ALEX Classroom Resources

ALEX Classroom Resources  
   View Standards     Standard(s): [MA2015] GEO (9-12) 5 :
5 ) Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. [G-CO5]

[MA2015] GEO (9-12) 35 :
35 ) Give an informal argument for the formulas for the circumference of a circle; area of a circle; and volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri's principle, and informal limit arguments. [G-GMD1]

[MA2015] PRE (9-12) 38 :
38 ) (+) Give an informal argument using Cavalieri's principle for the formulas for the volume of a sphere and other solid figures. [G-GMD2]

[MA2019] REG-7 (7) 19 :
19. Describe the two-dimensional figures created by slicing three-dimensional figures into plane sections.
[MA2019] REG-8 (8) 30 :
30. Use formulas to calculate the volumes of three-dimensional figures (cylinders, cones, and spheres) to solve real-world problems.
[MA2019] GEO-19 (9-12) 16 :
16. Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.
[MA2019] GEO-19 (9-12) 17 :
17. Model and solve problems using surface area and volume of solids, including composite solids and solids with portions removed.

a. Give an informal argument for the formulas for the surface area and volume of a sphere, cylinder, pyramid, and cone using dissection arguments, Cavalieri's Principle, and informal limit arguments.

b. Apply geometric concepts to find missing dimensions to solve surface area or volume problems.
Subject: Mathematics (9 - 12), Mathematics (7 - 12)
Title: Cone Surface Area | School Yourself Geometry
URL: https://aptv.pbslearningmedia.org/resource/geometry-cone-surface/cone-surface-area-school-yourself-geometry/
Description:

Use the Pythagorean theorem to unroll a cone and find its surface area with this interactive video from the School Yourself Geometry series.



   View Standards     Standard(s): [MA2015] GEO (9-12) 35 :
35 ) Give an informal argument for the formulas for the circumference of a circle; area of a circle; and volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri's principle, and informal limit arguments. [G-GMD1]

[MA2015] PRE (9-12) 38 :
38 ) (+) Give an informal argument using Cavalieri's principle for the formulas for the volume of a sphere and other solid figures. [G-GMD2]

[MA2019] REG-8 (8) 30 :
30. Use formulas to calculate the volumes of three-dimensional figures (cylinders, cones, and spheres) to solve real-world problems.
[MA2019] GEO-19 (9-12) 17 :
17. Model and solve problems using surface area and volume of solids, including composite solids and solids with portions removed.

a. Give an informal argument for the formulas for the surface area and volume of a sphere, cylinder, pyramid, and cone using dissection arguments, Cavalieri's Principle, and informal limit arguments.

b. Apply geometric concepts to find missing dimensions to solve surface area or volume problems.
Subject: Mathematics (9 - 12), Mathematics (8 - 12)
Title: Cavalieri's Principle (3D) | School Yourself Geometry
URL: https://aptv.pbslearningmedia.org/resource/geometry-cavalieri-3d/cavalieris-principle-3d-school-yourself-geometry/
Description:

Apply Cavalieri's principle to determine when two solids must definitely have the same volume with this interactive video from the School Yourself Geometry series. 



   View Standards     Standard(s): [MA2015] GEO (9-12) 35 :
35 ) Give an informal argument for the formulas for the circumference of a circle; area of a circle; and volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri's principle, and informal limit arguments. [G-GMD1]

[MA2015] PRE (9-12) 38 :
38 ) (+) Give an informal argument using Cavalieri's principle for the formulas for the volume of a sphere and other solid figures. [G-GMD2]

[MA2019] REG-8 (8) 30 :
30. Use formulas to calculate the volumes of three-dimensional figures (cylinders, cones, and spheres) to solve real-world problems.
[MA2019] GEO-19 (9-12) 17 :
17. Model and solve problems using surface area and volume of solids, including composite solids and solids with portions removed.

a. Give an informal argument for the formulas for the surface area and volume of a sphere, cylinder, pyramid, and cone using dissection arguments, Cavalieri's Principle, and informal limit arguments.

b. Apply geometric concepts to find missing dimensions to solve surface area or volume problems.
Subject: Mathematics (9 - 12), Mathematics (8 - 12)
Title: Volumes for Different Prisms (and Cylinders) | School Yourself Geometry
URL: https://aptv.pbslearningmedia.org/resource/geometry-other-prism-volume/prism-volume-school-yourself-geometry/
Description:

How can you find the volume of prisms that aren't rectangular? Learn how with this interactive video from the School Yourself Geometry series. 



   View Standards     Standard(s): [MA2015] PRE (9-12) 38 :
38 ) (+) Give an informal argument using Cavalieri's principle for the formulas for the volume of a sphere and other solid figures. [G-GMD2]

[MA2019] REG-8 (8) 30 :
30. Use formulas to calculate the volumes of three-dimensional figures (cylinders, cones, and spheres) to solve real-world problems.
[MA2019] GEO-19 (9-12) 17 :
17. Model and solve problems using surface area and volume of solids, including composite solids and solids with portions removed.

a. Give an informal argument for the formulas for the surface area and volume of a sphere, cylinder, pyramid, and cone using dissection arguments, Cavalieri's Principle, and informal limit arguments.

b. Apply geometric concepts to find missing dimensions to solve surface area or volume problems.
Subject: Mathematics (9 - 12), Mathematics (8 - 12)
Title: Sphere Volume | School Yourself Geometry
URL: https://aptv.pbslearningmedia.org/resource/geometry-sphere-volume/sphere-volume-school-yourself-geometry/
Description:

Use the Pythagorean theorem and apply Cavalieri's principle to cones and cylinders to find the volume of a sphere with this interactive video from the School Yourself Geometry series. 



   View Standards     Standard(s): [MA2019] REG-8 (8) 30 :
30. Use formulas to calculate the volumes of three-dimensional figures (cylinders, cones, and spheres) to solve real-world problems.
[MA2019] GEO-19 (9-12) 17 :
17. Model and solve problems using surface area and volume of solids, including composite solids and solids with portions removed.

a. Give an informal argument for the formulas for the surface area and volume of a sphere, cylinder, pyramid, and cone using dissection arguments, Cavalieri's Principle, and informal limit arguments.

b. Apply geometric concepts to find missing dimensions to solve surface area or volume problems.
Subject: Mathematics (8 - 12)
Title: You Pour, I Choose: Volumes of Cylinders
URL: https://aptv.pbslearningmedia.org/resource/mgbh-math-g-youpour/you-pour-i-choose-volumes-of-cylinders/
Description:

Compare the volume of varied cylindrical glasses filled to different heights. 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.

This resource is part of the Math at the Core: Middle School collection.



   View Standards     Standard(s): [MA2019] REG-8 (8) 30 :
30. Use formulas to calculate the volumes of three-dimensional figures (cylinders, cones, and spheres) to solve real-world problems.
[MA2019] GEO-19 (9-12) 17 :
17. Model and solve problems using surface area and volume of solids, including composite solids and solids with portions removed.

a. Give an informal argument for the formulas for the surface area and volume of a sphere, cylinder, pyramid, and cone using dissection arguments, Cavalieri's Principle, and informal limit arguments.

b. Apply geometric concepts to find missing dimensions to solve surface area or volume problems.
Subject: Mathematics (8 - 12)
Title: Meatballs: Volumes of Spheres and Cylinders
URL: https://aptv.pbslearningmedia.org/resource/mgbh-math-g-meatballs/meatballs-volumes-of-spheres-and-cylinders/
Description:

Use your problem-solving skills to find out if the pot will overflow when Dan adds meatballs to his pasta sauce. This interactive exercise focuses on using the volume equations for cylinders and spheres to figure out the multistep problem of how many meatballs it would take to fill the space left in the pot.

This resource is part of the Math at the Core: Middle School collection.



   View Standards     Standard(s): [MA2015] GEO (9-12) 5 :
5 ) Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. [G-CO5]

[MA2015] PRE (9-12) 38 :
38 ) (+) Give an informal argument using Cavalieri's principle for the formulas for the volume of a sphere and other solid figures. [G-GMD2]

[MA2019] REG-8 (8) 30 :
30. Use formulas to calculate the volumes of three-dimensional figures (cylinders, cones, and spheres) to solve real-world problems.
[MA2019] GEO-19 (9-12) 16 :
16. Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.
[MA2019] GEO-19 (9-12) 17 :
17. Model and solve problems using surface area and volume of solids, including composite solids and solids with portions removed.

a. Give an informal argument for the formulas for the surface area and volume of a sphere, cylinder, pyramid, and cone using dissection arguments, Cavalieri's Principle, and informal limit arguments.

b. Apply geometric concepts to find missing dimensions to solve surface area or volume problems.
[MA2019] GEO-19 (9-12) 36 :
36. Use geometric shapes, their measures, and their properties to model objects and use those models to solve problems.
Subject: Mathematics (9 - 12), Mathematics (8 - 12)
Title: Strange Shapes | MIT's Science Out Loud
URL: https://aptv.pbslearningmedia.org/resource/b043dcff-a47f-4027-95c9-1c47a53f5ade/strange-shapes/
Description:

In school, you learn about shapes with sides and edges, but there are weird shapes out there (beyond our 3 dimensions) that defy our normal idea of geometry. QuanQuan and Jenny explain, knit, and 3D print their way through these strange shapes.



   View Standards     Standard(s): [MA2015] GEO (9-12) 35 :
35 ) Give an informal argument for the formulas for the circumference of a circle; area of a circle; and volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri's principle, and informal limit arguments. [G-GMD1]

[MA2019] GEO-19 (9-12) 16 :
16. Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.
[MA2019] GEO-19 (9-12) 17 :
17. Model and solve problems using surface area and volume of solids, including composite solids and solids with portions removed.

a. Give an informal argument for the formulas for the surface area and volume of a sphere, cylinder, pyramid, and cone using dissection arguments, Cavalieri's Principle, and informal limit arguments.

b. Apply geometric concepts to find missing dimensions to solve surface area or volume problems.
Subject: Mathematics (9 - 12), Mathematics (9 - 12)
Title: Geometry Module 3, Topic B: Volume
URL: https://www.engageny.org/resource/geometry-module-3-topic-b-overview
Description:

Students study the basic properties of two-dimensional and three-dimensional space, noting how ideas shift between the dimensions. They learn that general cylinders are the parent category for prisms, circular cylinders, right cylinders, and oblique cylinders, and study why the cross-section of a cylinder is congruent to its base. Next students study the explicit definition of a cone and learn what distinguishes pyramids from general cones, and see how dilations explain why a cross-section taken parallel to the base of a cone is similar to the base.  Students revisit the scaling principle as it applies to volume and then learn Cavalieri’s principle, which describes the relationship between cross-sections of two solids and their respective volumes. This knowledge is all applied to derive the volume formula for cones, and then extended to derive the volume formula for spheres. Module 3 is a natural place to see geometric concepts in modeling situations. Modeling-based problems are found throughout Topic B and include the modeling of real-world objects, the application of density, the occurrence of physical constraints, and issues regarding cost and profit.



ALEX Classroom Resources: 8

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