Illustrative Math Alignment: Grade 8 Unit 3

This is part of a collection of math examples that focus on volume.

This Teacher's Guide provides an overview of the 24 worked-out examples that show how to calculate the surface area of different three-dimensional figures.

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This set of tutorials provides 24 examples of how to find the volume of various 3-dimensional geometric figures.

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This set of tutorials provides 24 examples of how to find the volume of various 3-dimensional geometric figures. NOTE: The download is a PPT file.

6/13/11. In this issue we explore the volcanic eruption in Chile that resulted in a huge plume of smoke and ash that was miles high. We explore the viscosity of lava that makes such eruptions possible.

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6/27/11. In this issue we look at the technology of hydraulic fracking. In particular, we estimate the amount of drilling required for such wells.

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8/1/11. In this issue we look at the physics of air pressure and the forces that give rise to heat waves.

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9/19/11. To commemorate the 10-year anniversary of the 911, we look at the geometry and architecture of the Freedom Tower, currently under construction.

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11/14/11. In this issue we commemorate the 125th anniversary of the Statue of Liberty. We also look at the geometry and architecture of this monument.

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11/28/11. In this issue we look at the geometry of parade balloons.

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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

This is the transcript for the video of same title. Video contents: All living things take up a certain amount of space, and therefore have volume. They also have a certain amount of surface area. The ratio of surface area to volume, which is a rational function, reveals important information about the organism. Students look at different graphs of these functions for different organisms.

This is the transcript for video entitled: "Geometry Applications--Volume of a Pyramid."

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

To see the complete collection of videos in the Video Library, click on this link.

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 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.

In spite of their massive size, submarines are precision instruments. A submarine must withstand large amounts of water pressure; otherwise, a serious breach can occur. Rational functions are used to study the relationship between water pressure and volume. Students graph rational functions to study the forces at work with a submarine.

This is part of a collection of videos from the Algebra Applications video series on the topic of Rational Functions.

All living things take up a certain amount of space, and therefore have volume. They also have a certain amount of surface area. The ratio of surface area to volume, which is a rational function, reveals important information about the organism. Students look at different graphs of these functions for different organisms.

This is part of a collection of videos from the Algebra Applications video series on the topic of Rational Functions.

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.

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.

We visit ancient Greece to learn about the Platonic Solids. This provides an introduction to the more general topic of three-dimensional figures.

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.

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.

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.

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.

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.

In this video, students see a derivation of the formula for the volume of a pyramid. This involves a hands-on activity using unit cubes, along with analysis, and a detailed algebraic derivation.

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.

In this program we look at applications of area and volume. We do this in the context of three real-world applications. In the first, we look at the sinking of the Titanic in the context of volume and density. In the second application we look at the glass pyramid at the Louvre Museum and calculate its surface area. In the third application we look at the Citibank Tower in New York City to study the ratio of surface area to volume to learn about heat loss in tall buildings.

The sinking of the Titanic provides an opportunity to explore volume, density, and buoyancy. Students construct a mathematical model of the Titanic to determine why it sank and what could have been done to prevent it from sinking.

The sinking of the Titanic provides an opportunity to explore volume, density, and buoyancy. Students construct a mathematical model of the Titanic to determine why it sank and what could have been done to prevent it from sinking.

The glass-paneled pyramid at the Louvre Museum in Paris is a tessellation of rhombus-shaped glass panels. Students create a model of the pyramid to calculate the number of panels used to cover the surface area of the pyramid.

The Citibank Tower in New York City presents some unique design challenges. In addition it has to cope with a problem that all tall structure have to deal with: heat loss. By managing the ratio of surface area to volume, a skyscraper can effective manage heat loss.