
  • Rectangular Prisms
  • Area Calculation

Learning Objectives

  • Students will be able to identify the net of a rectangular prism.
  • Students will be able to calculate the area of each face of a rectangular prism's net.
  • Students will be able to calculate the total surface area of a rectangular prism using its net.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing what surface area is and how it differs from area (2D) and volume (3D). Briefly discuss nets and how they represent 3D shapes in a 2D form. Show examples of different nets.
  • Video Exploration (10 mins)
    Play the Khan Academy video 'Finding surface area: nets of polyhedra'. Encourage students to take notes on the steps involved in calculating surface area using nets. Pause at key points to clarify any confusion.
  • Worked Example (10 mins)
    Work through the example from the video step-by-step on the board, emphasizing the calculation of the area of each rectangle in the net and the final summation. Reinforce the units (square centimeters).
  • Practice Problems (15 mins)
    Provide students with worksheets containing nets of rectangular prisms with varying dimensions. Have them calculate the surface area of each prism individually or in pairs. Circulate to provide assistance and answer questions.
  • Wrap-up and Review (5 mins)
    Review the key steps in finding surface area using nets. Address any remaining questions and preview the next lesson on volume.

Interactive Exercises

  • Net Creation
    Provide students with rectangular prism boxes that they can carefully cut along the edges to create their own nets. They can then measure the dimensions of each face and calculate the surface area.
  • Online Net Tool
    Use an online tool (e.g., GeoGebra) to explore different nets of rectangular prisms. Students can manipulate the nets and see how they fold into the 3D shape.

Discussion Questions

  • What is the difference between area and surface area?
  • Why is it helpful to use a net when finding the surface area of a 3D shape?
  • Can two different rectangular prisms have the same surface area? Explain.

Skills Developed

  • Spatial Reasoning
  • Area Calculation
  • Problem-Solving
  • Attention to Detail

Multiple Choice Questions

Question 1:

What is surface area?

Correct Answer: The sum of the areas of all the surfaces of a 3D shape

Question 2:

What is a 'net' in geometry?

Correct Answer: A flat shape that can be folded to form a 3D shape

Question 3:

If a rectangular face of a prism's net has a length of 6 cm and a width of 3 cm, what is its area?

Correct Answer: 18 cm²

Question 4:

A rectangular prism has dimensions 2cm x 4cm x 5cm. Which dimensions would you multiply to find the area of one of its faces?

Correct Answer: 2cm x 4cm

Question 5:

Which of the following units is used to measure surface area?

Correct Answer: cm²

Question 6:

A net of a rectangular prism has two squares of 4 square centimeters each and four rectangles with area of 8 square centimeters each. What is the surface area of the prism?

Correct Answer: 48 square centimeters

Question 7:

Why is understanding nets important for finding surface area?

Correct Answer: Nets allow us to unfold a 3D shape into a 2D shape to easily calculate the area of each face

Question 8:

How many faces does a rectangular prism have?

Correct Answer: 6

Question 9:

Which formula is used to calculate the area of a rectangle?

Correct Answer: l x w

Question 10:

What would be a reasonable next step if the calculated surface area is not a possible choice for an answer?

Correct Answer: Check that the area of all faces has been added

Fill in the Blank Questions

Question 1:

The surface area is the sum of the areas of all the ______ of a 3D shape.

Correct Answer: surfaces

Question 2:

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

Correct Answer: net

Question 3:

The area of a rectangle is calculated by multiplying its length by its ______.

Correct Answer: width

Question 4:

Surface area is measured in ______ units, such as square centimeters (cm²).

Correct Answer: square

Question 5:

A rectangular prism has ______ faces.

Correct Answer: six

Question 6:

In order to calculate the surface area of the net of a 3D shape you must first identify the _______ of each shape.

Correct Answer: area

Question 7:

A cube has all sides with equal _______

Correct Answer: length

Question 8:

The units for surface area are always expressed as _____ units.

Correct Answer: square

Question 9:

The number of rectangles on a net of a rectangular prism is ____.

Correct Answer: 6

Question 10:

A _____ prism has two ends that are not rectangles

Correct Answer: triangular

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).

Teaching Materials

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