Classroom Resource

Popcorn Picker: Volumes of Solid Shapes

Subject Area

Mathematics

Grade(s)

7, 8, 9, 10, 11, 12

Overview

Experiment with the volume of two cylinders made from the same size paper. This interactive exercise focuses on using what you know about cylinders to make a prediction about their volume and then requires calculating the actual volume to see if your prediction was accurate.

Mathematics (2019) Grade(s): 7

MA19.7.22

Solve real-world and mathematical problems involving area, volume, and surface area of two- and three- dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right rectangular prisms.

Unpacked Content

UP:MA19.7.22

Vocabulary

  • Area
  • volume
  • Surface area
  • Two-dimensional figures
  • Three-dimensional solids
  • Triangles
  • quadrilaterals
  • polygons
  • Cubes
  • Right rectangular prisms

Knowledge

Students know:
  • that volume of any right prism is the product of the height and area of the base.
  • The volume relationship between pyramids and prisms with the same base and height.
  • The surface area of prisms and pyramids can be found using the areas of triangular and rectangular faces.

Skills

Students are able to:
  • find the area and perimeter of two-dimensional objects composed of triangles, quadrilaterals, and polygons.
  • Use a net of a three-dimensional figure to determine the surface area.
  • Find the volume and surface area of pyramids, prisms, or three-dimensional objects composed of cubes, pyramids, and right prisms.

Understanding

Students understand that:
  • two-dimensional and three-dimensional figures can be decomposed into smaller shapes to find the area, surface area, and volume of those figures.
  • the area of the base of a prism multiplied by the height of the prism gives the volume of the prism.
  • the volume of a pyramid is 1/3 the volume of a prism with the same base.
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.39

Solve real-world and mathematical problems involving area, volume, and surface area of two- and three- dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right rectangular prisms. [Grade 7, 22]

Unpacked Content

UP:MA19.7A.39

Vocabulary

  • Area
  • volume
  • Surface area
  • Two-dimensional figures
  • Three-dimensional solids
  • Triangles
  • quadrilaterals
  • polygons
  • Cubs
  • Right rectangular prisms

Knowledge

Students know:
  • That volume of any right prism is the product of the height and area of the base.
  • The volume relationship between pyramids and prisms with the same base and height.
  • The surface area of prisms and pyramids can be found using the areas of triangular and rectangular faces.

Skills

Students are able to:
  • Find the area and perimeter of two-dimensional objects composed of triangles, quadrilaterals, and polygons.
  • Use a net of a three-dimensional figure to determine the surface area.
  • Find the volume and surface area of pyramids, prisms, or three-dimensional objects composed of cubes, pyramids, and right prisms.

Understanding

Students understand that:
  • Two-dimensional and three-dimensional figures can be decomposed into smaller shapes to find the area, surface area, and volume of those figures.
  • The area of the base of a prism multiplied by the height of the prism gives the volume of the prism.
  • The volume of a pyramid is 1/3 the volume of a prism with the same base.
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.
Mathematics (2019) Grade(s): 09-12 - Geometry with Data Analysis

MA19.GDA.17

Model and solve problems using surface area and volume of solids, including composite solids and solids with portions removed.

Unpacked Content

UP:MA19.GDA.17

Vocabulary

  • Dissection arguments
Principle
  • Cylinder
  • Pyramid
  • Cone
  • Ratio
  • Circumference
  • Parallelogram
  • Limits
  • Conjecture
  • Cross-section
  • Surface Area

    • Knowledge

    Students know:
    • Techniques to find the area and perimeter of parallelograms,Techniques to find the area of circles or polygons

    Skills

    Students are able to:
    • Accurately decompose circles, spheres, cylinders, pyramids, and cones into other geometric shapes.
    • Explain and justify how the formulas for surface area, and volume of a sphere, cylinder, pyramid, and cone may be created from the use of other geometric shapes.

    Understanding

    Students understand that:
    • Geometric shapes may be decomposed into other shapes which may be useful in creating formulas.
    • Geometric shapes may be divided into an infinite number of smaller geometric shapes, and the combination of those shapes maintain the area and volume of the original shape.
    Link to Resource
    https://aptv.pbslearningmedia.org/resource/mgbh-math-g-popcornpic/popcorn-picke…

    CR Resource Type

    Learning Activity

    Resource Provider

    PBS
    Accessibility
    License

    License Type

    PD

    Comments or Notes

    This resource contains the following resources in the top right corner: Popcorn Picker: Volumes of Solid Shapes - About this Activity and Popcorn Picker: Volumes of Solid Shapes - Activity. Both of these resources contain a clickable link on the webpage and are printable. 

    Approved Date

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