Cracking the Cube: Volume of Rectangular Prisms with Fractional Sides

Mathematics Grades 7th Grade 4:14 Video
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Lesson Description

Learn how to calculate the volume of rectangular prisms when their dimensions are fractions. Understand the formula and practice simplifying before multiplying!

Video Resource

Volume of a rectangular prism: fractional dimensions | Geometry | 6th grade | Khan Academy

Khan Academy

Duration: 4:14
Watch on YouTube

Key Concepts

  • Volume of a rectangular prism
  • Fractional dimensions
  • Area of the base
  • Simplifying fractions before multiplying
  • Improper fractions

Learning Objectives

  • Students will be able to calculate the volume of a rectangular prism with fractional dimensions.
  • Students will be able to convert mixed numbers to improper fractions.
  • Students will be able to simplify fractions before multiplying to make calculations easier.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the formula for the volume of a rectangular prism (Volume = Length x Width x Height). Remind students that this formula applies even when the dimensions are fractions. Briefly discuss real-world examples of rectangular prisms, like boxes or rooms.
  • Video Viewing (10 mins)
    Play the Khan Academy video "Volume of a rectangular prism: fractional dimensions | Geometry | 6th grade | Khan Academy." Encourage students to take notes on the key steps and formulas presented.
  • Guided Practice (15 mins)
    Work through example problems similar to those in the video. Emphasize converting mixed numbers to improper fractions before multiplying. Model simplifying fractions before multiplying to reduce the size of the numbers involved. For example, guide them through the problem in the video.
  • Independent Practice (15 mins)
    Provide students with a set of practice problems to solve independently. Circulate the classroom to offer assistance and answer questions.
  • Wrap-up and Assessment (5 mins)
    Review the key concepts and address any remaining questions. Administer a short quiz to assess student understanding.

Interactive Exercises

  • Fraction Frenzy Volume Challenge
    Divide students into small groups. Give each group a set of rectangular prism dimensions with fractional sides. Groups race to correctly calculate the volume. Offer small prizes for the first correct answer.

Discussion Questions

  • Why is it helpful to convert mixed numbers to improper fractions before multiplying?
  • How does simplifying fractions before multiplying make the calculation easier?
  • Can you think of a real-world situation where you might need to calculate the volume of a rectangular prism with fractional dimensions?
  • Explain why the volume is in units cubed?

Skills Developed

  • Calculating volume
  • Fraction multiplication
  • Simplifying fractions
  • Problem-solving

Multiple Choice Questions

Question 1:

What is the formula for the volume of a rectangular prism?

Correct Answer: Length x Width x Height

Question 2:

Why is it important to sometimes convert mixed numbers to improper fractions before multiplying?

Correct Answer: It makes multiplication easier.

Question 3:

What is the volume of a rectangular prism with length 1/2, width 1/3, and height 1/4?

Correct Answer: 1/24

Question 4:

What is the volume of a rectangular prism with the following dimensions: length = 1 1/2 units, width = 2/3 units, height = 1/4 units?

Correct Answer: 1/4 unit cubed

Question 5:

If a rectangular prism has a volume of 1/8 units cubed, what does that mean?

Correct Answer: It can hold 1/8 of a unit cube.

Question 6:

Simplify 4/6 x 9/16?

Correct Answer: 3/8

Question 7:

When multiplying the dimensions of a rectangular prism the units for the volume are?

Correct Answer: Units cubed

Question 8:

What is 1 1/3 converted to an improper fraction?

Correct Answer: 4/3

Question 9:

Which statement is true?

Correct Answer: Volume equals area times height

Question 10:

A cube is a rectangular prism, True or False?

Correct Answer: True

Fill in the Blank Questions

Question 1:

The volume of a rectangular prism is found by multiplying its _______, _______, and ________.

Correct Answer: length, width, height

Question 2:

Before multiplying fractions, it is sometimes helpful to ________ them.

Correct Answer: simplify

Question 3:

A mixed number consists of a whole number and a ________.

Correct Answer: fraction

Question 4:

Volume is measured in _______ units.

Correct Answer: cubic

Question 5:

The area of the base is equal to length _____ width.

Correct Answer: times

Question 6:

The top number of a fraction is called a _______.

Correct Answer: numerator

Question 7:

The bottom number of a fraction is called a _______.

Correct Answer: denominator

Question 8:

If the length, width and height are 1/2, 1/2, 1/2 then the volume is _________.

Correct Answer: 1/8

Question 9:

1 equals 4/4 which equals _____/6.

Correct Answer: 6

Question 10:

Convert 2 1/2 to an improper fraction is _____/2.

Correct Answer: 5

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.1.3:Using a variety of tools and strategies, develop the concept that the volume of rectangular prisms can be found by counting the total number of same-sized unit cubes that fill a shape without gaps or overlaps. Use appropriate measurements (e.g., cm3). 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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