Unboxing Surface Area: Calculating the Area Around 3D Shapes

Mathematics Grades 7th Grade 2:24 Video
Print Lesson Plan Watch Video

Lesson Description

Learn how to calculate the surface area of a rectangular prism (like a box) by finding the area of each face and adding them together. This lesson uses a cereal box as a real-world example.

Video Resource

Surface area of a box

Khan Academy

Duration: 2:24
Watch on YouTube

Key Concepts

  • Surface Area
  • Rectangular Prism
  • Area of a Rectangle
  • Net of a 3D Shape

Learning Objectives

  • Students will be able to identify the faces of a rectangular prism.
  • Students will be able to calculate the area of each face of a rectangular prism.
  • Students will be able to calculate the total surface area of a rectangular prism by summing the areas of all its faces.

Educator Instructions

  • Introduction (5 mins)
    Begin by asking students what they know about area. Then, introduce the concept of surface area as the total area covering the outside of a 3D object. Show different boxes and ask if they were going to wrap it in paper, how much paper would they need?
  • Video Viewing (10 mins)
    Play the Khan Academy video 'Surface area of a box'. Instruct students to take notes on the steps the instructor uses to calculate the surface area.
  • Guided Practice (15 mins)
    Work through an example problem together as a class, similar to the one in the video. Choose a different rectangular prism (e.g., a tissue box) and guide students through calculating the area of each face and then the total surface area. Emphasize the importance of units (square centimeters, square inches, etc.).
  • Independent Practice (15 mins)
    Provide students with several rectangular prisms of varying dimensions. Have them independently calculate the surface area of each. Encourage them to show their work clearly and label their answers with the correct units. Optional: Provide nets of rectangular prisms for students to cut out, assemble, and then calculate the surface area.
  • Wrap-up (5 mins)
    Review the key concepts of the lesson and answer any remaining questions. Discuss real-world applications of surface area, such as calculating the amount of paint needed to cover a wall or the amount of material needed to make a box.

Interactive Exercises

  • Surface Area Scavenger Hunt
    Have students find rectangular prisms in the classroom or at home (e.g., books, boxes, containers). They should measure the dimensions of each prism and calculate its surface area. Then, have them share their findings with the class.

Discussion Questions

  • Why is it important to understand surface area?
  • How does knowing the dimensions of a rectangular prism help us find its surface area?
  • Can two rectangular prisms with different dimensions have the same surface area? Explain.

Skills Developed

  • Problem-solving
  • Spatial Reasoning
  • Measurement
  • Calculation

Multiple Choice Questions

Question 1:

What is the surface area of a rectangular prism?

Correct Answer: The total area of all the faces of the prism

Question 2:

A rectangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. What is the area of one of the largest faces?

Correct Answer: 15 cm²

Question 3:

How many faces does a rectangular prism have?

Correct Answer: 6

Question 4:

If you know the area of the front of a box, what other face do you automatically know the area of?

Correct Answer: The back

Question 5:

What formula do you use to find the area of a rectangle?

Correct Answer: Length x Width

Question 6:

A cube has sides of 4 inches each. What is the surface area?

Correct Answer: 96 square inches

Question 7:

Why do we use 'square' units (like cm²) when measuring surface area?

Correct Answer: Because area is a 2-dimensional measurement.

Question 8:

Which of these is NOT a real-world application of knowing surface area?

Correct Answer: Finding the volume of water in a pool

Question 9:

What is the surface area of a cube with sides of 1cm?

Correct Answer: 6cm²

Question 10:

What is the area of the top of a rectangular prism with depth of 5cm and width of 10cm?

Correct Answer: 50cm²

Fill in the Blank Questions

Question 1:

The total area of all the faces of a 3D object is called its ________ ________.

Correct Answer: surface area

Question 2:

A rectangular prism has _____ faces.

Correct Answer: 6

Question 3:

To find the surface area, you need to calculate the ______ of each face.

Correct Answer: area

Question 4:

The formula for the area of a rectangle is Length _____ Width.

Correct Answer: times

Question 5:

If a box has a front face with an area of 25 cm², its back face also has an area of _____ cm².

Correct Answer: 25

Question 6:

Surface area is measured in ________ units, like square centimeters (cm²).

Correct Answer: square

Question 7:

A 3D shape shaped like a cereal box is a _________ _________.

Correct Answer: rectangular prism

Question 8:

A cube's surface area is the same number 6 multiplied by one ________ squared.

Correct Answer: side

Question 9:

We use square units, such as cm squared, for area because area is a _____ dimensional measurement.

Correct Answer: two

Question 10:

The sides that can't be seen are the _____ and the ________.

Correct Answer: back, bottom

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.N.2.5:Model and solve problems using rational numbers involving addition, subtraction, multiplication, division, and positive integer exponents.

Teaching Materials

Download ready-to-use materials for this lesson:

Student Worksheet Classroom Slides Assessment Quiz
Add to Google Classroom

User Actions

Sign in to save this lesson plan to your favorites.

Sign In

Share This Lesson

Related Lesson Plans