Formulas: Volume

Learning Resource Type

Classroom Resource

Subject Area

Mathematics

Grade(s)

5, 7, 8

Overview

Volume is the measure of how much space there is within a three-dimensional object (one with length, width, and height). Watch the video for an explanation of the formula for volume.

Mathematics (2019) Grade(s): 5

MA19.5.19

Relate volume to the operations of multiplication and addition, and solve real-world and mathematical problems involving volume.

UP:MA19.5.19

Vocabulary

  • Volume
  • Unit cube
  • Rectangular prism
  • Base
  • Base-area
  • Dimensions
  • Face
  • Length
  • Width
  • Height
  • Layers
  • Edge
  • Equivalent
  • Conservation of volume
  • Attribute
  • Composition
  • Decomposition
  • Formula

Knowledge

Students know:
  • Measurable attributes of area and how it relates to finding the volume of objects.
  • Units of measurement for volume, specifically unit cubes.

Skills

Students are able to:
  • Solve word problems involving volume.
  • Use associative property of multiplication to find volume.
  • Relate operations of multiplication and addition to finding volume.
  • Apply formulas to find volume of right rectangular prisms.
  • Find volume of solid figures composed of two rectangular prisms.

Understanding

Students understand that:
  • Volume is a derived attribute based on a length unit and can be computed as the product of three length measurements or as the product of one base area and one length measurement.
  • Volume is an extension of area and can be found as the area of the base being repeated for a given number of layers.
Mathematics (2019) Grade(s): 8

MA19.8.30

Use formulas to calculate the volumes of three-dimensional figures (cylinders, cones, and spheres) to solve real-world problems.

UP:MA19.8.30

Vocabulary

  • Radius
  • Pi
  • Volume
  • Cylinder
  • Cone
  • Sphere

Knowledge

Students know:
  • The volume formulas for cylinders, cones, and spheres.
  • That 3.14 is an approximation of pi commonly used in these volume formulas.
  • That composite three dimensional objects in the real-world can be created by combining cylinders, cones, and spheres in part or whole.

Skills

Students are able to:
  • Calculate the volume of cones, cylinders, and spheres given in real-world contexts. often times approximating solutions to a specified decimal place.
  • Identify the components of a composite figure as being portions of or whole cylinders, cones, and spheres.
  • Combine the results of calculations to find volume for real-world composite figures.

Understanding

Students understand that:
  • the application of volume formulas and the relationship between these three formulas can be used in combinations when determining solutions involving real-world cylinders, cones, and spheres.
Mathematics (2019) Grade(s): 7 - Grade 7 Accelerated

MA19.7A.41

Use formulas to calculate the volumes of three-dimensional figures to solve real-world problems. [Grade 8, 30]

UP:MA19.7A.41

Vocabulary

  • Radius
  • Pi
  • Volume
  • Cylinder
  • Cone
  • Sphere

Knowledge

Students know:
  • the volume formulas for cylinders, cones, and spheres.
  • That 3.14 is an approximation of pi commonly used in these volume formulas.
  • That composite three dimensional objects in the real-world can be created by combining cylinders, cones, and spheres in part or whole.

Skills

Students are able to:
  • calculate the volume of cones, cylinders, and spheres given in real-world contexts. often times approximating solutions to a specified decimal place.
  • Identify the components of a composite figure as being portions of or whole cylinders, cones, and spheres.
  • Combine the results of calculations to find volume for real-world composite figures.

Understanding

Students understand that:
  • the application of volume formulas and the relationship between these three formulas can be used in combinations when determining solutions involving real-world cylinders, cones, and spheres.

CR Resource Type

Informational Material

Resource Provider

PBS

License Type

BY-NC-ND
https://aptv.pbslearningmedia.org/resource/ketae.geo.volume/formulas-volume/

Comments or Notes

This resource contais a background essay and discussion questions.

Approved Date

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