Illustrative Math Alignment: Grade 8 Unit 3

Topic

Fractions

Description

The image shows a 3D figure made up of unit cubes. The figure is stacked in a staggered manner, with some cubes placed directly on top of others. Below the figure, there is a breakdown showing the individual cubes counted to determine the volume. Example 5: The caption asks for the volume of the figure, which is made up of unit cubes. The solution involves counting the cubes to find the 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.

Topic

Rational Functions

Description

Explains submarine pressure and volume relationships using rational functions, illustrating depth impacts on vessel integrity and scuba safety.

Relevance: This video provides a practical perspective on Rational Functions, making abstract concepts more accessible through real-world applications.

Topic

Rational Functions

Description

Examines surface area to volume ratios in animals using rational functions, connecting these ratios to evolutionary adaptations in different climates.

Relevance: This video provides a practical perspective on Rational Functions, making abstract concepts more accessible through real-world applications.

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.

Topic

3D Geometry

Topic

Area and Volume

Topic

Area and Volume

Description

This segment explores the concept of density, using the Titanic to demonstrate buoyancy and the relationship between mass and volume. It introduces direct variation, rational functions, and how these principles apply to ship design for optimal floating capacity.

Topic

Area and Volume

Description

This segment explores the concept of density, using the Titanic to demonstrate buoyancy and the relationship between mass and volume. It introduces direct variation, rational functions, and how these principles apply to ship design for optimal floating capacity.

Topic

Area and Volume

Description

This segment focuses on surface area, using the Louvre Pyramid to highlight geometric tessellations and triangular net calculations. It explains the surface area formula for pyramids and how these calculations are applied in architectural design and material efficiency.

Topic

Area and Volume

Description

This segment explores the surface area-to-volume ratio using the Citigroup Building as an example. It discusses how this ratio impacts energy efficiency in buildings and compares it to natural examples like polar bears and snakes for context.