Learning Resource Type

Classroom Resource

Formulas: Volume

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.

    Unpacked Content

    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.

    Unpacked Content

    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]

    Unpacked Content

    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.
    Link to Resource

    CR Resource Type

    Informational Material

    Resource Provider

    PBS
    Accessibility
    License

    License Type

    BY-NC-ND
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