Illustrative Math Alignment: Grade 7 Unit 9

Topic

Volume

Description

This image shows a hollow triangular prism with outer dimensions labeled as x, y, and z, and inner dimensions reduced by 2 units each. It demonstrates how to calculate the volume by subtracting the hollow region from the full prism. This image illustrates Example 8: "Find the volume of this hollow triangular prism." The solution uses V = 1/2 * b1 * h1 * l1 - 1/2 * b2 * h2 * l2, which simplifies to V = z(xy - (x - 2)(y - 2)) = z(x + y - 2)..

Topic

Volume

Description

A green cylinder with a radius of 10 units and a height of 8 units. The radius is marked on the top surface, and the height is marked on the side. This image illustrates Example 9: The task is to find the volume of the cylinder. The volume formula V = πr2h is used. Substituting the values r = 10 and h = 8, the volume is calculated as V= 800π.

This set of tutorials provides 36 examples of how to classify polygons based on side and angle characteristics.

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This Teacher's Guide provides an overview of the 24 worked-out examples that show how to calculate the area and perimeter of different quadrilaterals.

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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 40 examples of how to find the area and perimeter of triangles.

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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 40 examples of how to find the area and perimeter of triangles. NOTE: The download is a PPT file.

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.

November 2014. In this issue of Math in the News we examine the historic landing of a spacecraft on an asteroid in space.

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September 2016. In this issue of Math in the News, we look at back-to-school purchases and the impact that different tax rates have on the total cost.

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December 2022. In this issue of Math in the News we look at box office hits and misses from Disney. The House of Blockbosters every now and then misfires. It's useful to analyze box office data to see what we can learn from the hits and misses. 

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February 2023. In this issue of Math in the News we look at NFL statistics for the number of concussions. The NFL now tracks concussion, and this is an opportunity to analyze this data and draw conclusions.

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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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8/22/11. In this issue we look at the way in which the U.S. government borrows money. This involves an exploration of Treasury bonds and notes.

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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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10/17/11. In this issue we look at the earthquake damage that the Washington Monument recently experienced. Some dramatic footage reveals cracks in the exterior of the monument.

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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 we look at the Burj Khalifa Tower, made popular with the release of the Mission Impossible movie.

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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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4/18/11. In this issue we look at income taxes. We analyze who pays what proportion of income taxes based on income level.

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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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March 2014. In this issue of Math in the News we look at the impact of a harsh winter on Florida's orange crop. In addition we look at an ongoing problem that orange production has had with a crop infestation. This provides opportunities to apply percent change formulas to real-world data.

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July 2015. This edition of Math in the News focuses on the severe drought currently taking place in California, and how it has impacted the water resources available to the state. In this edition, students will see how to use percentages given to determine actual amounts, and to determine percents out of a whole.

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July 2015. This Math in the News explores the construction of the iconic landmark the Washington Monument and its recent renovations due to the 2011 earthquake. Students will be able to convert dollar values based on inflation and determine the combined expense of the Washington Monument between construction and recent renovations.

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May 2014. In this issue of Math in the News we explore Bitcoin. We look at how it's used for making purchases and how it differs from other currencies. This provides an opportunity to apply the concept of currency exchange.

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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

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

To access the full video [Geometry Applications: Area and Volume, Segment 1: Volume and Density]: https://media4math.com/library/geometry-applications-area-and-volume-segment-1-volume-and-density

This video includes a Video Transcript: https://www.media4math.com/library/video-transcript-geometry-applications-area-and-volume-segment-1-volume-and-density

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

To access the full video [Geometry Applications: Area and Volume, Segment 2: Surface Area]: https://media4math.com/library/geometry-applications-area-and-volume-segment-2-surface-area

This video includes a Video Transcript: https://www.media4math.com/library/video-transcript-geometry-applications-area-and-volume-segment-2-surface-area

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

To access the full video [Geometry Applications: Area and Volume, Segment 3: Ratio of Surface Area to Volume]: https://www.media4math.com/library/geometry-applications-area-and-volume-segment-3-ratio-surface-area-volume

Frank Lloyd Wright’s architectural masterpiece Falling Water is also a stunning assembly of quadrilateral shapes. Some of the rectangular forms in this building seem to defy gravity, as we explore the properties of squares and rectangles that allowed Frank Lloyd Wright to push the envelope of design and structure. Note: The download for this resources is the Promethean Flipchart.

This video includes a video transcript: https://media4math.com/library/video-transcript-geometry-applications-quadrilaterals-segment-2-squares-and-rectangles

The Puerta de Europa towers in Madrid bring parallelograms front and center. These tilted towers, looking like modern-day towers of Pisa seem to defy gravity, but rely on the stability brought about by its quadrilateral structure. The underlying parallelogram and trapezoidal designs are explored and analyzed. Note: The download for this resources is the Promethean Flipchart.

The full video can be found here: https://media4math.com/library/geometry-applications-quadrilaterals-segment-3-parallelograms-and-trapezoids

This video includes a Video Transcript: https://www.media4math.com/library/video-transcript-geometry-applications-quadrilaterals-segment-3-parallelograms-and

What Are Algebra Tiles?

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 quadrilaterals. We do this in the context of two real-world applications. In the first, we explore the architecture of Frank Lloyd Wright as an application of squares and rectangles; in particular, we look at his Fallingwater house. In the second application we look at a unique parallelogram-shaped building in Spain, known as the Puerta de Europa. It provides an opportunity to explore the properties of parallelograms and trapezoids.

This is the transcript for the video of same title. Video contents: Stonehenge is best known as a circular structure. But it's the post and lintel construction used that is noteworthy, and this type of construction involves quadrilateral shapes. From the familiar door frames of houses to the majestic entryways of ancient temples, post and lintel construction provides a clear introduction to the nature of quadrilaterals. This segment also describes the key concepts developed throughout the program.

This is the transcript for the video of same title. Video contents: Frank Lloyd Wright's architectural masterpiece Falling Water is also a stunning assembly of quadrilateral shapes. Some of the rectangular forms in this building seem to defy gravity, as we explore the properties of squares and rectangles that allowed Frank Lloyd Wright to push the envelope of design and structure.

This is the transcript for the video of same title. Video contents: The Puerta de Europa towers in Madrid bring parallelograms front and center. These tilted towers, looking like modern-day towers of Pisa seem to defy gravity, but rely on the stability brought about by its quadrilateral structure. The underlying parallelogram and trapezoidal designs are explored and analyzed.