Illustrative Math Alignment: Grade 8 Unit 3

12/7/11. In this issue we look at the heroic work of salvaging and retrofitting many of the ships sunk during the attack on Pearl Harbor.

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12/12/11. In this issue we look at the MLK Memorial and the special properties of granite that presented some design challenges in the construction of the statue.

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January 2012. In this issue of Math in the News we analyze how the Costa Concordia sank.

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April 2012. In this issue of Math in the News we analyze the sinking of the Titanic. It has been a hundred years, yet the story of the sinkin g of the Titanic still fascinates.

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May 2012. In this issue of Math in the News we look at the architecture of the Freedom Tower, now that it has become the tallest building in NYC.

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August 2013. In this issue we look at the geometry of funnel cakes. You'll like the sweet results.

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5/9/11. In this issue we look at tornado season. In particular we study why the swirling winds of a tornado are so damaging.

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5/16/11. In this issue we look at the flooding along the Mississippi. In particular we analyze the flooding along Memphis, Tennessee. We develop a model for predicting the amount of flooding.

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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. Note: The download for this resources is the Promethean Flipchart.

For access to the full video [Geometry Applications: 3D Geometry, Segment 2: Pyramids]: https://media4math.com/library/geometry-applications-3d-geometry-segment-2-pyramids

This video includes a Video Transcript [Video Transcript: Geometry Applications: 3D Geometry, Segment 2: Pyramids]: https://www.media4math.com/library/video-transcript-geometry-applications-3d-geometry-segment-2-pyramids

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. Note: The download for this resources is the Promethean Flipchart.

To access the full video [Geometry Applications: 3D Geometry, Segment 3: Cylinders]: https://media4math.com/library/geometry-applications-3d-geometry-segment-3-cylinders

This video includes a Video Transcript [Video Transcript: Geometry Applications: 3D Geometry, Segment 3: Cylinders]: https://www.media4math.com/library/video-transcript-geometry-applications-3d-geometry-segment-3-cylinders

Topic

3D Geometry

Definition

A horizontal cross-section of a cylinder is the intersection of the cylinder with a horizontal 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

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

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: In this program we explore the properties of circles. We do this in the context of two real-world applications. In the first, we look at the design of the Roman Coliseum and explore how circular shapes could have been used to design this elliptical structure. In the second application we look at the Roman Pantheon, specifically its spherical dome, to see how the properties of chords and secants help clarify its unique design.

This is the transcript for the video of same title. Video contents: We visit Chaco Canyon in New Mexico to explore the circular kivas and in the process discover how circular buildings have been used to study the heavens.

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

This is the transcript for the video of same title. Video contents: The Roman Coliseum is a large elliptical structure. Yet, the Romans likely used circular arcs to build it. This segment explores the properties of circles and shows how arcs can be used to create elliptical shapes.

This is the transcript for the video of same title. Video contents: The Roman Pantheon is a domed structure that shows a keen awareness of the position of the sun throughout the year. The source of light from the top of the dome allows for the exploration of chords, inscribed angles, central angles, and intercepted arcs.

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 that are crossword puzzles of math vocabulary.

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