Illustrative Math Alignment: Grade 8 Unit 3

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

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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.

Linear Expressions, Equations, and Functions

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.

Linear Expressions, Equations, and Functions

Linear Expressions, Equations, and Functions

Linear Expressions, Equations, and Functions

Linear Expressions, Equations, and Functions

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 Investigation we look at linear models for objects moving at a constant speed. This video is Segment 1 of a 4 segment series related to Algebra Nspirations: Linear Functions.

In this Math Lab we explore slope in the context of the steepness of staircases. This video is Segment 2 of a 4 segment series related to Algebra Nspirations: Linear Functions.

In this Investigation we look at a linear regression for carbon dioxide emission data. This video is Segment 3 of a 4 segment series related to Algebra Nspirations: Linear Functions.

In this Math Lab we explore a linear model through a data-gathering activity. This video is Segment 4 of a 4 segment series related to Algebra Nspirations: Linear 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.

In this TI-Nspire CX tutorial explore the properties of parallel and perpendicular lines. Use a slider to define the slope and then graph parallel and perpendicular lines linked to this slider. Note: This video does not contain audio.

This is part of a collection of math worksheets that are crossword puzzles of math vocabulary.

Related Resources

Worksheet Library

This is part of a collection of math worksheets on the use of the TI-Nspire graphing calculator. Each worksheet supports a companion TI-Nspire Mini-Tutorial video. It provides all the keystrokes for the activity.

Related Resources

Worksheet Library

This is part of a collection of math worksheets on the use of the TI-Nspire graphing calculator. Each worksheet supports a companion TI-Nspire Mini-Tutorial video. It provides all the keystrokes for the activity.

Related Resources

Worksheet Library

This is part of a collection of math worksheets on the use of the TI-Nspire graphing calculator. Each worksheet supports a companion TI-Nspire Mini-Tutorial video. It provides all the keystrokes for the activity.

Related Resources

Worksheet Library

This is part of a collection of math worksheets on the use of the TI-Nspire graphing calculator. Each worksheet supports a companion TI-Nspire Mini-Tutorial video. It provides all the keystrokes for the activity.

Related Resources

Worksheet Library

This is part of a collection of math worksheets on the use of the TI-Nspire graphing calculator. Each worksheet supports a companion TI-Nspire Mini-Tutorial video. It provides all the keystrokes for the activity.

Related Resources

Worksheet Library

This is part of a collection of math worksheets on the use of the TI-Nspire graphing calculator. Each worksheet supports a companion TI-Nspire Mini-Tutorial video. It provides all the keystrokes for the activity.

Related Resources

Worksheet Library

This is part of a collection of math worksheets on the use of the TI-Nspire graphing calculator. Each worksheet supports a companion TI-Nspire Mini-Tutorial video. It provides all the keystrokes for the activity.

Related Resources

Worksheet Library

This is part of a collection of math worksheets on the use of the TI-Nspire graphing calculator. Each worksheet supports a companion TI-Nspire Mini-Tutorial video. It provides all the keystrokes for the activity.

Related Resources

Worksheet Library