Unfolding Surface Area: Mastering Nets

Mathematics Grades 7th Grade 3:33 Video
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Lesson Description

Learn to calculate surface area by understanding and using nets of 3D figures. This lesson provides a visual and hands-on approach to surface area calculations.

Video Resource

Finding surface area using net

Khan Academy

Duration: 3:33
Watch on YouTube

Key Concepts

  • Surface Area
  • Nets of 3D Figures
  • Area of 2D Shapes (rectangles, triangles)

Learning Objectives

  • Students will be able to identify the net of a 3D figure.
  • Students will be able to calculate the surface area of a 3D figure by using its net.
  • Students will be able to calculate the area of various 2D shapes (rectangles and triangles).

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the concept of surface area. Ask students what surface area means to them in everyday language. Briefly discuss how surface area differs from volume. Show examples of 3D figures and their corresponding real-world objects (e.g., a rectangular prism and a shoebox).
  • Video Viewing (10 mins)
    Play the Khan Academy video 'Finding surface area using net'. Instruct students to pay close attention to how the 3D figure is unfolded into a 2D net and how each face's area is calculated.
  • Guided Practice (15 mins)
    Work through a similar example problem on the board, step-by-step. First, draw the net of a given rectangular prism. Then, label each face with its dimensions. Finally, calculate the area of each face and sum them up to find the total surface area. Encourage student participation by asking guiding questions at each step.
  • Independent Practice (15 mins)
    Provide students with a worksheet containing several 3D figures and their nets (or ask them to draw the nets themselves). Have them calculate the surface area of each figure. Circulate the classroom to provide assistance and answer questions.
  • Wrap-up & Discussion (5 mins)
    Review the key concepts covered in the lesson. Ask students to share their strategies for finding surface area using nets. Briefly introduce the concept of different nets representing the same 3D figure.

Interactive Exercises

  • Net Matching Game
    Provide students with cards showing 3D figures and their corresponding nets. Have them match the figures to their nets. This can be done individually or in small groups.
  • Build-a-Net Activity
    Provide students with construction paper, scissors, and tape. Have them design and build their own nets for given 3D figures. Then, have them calculate the surface area of their constructed figures.

Discussion Questions

  • Why is using a net helpful for finding surface area?
  • Can a 3D figure have more than one possible net? Explain.
  • How can you check your answer to make sure you've calculated the surface area correctly?

Skills Developed

  • Spatial Reasoning
  • Problem-Solving
  • Area Calculation

Multiple Choice Questions

Question 1:

What is a 'net' in geometry?

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

Question 2:

To find the surface area of a rectangular prism using its net, what do you need to do?

Correct Answer: Find the area of each face and add them together.

Question 3:

A rectangular prism has a net made up of rectangles with the following areas: 10 sq cm, 10 sq cm, 15 sq cm, 15 sq cm, 6 sq cm, and 6 sq cm. What is the total surface area of the prism?

Correct Answer: 62 sq cm

Question 4:

Which of the following is NOT a step in finding the surface area of a figure using a net?

Correct Answer: Calculating the volume of the figure

Question 5:

A triangle in a net has a base of 6 cm and a height of 4 cm. What is its area?

Correct Answer: 12 sq cm

Question 6:

If two rectangular prisms have the same surface area, what can you conclude?

Correct Answer: They could have different dimensions.

Question 7:

Why is it important to correctly draw or identify the net of a 3D shape before calculating surface area?

Correct Answer: To make sure you count all the faces of the 3D shape.

Question 8:

Which of the following 3D shapes can be unfolded into a net?

Correct Answer: Cube

Question 9:

A rectangular face of a prism measures 5 inches by 8 inches. What is the area of that face?

Correct Answer: 40 square inches

Question 10:

What unit is used to measure surface area?

Correct Answer: Square Centimeters

Fill in the Blank Questions

Question 1:

The total area of all the surfaces of a 3D figure is called the __________ __________.

Correct Answer: surface area

Question 2:

A 2D pattern that can be folded to form a 3D figure is called a __________.

Correct Answer: net

Question 3:

To find the surface area using a net, you need to calculate the __________ of each face and then add them together.

Correct Answer: area

Question 4:

The area of a rectangle is found by multiplying its __________ and __________.

Correct Answer: length and width

Question 5:

The area of a triangle is 1/2 times the __________ multiplied by the __________.

Correct Answer: base and height

Question 6:

Surface area is measured in __________ units.

Correct Answer: square

Question 7:

A cube has six identical __________ faces.

Correct Answer: square

Question 8:

The formula for the area of a rectangle is A = __________.

Correct Answer: lw

Question 9:

A net helps visualize all the __________ of a 3D figure at once.

Correct Answer: faces

Question 10:

If a rectangle has a length of 8 cm and a width of 5 cm, its area is __________ square cm.

Correct Answer: 40

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.2:Use mathematical models and problems to calculate and justify the area of trapezoids and the area and perimeter of composite figures with rational measurements. 7.N.2.5:Model and solve problems using rational numbers involving addition, subtraction, multiplication, division, and positive integer exponents.

Teaching Materials

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