Illustrative Math Alignment: Grade 8 Unit 3

Topic

3D Geometry

Definition

A vertical cross-section of a cube is the intersection of the cube with a vertical plane, resulting in a square.

This is part of a collection of math video definitions related to the topic of 3D Geometry. These videos have Spanish audio. Note: The download is an MP4 video.

Topic

3D Geometry

Definition

A cone is a three-dimensional geometric shape with a circular base and a single vertex, called the apex, not in the plane of the circle.

Description

Cones are prevalent in both natural and man-made structures, such as traffic cones and volcanoes. In mathematics, cones are studied for their properties, including surface area and volume. The volume V of a cone is given by the formula

V = 1/3 πr2h

This is part of a collection of math video definitions related to the topic of 3D Geometry. These videos have Spanish audio. Note: The download is an MP4 video.

Topic

3D Geometry

Definition

A vertical cross-section of a dodecahedron is the intersection of the dodecahedron with a vertical plane, resulting in a polygon.

This is part of a collection of math video definitions related to the topic of 3D Geometry. These videos have Spanish audio. Note: The download is an MP4 video.

Topic

3D Geometry

Definition

A vertical cross-section of a sphere is the intersection of the sphere with a vertical plane, resulting in a circle.

This is part of a collection of math video definitions related to the topic of 3D Geometry. These videos have Spanish audio. Note: The download is an MP4 video.

Topic

3D Geometry

Definition

A vertical cross-section of a tetrahedron is the intersection of the tetrahedron with a vertical plane, resulting in a triangle or another polygon.

This is part of a collection of math video definitions related to the topic of 3D Geometry. These videos have Spanish audio. Note: The download is an MP4 video.

Topic

3D Geometry

Definition

A vertical cross-section of an antiprism is the intersection of the antiprism with a vertical plane, resulting in a polygon.

This is part of a collection of math video definitions related to the topic of 3D Geometry. These videos have Spanish audio. Note: The download is an MP4 video.

Topic

3D Geometry

Definition

A vertical cross-section of an icosahedron is the intersection of the icosahedron with a vertical plane, resulting in a polygon.

This is part of a collection of math video definitions related to the topic of 3D Geometry. These videos have Spanish audio. Note: The download is an MP4 video.

Topic

3D Geometry

Definition

Vertical cross-sections of a cone are the intersections of the cone with vertical planes, resulting in shapes like triangles or parabolas.

This is part of a collection of math video definitions related to the topic of 3D Geometry. These videos have Spanish audio. Note: The download is an MP4 video.

Topic

3D Geometry

Definition

Vertical cross-sections of a cylinder are the intersections of the cylinder with vertical planes, resulting in rectangles or ellipses.

This is part of a collection of math video definitions related to the topic of 3D Geometry. These videos have Spanish audio. Note: The download is an MP4 video.

Topic

3D Geometry

Definition

Vertical cross-sections of a square pyramid are the intersections of the pyramid with vertical planes, resulting in triangles or trapezoids.

This is part of a collection of math video definitions related to the topic of 3D Geometry. These videos have Spanish audio. Note: The download is an MP4 video.

Topic

3D Geometry

Definition

Vertical cross-sections of a triangular prism are the intersections of the prism with vertical planes, resulting in rectangles or triangles.

This is part of a collection of math video definitions related to the topic of 3D Geometry. These videos have Spanish audio. Note: The download is an MP4 video.

Topic

3D Geometry

Definition

Volume is the amount of space occupied by a three-dimensional object.

Description

Volume is a fundamental concept in geometry, representing the amount of space a three-dimensional object occupies. It is essential for calculating the capacity of containers, the displacement of fluids, and the mass of objects. Understanding volume involves using formulas specific to each shape, such as 

V = l × w × h

 for a rectangular prism or 

V = 4/3 πr3

This is part of a collection of math video definitions related to the topic of 3D Geometry. These videos have Spanish audio. Note: The download is an MP4 video.

Topic

3D Geometry

Definition

Cross-sections of a cube are the intersections of a plane with the cube, resulting in various two-dimensional shapes.

This is part of a collection of math video definitions related to the topic of 3D Geometry. These videos have Spanish audio. Note: The download is an MP4 video.

Topic

3D Geometry

Definition

Cross-sections of a sphere are circular slices obtained by cutting the sphere with a plane.

This is part of a collection of math video definitions related to the topic of 3D Geometry. These videos have Spanish audio. Note: The download is an MP4 video.

Topic

3D Geometry

Definition

A cube is a three-dimensional geometric figure with six equal square faces.

Description

Cubes are fundamental in geometry due to their symmetry and simplicity. They are used in various applications, such as packaging and architecture, where efficient space utilization is essential. The volume V of a cube is calculated as 

V = a3

This is part of a collection of math video definitions related to the topic of 3D Geometry. These videos have Spanish audio. Note: The download is an MP4 video.

Topic

3D Geometry

Definition

A cylinder is a three-dimensional geometric shape with two parallel circular bases connected by a curved surface.

Description

Cylinders are common in everyday objects, such as cans and pipes. In mathematics, cylinders are studied for their properties, including surface area and volume. The volume V of a cylinder is given by the formula 

V = πr2h

This is part of a collection of math video definitions related to the topic of 3D Geometry. These videos have Spanish audio. Note: The download is an MP4 video.

This is the transcript for the video of same title. Video contents: In this program we explore the properties of three-dimensional figures. We do this in the context of two real-world applications. In the first, we look at the three-dimensional structure of Mayan pyramids. These stair-step structures provide a unique opportunity to also explore sequences and series. In the second application we look at the Shanghai Tower as an example of cylindrically shaped structures.

This is the transcript for the video of same title. Video contents: We visit ancient Greece to learn about the Platonic Solids. This provides an introduction to the more general topic of three-dimensional figures.

To see the complete collection of video transcriptsy, click on this link.

This is the transcript for the video of same title. Video contents: Rectangular Prisms. Mayan pyramids are essentially stacks of rectangular prisms. The volume of each successive level is a percentage decrease of its lower neighbor. This introduces the notion of a geometric sequence and series, including an infinite series.

This is the transcript for the video of same title. Video contents: The Shanghai Tower in China is a stack of cylindrical shapes, where each successive layer is a percentage decrease of its lower neighbor. As with the previous section, this introduces the notion of a geometric sequence and series.

This is the transcript for the video of same title. Video contents: Cargo ships transport tons of merchandise from one country to another and accounts for most of the global economy. Loading and unloading these ships requires a great deal of organization and provides an ideal example of three-dimensional translations.

This is part of a series of video animations of three-dimensional figures. These animations show different views of these figures: top, side, and bottom. Many of these figures are a standard part of the geometry curriculum and being able to recognize them is important.

Study these animations to learn the basic properties of these 3D figures. In particular, make a note of their sides, edges, and vertices. Look for any symmetries they have. Look for polygon shapes that are familiar. Finally, think of real-world examples that use these  figures.

Below we also include information about Platonic solids and 2D nets of these 3D figures. To get a better understanding of these 3D figures, study these basic forms.

Topic

3D Geometry

Topic

3D Geometry

Description

This segment introduces Platonic solids, including tetrahedron, cube, and dodecahedron, emphasizing their congruent edges, vertices, and angles. It connects these geometric figures to both natural and man-made structures, setting the stage for exploring 3D geometry applications.

This video offers a comprehensive look at the mathematical concepts behind 3D Geometry. Students will gain insights into practical applications and theoretical understanding of the topic, enhancing their ability to visualize and apply these concepts.

Topic

3D Geometry

Description

This segment explores pyramids, particularly Mayan and Egyptian structures, to distinguish rectangular and square bases. It discusses the volume of truncated pyramids using proportional relationships and introduces the concept of tiered volume reduction through geometric sequences.

This video offers a comprehensive look at the mathematical concepts behind 3D Geometry. Students will gain insights into practical applications and theoretical understanding of the topic, enhancing their ability to visualize and apply these concepts.

Topic

3D Geometry

Description

This segment examines cylinders, using the Shanghai Tower as a case study. It highlights how adjustments to height and radius affect volume and surface area, demonstrating these principles with geometric calculations and their architectural applications in energy efficiency.

This video offers a comprehensive look at the mathematical concepts behind 3D Geometry. Students will gain insights into practical applications and theoretical understanding of the topic, enhancing their ability to visualize and apply these concepts.

This is part of a collection of math worksheets on the topic of 2D and 3D geometry.

Related Resources

Worksheet Library