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Illustrative Math-Media4Math Alignment

 

 

Illustrative Math Alignment: Grade 8 Unit 3

Functions and Volume

Lesson 11: Filling Containers

Use the following Media4Math resources with this Illustrative Math lesson.

Thumbnail Image Title Body Curriculum Topic
Closed Captioned Video: Algebra Applications: Rational Functions, Segment 2: Biology Closed Captioned Video: Algebra Applications: Rational Functions, 2 Closed Captioned Video: Algebra Applications: Rational Functions, Segment 2: Biology

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.

Rational Expressions and Rational Functions and Equations
Closed Captioned Video: Algebra Nspirations: Linear Functions Closed Captioned Video: Algebra Nspirations: Linear Functions Closed Captioned Video: Algebra Nspirations: Linear Functions

In this program, internationally acclaimed mathematics educator Dr. Monica Neagoy, explores the nature of linear functions through the use TI graphing calculators. Examples ranging from air travel, construction, engineering, and space travel provide real-world examples for discovering algebraic concepts. All examples are solved algebraically and then reinforced through the use of the TI-Nspire. Algebra teachers looking to integrate hand-held technology and visual media into their instruction will benefit greatly from this series. Concepts explored: Standard form, slope-intercept form, point-slope form, solving linear equations.

Applications of Linear Functions
Closed Captioned Video: Algebra Nspirations: Linear Functions, Segment 1 Closed Captioned Video: Algebra Nspirations: Linear Functions, 1 Closed Captioned Video: Algebra Nspirations: Linear Functions, Segment 1

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. Segments 1 and 2 are grouped together.

Applications of Linear Functions
Closed Captioned Video: Algebra Nspirations: Linear Functions, Segment 3 Closed Captioned Video: Algebra Nspirations: Linear Functions, 3 Closed Captioned Video: Algebra Nspirations: Linear Functions, Segment 3

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. Segments 3 and 4 are grouped together.

Applications of Linear Functions
Closed Captioned Video: Geometry Applications--Pyramid Volume Closed Captioned Video: Geometry Applications--Pyramid Volume Closed Captioned Video: Geometry Applications--Pyramid Volume

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.

Pyramids
Closed Captioned Video: Geometry Applications: 3D Geometry Closed Captioned Video: Geometry Applications: 3D Geometry Closed Captioned Video: Geometry Applications: 3D Geometry

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.

— CLICK THE PREVIEW BUTTON TO SEE THE VIDEO —

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.

3-Dimensional Figures and Applications of 3D Geometry
Closed Captioned Video: Geometry Applications: 3D Geometry, Segment 1: Introduction. Closed Captioned Video: Geometry Applications: 3D Geometry, 1 Closed Captioned Video: Geometry Applications: 3D Geometry, Segment 1: Introduction.

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

— CLICK THE PREVIEW BUTTON TO SEE THE VIDEO —

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.

3-Dimensional Figures and Applications of 3D Geometry
Closed Captioned Video: Geometry Applications: 3D Geometry, Segment 2: Pyramids Closed Captioned Video: Geometry Applications: 3D Geometry, 2 Closed Captioned Video: Geometry Applications: 3D Geometry, Segment 2: Pyramids

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.

— CLICK THE PREVIEW BUTTON TO SEE THE VIDEO —

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.

3-Dimensional Figures, Pyramids and Applications of 3D Geometry
Closed Captioned Video: Geometry Applications: 3D Geometry, Segment 3: Cylinders Closed Captioned Video: Geometry Applications: 3D Geometry, 3 Closed Captioned Video: Geometry Applications: 3D Geometry, Segment 3: Cylinders

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.

— CLICK THE PREVIEW BUTTON TO SEE THE VIDEO —

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.

3-Dimensional Figures, Cylinders and Applications of 3D Geometry
Closed Captioned Video: Geometry Applications: Area and Volume Closed Captioned Video: Geometry Applications: Area and Volume Closed Captioned Video: Geometry Applications: Area and Volume

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.

Applications of Surface Area and Volume, Surface Area and Volume
Closed Captioned Video: Geometry Applications: Area and Volume, Segment 1: Volume and Density. Closed Captioned Video: Geometry Applications: Area and Volume, 1 Closed Captioned Video: Geometry Applications: Area and Volume, Segment 1: Volume and Density.

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.

Applications of Surface Area and Volume, Surface Area and Volume
Closed Captioned Video: Geometry Applications: Area and Volume, Segment 1: Volume and Density. Closed Captioned Video: Geometry Applications: Area and Volume, 1 Closed Captioned Video: Geometry Applications: Area and Volume, Segment 1: Volume and Density.

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.

Applications of Surface Area and Volume, Surface Area and Volume
Closed Captioned Video: Geometry Applications: Area and Volume, Segment 2: Surface Area. Closed Captioned Video: Geometry Applications: Area and Volume, 2 Closed Captioned Video: Geometry Applications: Area and Volume, Segment 2: Surface Area.

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.

Applications of Surface Area and Volume, Surface Area and Volume
Closed Captioned Video: Geometry Applications: Area and Volume, Segment 3: Ratio of Surface Area to Volume. Closed Captioned Video: Geometry Applications: Area and Volume, 3 Closed Captioned Video: Geometry Applications: Area and Volume, Segment 3: Ratio of Surface Area to Volume.

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.

Applications of Surface Area and Volume, Surface Area and Volume
Formulas--Volume of a Cube Formulas--Volume of a Cube Formulas--Volume of a Cube

The formula for the Volume of a Cube.

This is part of a collection of math formulas. To see the complete collection of formulas, click on this link. Note: The download is a JPG file.

Related Resources

To see resources related to this topic click on the Related Resources tab above.

Volume
Formulas--Volume of a Cylinder Formulas--Volume of a Cylinder Formulas--Volume of a Cylinder

The formula for the Volume of a Cylinder.

This is part of a collection of math formulas. To see the complete collection of formulas, click on this link. Note: The download is a JPG file.

Related Resources

To see resources related to this topic click on the Related Resources tab above.

Volume and Cylinders
Formulas--Volume of a Rectangular Prism Formulas--Volume of a Rectangular Prism Formulas--Volume of a Rectangular Prism

The formula for the Volume of a Recantular Prism.

This is part of a collection of math formulas. To see the complete collection of formulas, click on this link. Note: The download is a JPG file.

Related Resources

To see resources related to this topic click on the Related Resources tab above.

Volume
Formulas--Volume of a Sphere Formulas--Volume of a Sphere Formulas--Volume of a Sphere

The formula for the Volume of a Sphere.

This is part of a collection of math formulas. To see the complete collection of formulas, click on this link. Note: The download is a JPG file.

Related Resources

To see resources related to this topic click on the Related Resources tab above.

Volume
Formulas--Volume of a Square Pyramid Formulas--Volume of a Square Pyramid Formulas--Volume of a Square Pyramid

The formula for the Volume of a Square Pyramid.

This is part of a collection of math formulas. To see the complete collection of formulas, click on this link. Note: The download is a JPG file.

Related Resources

To see resources related to this topic click on the Related Resources tab above.

Volume
Formulas--VolumeOfTriangularPrism.jpg Formulas--Volume of a Triangular Prism

Note: The download is a JPG file.

Related Resources

To see the complete collection of Formulas, click on this link: https://media4math.com/math-formulas
Volume
Formulas--VolumeOfTriangularPyramid.jpg Formulas--Volume of a Triangular Pyramid Volume of a Triangular Pyramid

Watch this video to learn about the volume of a pyramid. (The video transcript is also included.)

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Video Transcript

Pyramids are majestic and a bit mysterious. Arising from deserts and jungles, they are grand in size and sleek in appearance.

Mathematically, pyramids also have an air of mystery. Let’s take a closer look.

Here is a cube of side s. Its volume couldn’t be more straightforward: s • s •s, or s-cubed. Its name, its shape, its volume are straightforward.

Volume
Geometry Applications Teachers Guide: 3D Geometry Geometry Applications Teachers Guide: 3D Geometry Geometry Applications Teachers Guide: 3D Geometry

This is the Teacher's Guide that accompanies Geometry Applications: 3D Geometry.

This is part of a collection of teacher's guides. To see the complete collection of teacher's guides, click on this link. Note: The download is a PDF file.

Related Resources

To see resources related to this topic click on the Related Resources tab above.

Applications of 3D Geometry
Google Earth Voyager Story: The Geometry of Sustainable Architecture, Part 1 Google Earth Voyager Story: The Geometry of Sustainable Architecture, Part 1 Google Earth Voyager Story: The Geometry of Sustainable Architecture, Part 1

Topic

Geometric Models

Applications of Surface Area and Volume and Rational Functions and Equations
Google Earth Voyager Story: The Geometry of Sustainable Architecture, Part 2 Google Earth Voyager Story: The Geometry of Sustainable Architecture, Part 2 Google Earth Voyager Story: The Geometry of Sustainable Architecture, Part 2

Topic

Geometric Models

Surface Area, Volume and Rational Functions and Equations
Google Earth Voyager Story: The Mathematics of Pyramids, Part 1 Google Earth Voyager Story: The Mathematics of Pyramids, Part 1 Google Earth Voyager Story: The Mathematics of Pyramids, Part 1

Topic

Geometric Models

Pyramids
Google Earth Voyager Story: The Mathematics of Pyramids, Part 2 Google Earth Voyager Story: The Mathematics of Pyramids, Part 2 Google Earth Voyager Story: The Mathematics of Pyramids, Part 2

Topic

Geometric Models

Pyramids
INSTRUCTIONAL RESOURCE: Algebra Application: Creating an Exercise Chart INSTRUCTIONAL RESOURCE: Algebra Application: Creating an Exercise Chart INSTRUCTIONAL RESOURCE: Algebra Application: Creating an Exercise Chart

In this Algebra Application, students develop a linear mathematical model based on the maximum heart rate during exercise based on age. Using this model, students investigate heart rate for moderate and vigorous workouts. The math topics covered include: Mathematical modeling, Linear functions, Families of functions, Computational thinking. The culminating activity is for students to create a simple program (using either a spreadsheet or a programming language like Python) to develop an exercise chart. This is a great back-to-school activity for middle school or high school students. A relevant real-world application allows them to review math concepts.

Applications of Linear Functions and Slope-Intercept Form
INSTRUCTIONAL RESOURCE: Algebra Application: Linear Functions: Circumference vs. Diameter INSTRUCTIONAL RESOURCE: Algebra Application: Linear Functions: Circumference vs. Diameter INSTRUCTIONAL RESOURCE: Algebra Application: Linear Functions: Circumference vs. Diameter

In this Algebra Application, students study the direction between diameter and circumference of a circle. Through measurement and data gathering students analyze the line of best fit and explore ways of calculating pi. The math topics covered include: Mathematical modeling, Linear functions, Data gathering and analysis, Ratios, Direct variation. This is a great back-to-school activity for middle school or high school students. This is also a great crossover activity that ties algebra and geometry.

Applications of Linear Functions, Applications of Ratios, Proportions, and Percents and Applications of Circles
PowerPointPresentations.jpg Instructional Resource: Applications of Linear Functions: Circumference vs. Diameter

In this Slide Show, apply concepts of linear functions to the context of circumference vs. diameter.

Note: The download is a PPT file.

Related Resources

To see the complete collection of Tutorials on this topic, click on this link: https://bit.ly/3g0P3cN
Applications of Linear Functions
PowerPointPresentations.jpg Instructional Resource: Applications of Linear Functions: Cost vs. Time

In this Slide Show, apply concepts of linear functions to the context of cost vs. time data and graphs.

Note: The download is a PPT file.

Related Resources

To see the complete collection of Tutorials on this topic, click on this link: https://bit.ly/3g0P3cN
Applications of Linear Functions
PowerPointPresentations.jpg Instructional Resource: Applications of Linear Functions: Cricket Chirps

In this Slide Show, apply concepts of linear functions to the context of cricket chirps.

Note: The download is a PPT file.

Related Resources

To see the complete collection of Tutorials on this topic, click on this link: https://bit.ly/3g0P3cN
Applications of Linear Functions
PowerPointPresentations.jpg Instructional Resource: Applications of Linear Functions: Distance vs. Time

In this Slide Show, apply concepts of linear functions to the context of distance vs. time data and graphs.

Note: The download is a PPT file.

Related Resources

To see the complete collection of Tutorials on this topic, click on this link: https://bit.ly/3g0P3cN
Applications of Linear Functions
PowerPointPresentations.jpg Instructional Resource: Applications of Linear Functions: Hooke's Law

In this Slide Show, apply concepts of linear functions to the context of Hooke's law.

Note: The download is a PPT file.

Related Resources

To see the complete collection of Tutorials on this topic, click on this link: https://bit.ly/3g0P3cN
Applications of Linear Functions and Proportions
PowerPointPresentations.jpg Instructional Resource: Applications of Linear Functions: Momentum and Impulse

In this Slide Show, apply concepts of linear functions to the context of momentum and impulse.

Note: The download is a PPT file.

Related Resources

To see the complete collection of Tutorials on this topic, click on this link: https://bit.ly/3g0P3cN
Applications of Linear Functions
PowerPointPresentations.jpg Instructional Resource: Applications of Linear Functions: Perimeter of a Rectangle

In this Slide Show, apply concepts of linear functions to the context of rectangular perimeter.

Note: The download is a PPT file.

Related Resources

To see the complete collection of Tutorials on this topic, click on this link: https://bit.ly/3g0P3cN
Applications of Linear Functions
PowerPointPresentations.jpg Instructional Resource: Applications of Linear Functions: Saving Money

In this Slide Show, apply concepts of linear functions to the context of saving money.

Note: The download is a PPT file.

Related Resources

To see the complete collection of Tutorials on this topic, click on this link: https://bit.ly/3g0P3cN
Applications of Linear Functions
PowerPointPresentations.jpg Instructional Resource: Applications of Linear Functions: Speed and acceleration

In this Slide Show, apply concepts of linear functions to the context of speed and acceleration.

Note: The download is a PPT file.

Related Resources

To see the complete collection of Tutorials on this topic, click on this link: https://bit.ly/3g0P3cN
Applications of Linear Functions
PowerPointPresentations.jpg Instructional Resource: Applications of Linear Functions: Temperature Conversion

In this Slide Show, apply concepts of linear functions to the context of converting Celsius and Fahrenheit temperatures.

Note: The download is a PPT file.

Related Resources

To see the complete collection of Tutorials on this topic, click on this link: https://bit.ly/3g0P3cN
Applications of Linear Functions
INSTRUCTIONAL RESOURCE: Desmos Tutorial: Matching Coordinates to Absolute Value Functions INSTRUCTIONAL RESOURCE: Desmos Tutorial: Matching Coordinates to Absolute Value Functions INSTRUCTIONAL RESOURCE: Desmos Tutorial: Matching Coordinates to Absolute Value Functions

In this Slide Show, use the Desmos graphing calculator to explore absolute value functions. To see the complete collection of Desmos Resources click on this link.

Note: The download is a PPT file. This is part of a collection of Desmos tutorials on a variety of math topics. To see the complete collection of these resources, click on this link.

Library of Instructional Resources

To see the complete library of Instructional Resources , click on this link.

Special Functions
INSTRUCTIONAL RESOURCE: Desmos Tutorial: Matching Coordinates to Linear Functions INSTRUCTIONAL RESOURCE: Desmos Tutorial: Matching Coordinates to Linear Functions INSTRUCTIONAL RESOURCE: Desmos Tutorial: Matching Coordinates to Linear Functions

In this Slide Show, use the Desmos graphing calculator to explore linear functions. To see the complete collection of Desmos Resources click on this link.

Note: The download is a PPT file. This is part of a collection of Desmos tutorials on a variety of math topics. To see the complete collection of these resources, click on this link.

Library of Instructional Resources

To see the complete library of Instructional Resources , click on this link.

Applications of Linear Functions
INSTRUCTIONAL RESOURCE: Tutorial: Graphing Linear Functions INSTRUCTIONAL RESOURCE: Tutorial: Graphing Linear Functions INSTRUCTIONAL RESOURCE: Tutorial: Graphing Linear Functions

In this Slide Show, learn about graphs of linear functions.

This is part of a collection of tutorials on a variety of math topics. To see the complete collection of these resources, click on this link. Note: The download is a PPT file.

Library of Instructional Resources

To see the complete library of Instructional Resources , click on this link.

Applications of Linear Functions
INSTRUCTIONAL RESOURCE: Tutorial: Linear Function Models INSTRUCTIONAL RESOURCE: Tutorial: Linear Function Models INSTRUCTIONAL RESOURCE: Tutorial: Linear Function Models

In this Slide Show, learn about linear function models.

This is part of a collection of tutorials on a variety of math topics. To see the complete collection of these resources, click on this link. Note: The download is a PPT file.

Library of Instructional Resources

To see the complete library of Instructional Resources , click on this link.

Applications of Linear Functions
INSTRUCTIONAL RESOURCE: Math Examples--Equations of Parallel and Perpendicular Lines INSTRUCTIONAL RESOURCE: Math Examples 12 INSTRUCTIONAL RESOURCE: Math Examples--Equations of Parallel and Perpendicular Lines

The complete set of 32 examples that make up this set of tutorials.

This is part of a collection of math examples for a variety of math topics. To see the complete collection of these resources, click on this link. Note: The download is a PPT file.

Library of Instructional Resources

To see the complete library of Instructional Resources , click on this link.

Applications of Linear Functions and Graphs of Linear Functions
INSTRUCTIONAL RESOURCE: Math Examples--Parallel and Perpendicular Lines INSTRUCTIONAL RESOURCE: Math Examples 35 INSTRUCTIONAL RESOURCE: Math Examples--Parallel and Perpendicular Lines

This set of tutorials provides 32examples that involve finding the equation of a line parallel or perpendicular to a given line and through a given point.

This is part of a collection of math examples for a variety of math topics. To see the complete collection of these resources, click on this link. Note: The download is a PPT file.

Library of Instructional Resources

To see the complete library of Instructional Resources , click on this link.

Applications of Linear Functions and Graphs of Linear Functions
INSTRUCTIONAL RESOURCE: Math Examples--Surface Area INSTRUCTIONAL RESOURCE: Math Examples 55 INSTRUCTIONAL RESOURCE: Math Examples--Surface Area

This set of tutorials provides an overview of the 24 worked-out examples that show how to calculate the surface area of different three-dimensional figures.

This is part of a collection of math examples for a variety of math topics. To see the complete collection of these resources, click on this link. Note: The download is a PPT file.

Library of Instructional Resources

To see the complete library of Instructional Resources , click on this link.

Surface Area
INSTRUCTIONAL RESOURCE: Nspire App Tutorial: Graphs of Absolute Value Functions INSTRUCTIONAL RESOURCE: Nspire App Tutorial: Graphs of Absolute Value Functions

In this Slide Show, absolute value functions are graphed, including graphs centered at the origin, graphs displaced along the x-axis, and graphs displaced along the y-axis. This presentation requires the use of the TI-Nspire iPad App. Note: the download is a PPT.

Special Functions
INSTRUCTIONAL RESOURCE: Nspire App Tutorial: Graphs of Inequalities INSTRUCTIONAL RESOURCE: Nspire App Tutorial: Graphs of Inequalities

In this Slide Show, the Graph Window is used to graph linear inequalities. This presentation requires the use of the TI-Nspire iPad App. Note: the download is a PPT.

Inequalities and Applications of Linear Functions
INSTRUCTIONAL RESOURCE: Nspire App Tutorial: Graphs of Inequalities with Sliders INSTRUCTIONAL RESOURCE: Nspire App Tutorial: Graphs of Inequalities with Sliders

In this Slide Show, the Graph Window is used to graph inequalities using sliders. This presentation requires the use of the TI-Nspire iPad App. Note: the download is a PPT.

Inequalities and Applications of Linear Functions
INSTRUCTIONAL RESOURCE: Nspire App Tutorial: Graphs of Linear Functions INSTRUCTIONAL RESOURCE: Nspire App Tutorial: Graphs of Linear Functions

In this Slide Show, linear functions are graphed. This presentation requires the use of the TI-Nspire iPad App. Note: the download is a PPT.

Applications of Linear Functions
INSTRUCTIONAL RESOURCE: Nspire App Tutorial: Parallel and Perpendicular Lines INSTRUCTIONAL RESOURCE: Nspire App Tutorial: Parallel and Perpendicular Lines

In this Slide Show, 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.

Parallel Lines and Perpendicular Lines