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Illustrative Math-Media4Math Alignment

 

 

Illustrative Math Alignment: Grade 8 Unit 3

Functions and Volume

Lesson 17: Scaling One Dimension

Use the following Media4Math resources with this Illustrative Math lesson.

Thumbnail Image Title Body Curriculum Topic
Math Example--Volume Concepts--Calculating Volume: Example 21 Math Example--Volume Concepts--Calculating Volume: Example 21 Math Example--Volume Concepts--Calculating Volume: Example 21

Topic

Volume

Description

A hollow cube with an outer edge of 9 and an inner hollow region with an edge of 7. The image shows how to calculate the volume by subtracting the volume of the inner cube from the outer cube. This image illustrates Example 21: Find the volume of a hollow cube. The formula used is V = s13 - s23, where s1 is the outer edge (9) and s2 is the inner edge (7). The solution calculates 9^3 - 7^3 = 386..

Volume
Math Example--Volume Concepts--Calculating Volume: Example 22 Math Example--Volume Concepts--Calculating Volume: Example 22 Math Example--Volume Concepts--Calculating Volume: Example 22

Topic

Volume

Description

A hollow cube with an outer edge of x and an inner hollow region with an edge of x - 2. The image shows how to calculate the volume by subtracting the volume of the inner cube from the outer cube. This image illustrates Example 22: Find the volume of a hollow cube. The formula used is V = s13 - s23, where s1 = x and s2 = x - 2. Expanding and simplifying gives V = 6x2 - 12x + 8.

Volume
Math Example--Volume Concepts--Calculating Volume: Example 23 Math Example--Volume Concepts--Calculating Volume: Example 23 Math Example--Volume Concepts--Calculating Volume: Example 23

Topic

Volume

Description

 

A cone with a height of 12 and a radius of 4. The image shows how to calculate its volume using the cone volume formula (V = 1/3 * π * r2 * h). This image illustrates Example 23: Find the volume of a cone. The formula used is V = (1/3) * π * r2 * h, where r = 4 and h = 12. Substituting these values gives V = (1/3) * π * (42) * 12 = 64π.

Volume
Math Example--Volume Concepts--Calculating Volume: Example 24 Math Example--Volume Concepts--Calculating Volume: Example 24 Math Example--Volume Concepts--Calculating Volume: Example 24

Topic

Volume

Description

A cone with a height labeled as y and a radius labeled as x. The image shows how to calculate its volume using the cone volume formula (V = 1/3 * π * r2 * h). This image illustrates Example 24: Find the volume of a cone. The formula used is V = (1/3) * π * r2 * h, where r = x and h = y. Substituting these variables gives V = (x^2 * y)/3 * π.

Volume
Math Example--Volume Concepts--Calculating Volume: Example 3 Math Example--Volume Concepts--Calculating Volume: Example 3 Math Example--Volume Concepts--Calculating Volume: Example 3

Topic

Volume

Description

A hollow rectangular prism with outer dimensions: length = 60, width = 20, and height = 16. The inner hollow part has dimensions: length = 60, width = 18, and height = 14. The image shows how to subtract volumes to find the hollow volume. This image illustrates Example 3: The caption explains how to calculate the volume of a hollow rectangular prism by subtracting the inner volume from the outer volume. V = (60 * 20 * 16) - (60 * 18 * 14) = 4080.

Volume
Math Example--Volume Concepts--Calculating Volume: Example 4 Math Example--Volume Concepts--Calculating Volume: Example 4 Math Example--Volume Concepts--Calculating Volume: Example 4

Topic

Volume

Description

A hollow rectangular prism with outer dimensions labeled as x, y, and z, and inner hollow dimensions labeled as x - 2 and y - 2. The image shows a symbolic calculation for finding the hollow volume using variables. This image illustrates Example 4: The caption describes how to calculate the volume of a hollow rectangular prism by subtracting the inner volume from the outer volume using variables: V = xyz - z(y - 2)(x - 2) = 2z(y + x - 2).

Volume
Math Example--Volume Concepts--Calculating Volume: Example 5 Math Example--Volume Concepts--Calculating Volume: Example 5 Math Example--Volume Concepts--Calculating Volume: Example 5

Topic

Volume

Description

The image shows a triangular prism with dimensions labeled as base (7), height (10), and length (25). It is part of an example on how to calculate the volume of a solid triangular prism. This image illustrates Example 5: "Find the volume of this triangular prism." The solution involves substituting the given measurements into the volume formula for a triangular prism: V = 1/2 * b * h * l = 1/2 * 7 * 10 * 25 = 875.

Volume
Math Example--Volume Concepts--Calculating Volume: Example 6 Math Example--Volume Concepts--Calculating Volume: Example 6 Math Example--Volume Concepts--Calculating Volume: Example 6

Topic

Volume

Description

The image depicts a triangular prism with dimensions labeled as x, y, and z. The example demonstrates how to calculate the volume using a general formula for a triangular prism. This image illustrates Example 6: "Find the volume of this triangular prism." The solution uses the formula V = 1/2 * b * h * l, which is simplified to V = 1/2 * x * y * z..

Volume
Math Example--Volume Concepts--Calculating Volume: Example 7 Math Example--Volume Concepts--Calculating Volume: Example 7 Math Example--Volume Concepts--Calculating Volume: Example 7

Topic

Volume

Description

The image shows a hollow triangular prism with outer dimensions labeled as base (10), height (7), and length (35), and inner dimensions labeled as base (8) and height (5). The example calculates the volume by subtracting the hollow region from the full prism. This image illustrates Example 7: "Find the volume of this hollow triangular prism." The solution calculates the full volume using V = 1/2 * b1 * h1 * l1 - 1/2 * b2 * h2 * l2, which simplifies to V = 1/2 * 10 * 7 * 35 - 1/2 * 8 * 5 * 35 = 525..

Volume
Math Example--Volume Concepts--Calculating Volume: Example 8 Math Example--Volume Concepts--Calculating Volume: Example 8 Math Example--Volume Concepts--Calculating Volume: Example 8

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)..

Volume
Math Example--Volume Concepts--Calculating Volume: Example 9 Math Example--Volume Concepts--Calculating Volume: Example 9 Math Example--Volume Concepts--Calculating Volume: Example 9

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.

Volume
MATH EXAMPLES--Teacher's Guide: Equations of Parallel and Perpendicular Lines MATH EXAMPLES--Teacher's Guide: Equations of Parallel and Perpendicular Lines MATH EXAMPLES--Teacher's Guide: Equations of Parallel and Perpendicular Lines

This Teacher's Guide provides an overview of the 32 worked-out examples that show how to find the equation of a line parallel or perpendicular to a given line and through a given point.

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.

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Applications of Linear Functions and Graphs of Linear Functions
MATH EXAMPLES--Teacher's Guide: Surface Area MATH EXAMPLES--Teacher's Guide: Surface Area MATH EXAMPLES--Teacher's Guide: Surface Area

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.

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.

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Surface Area
MATH EXAMPLES--Teacher's Guide: Volume MATH EXAMPLES--Teacher's Guide: Volume MATH EXAMPLES--Teacher's Guide: Volume

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

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.

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Volume
MATH EXAMPLES--Volume MATH EXAMPLES--Volume MATH EXAMPLES--Volume

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.

Volume
Math in the News: Issue 13--Living Near Volcanoes Math in the News: Issue 13--Living Near Volcanoes Math in the News: Issue 13--Living Near Volcanoes

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.

This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.

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Volume
Math in the News: Issue 15--Fracking for Oil Math in the News: Issue 15--Fracking for Oil Math in the News: Issue 15--Fracking for Oil

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.

This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.

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Volume
Math in the News: Issue 27--Emerging from the Ashes of 9/11 Math in the News: Issue 27--Emerging from the Ashes of 9/11 Math in the News: Issue 27--Emerging from the Ashes of 9/11

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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3-Dimensional Figures
Math in the News: Issue 35--125 and Counting Math in the News: Issue 35--125 and Counting Math in the News: Issue 35--125 and Counting

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.

This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.

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Surface Area and Volume
Math in the News: Issue 37--A Parade of Geometry Math in the News: Issue 37--A Parade of Geometry Math in the News: Issue 37--A Parade of Geometry

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

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Surface Area and Volume
Math in the News: Issue 38--December 7, 1941 Math in the News: Issue 38--December 7, 1941 Math in the News: Issue 38--December 7, 1941

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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Surface Area and Volume
Math in the News: Issue 39--Monument to a Hero Math in the News: Issue 39--Monument to a Hero Math in the News: Issue 39--Monument to a Hero

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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Surface Area and Volume
Math in the News: Issue 44--Sunk: The Costa Concordia Math in the News: Issue 44--Sunk: The Costa Concordia Math in the News: Issue 44--Sunk: The Costa Concordia

January 2012. In this issue of Math in the News we analyze how the Costa Concordia sank.

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Surface Area and Volume
Math in the News: Issue 53--Titanic: A Century Later Math in the News: Issue 53--Titanic: A Century Later Math in the News: Issue 53--Titanic: A Century Later

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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Surface Area and Volume
Math in the News: Issue 56--The Freedom Tower Math in the News: Issue 56--The Freedom Tower Math in the News: Issue 56--The Freedom Tower

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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3-Dimensional Figures
Math in the News: Issue 73--County Fairs and Funnel Cakes Math in the News: Issue 73--County Fairs and Funnel Cakes Math in the News: Issue 73--County Fairs and Funnel Cakes

August 2013. In this issue we look at the geometry of funnel cakes. You'll like the sweet results.

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Surface Area and Volume
Math in the News: Issue 75--A Swim for the Ages Math in the News: Issue 75--A Swim for the Ages Math in the News: Issue 75--A Swim for the Ages

August 2013. In this issue we look at Diana Nyad's remarkable swim from Cuba to Florida. It becomes an opportunity to explore Average Speed.

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Data Analysis
Math in the News: Issue 8--Tornado Damage Math in the News: Issue 8--Tornado Damage Math in the News: Issue 8--Tornado Damage

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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Data Analysis
Math in the News: Issue 9--Mississippi Floods Math in the News: Issue 9--Mississippi Floods Math in the News: Issue 9--Mississippi Floods

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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Volume
Promethean Flipchart: Algebra Applications: Cycling

The relationship between slope and grade in cycling is explored. Go on a tour of Italy through the mountains of Tuscany and apply students' understanding of slope. Note: The download for this resources is the Promethean Flipchart.

To access the full video: [Algebra Applications: Linear Functions, Segment 2: Cycling]: https://www.media4math.com/library/video-algebra-applications-linear-functions-segment-2-cycling

This video includes a Video Transcript: [Algebra Applications: Linear Functions, Segment 2: Cycling]: https://www.media4math.com/library/video-transcript-algebra-applications-linear-functions-segment-2-cycling

Applications of Linear Functions
Promethean Flipchart: Algebra Applications: Exercise

Exercise needs to become a consistent part of everyone's lifestyle. In particular, aerobic exercises, which vigorously exerts the heart, is an important form of exercise. The maximum heart rate from aerobic exercise is a linear function dependent on age. Students are asked to develop a data table based on the function. Note: The download for this resources is the Promethean Flipchart.

To access the full video: [Algebra Applications: Linear Functions, Segment 4: Exercise]: https://www.media4math.com/library/video-algebra-applications-linear-functions-segment-4-exercise

Applications of Linear Functions
Promethean Flipchart: Algebra Applications: Oil Drilling

The potential for oil exploration in the controversial Alaska National Wildlife Refuge (ANWR) sets the scene for this problem. A linear regression of oil consumption data over the past 25 years reveals an interesting pattern. How could new oil fields like ANWR help in breaking our dependence on foreign oil? Note: The download for this resources is the Promethean Flipchart.

To access the full video [Algebra Applications: Linear Functions, Segment 3: Oil Exploration]: https://www.media4math.com/library/video-algebra-applications-linear-functions-segment-3-oil-exploration

Applications of Linear Functions
Promethean Flipchart: Algebra Nspirations: Exponential Functions

Almost everyone has an intuitive understanding that exponential growth means rapid growth. Written and hosted by internationally acclaimed math educator Dr. Monica Neagoy, this video builds on students’ intuitive notions, explores exponential notation, and analyzes properties of exponential function graphs, with the help of TI-Nspire features such as sliders and graph transformations. Using exponential functions to model finance applications and a Newton’s law of cooling problem further help students build a solid foundation for these fundamental algebraic concepts. Concepts explored: functions, exponents, exponential functions Note: The download for this resources is the Promethean Flipchart.

Applications of Exponential and Logarithmic Functions
Promethean Flipchart: Algebra Nspirations: Functions and Relations

Functions are relationships between quantities that change. Written and hosted by internationally acclaimed math educator Dr. Monica Neagoy, this video explores the definition of a function, its vocabulary and notations, and distinguishes the concept of function from a general relation. Multiple representations of functions are provided using the TI-Nspire, while dynamic visuals and scenarios put them into real-world contexts. Concepts explored: functions, relations, equations, quadratic functions, linear functions, multiple representations Note: The download for this resources is the Promethean Flipchart.

This video includes a Video Transcript: https://www.media4math.com/library/video-transcript-algebra-nspirations-functions-and-relations

Applications of Functions and Relations
Promethean Flipchart: 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 Note: The download for this resources is the Promethean Flipchart.

This video includes a Teacher's Guide: https://www.media4math.com/library/algebra-nspirations-teachers-guide-linear-functions

Applications of Linear Functions
Promethean Flipchart: Algebra Nspirations: Logarithmic Functions

This video begins with the historical invention of logarithms that forever changed the world of computation—until the advent of calculators more than 300 years later. Written and hosted by internationally acclaimed math educator Dr. Monica Neagoy, it proceeds to derive the properties of logs, examine logarithmic functions and graphs, and finally explore the well-known Richter logarithmic scale. Concepts explored: functions and inverse functions, logarithms, exponential functions, logarithmic functions Note: The download for this resources is the Promethean Flipchart.

To access the full video: [Algebra Nspirations: Logarithms and Logarithmic Functions]: https://www.media4math.com/library/algebra-nspirations-logarithms-and-logarithmic-functions

Applications of Exponential and Logarithmic Functions
Promethean Flipchart: Algebra Nspirations: Quadratic Functions

In this program, the TI-Nspire is used to explore the nature of quadratic functions. Examples ranging from space travel and projectile motion provide real-world examples for discovering algebraic concepts. All examples are solved graphically. The teacher’s guide provides all keystrokes shown in the video, as well as providing support for TI-84 users. Algebra teachers looking to integrate hand-held technology and visual media into their instruction will benefit greatly from this series. Concepts explored: Quadratic functions and equations, standard form, graphing quadratic equations, solving quadratic equations graphically Note: The download for this resource is the Promethean Flipchart.

Applications of Quadratic Functions
Promethean Flipchart: Algebra Nspirations: Rational Functions

After briefly reviewing the concept of inverse variation, this video explores Boyle’s law, a real world example of an inversely proportional relationship between pressure and volume of a gas. Written and hosted by internationally acclaimed math educator Dr. Monica Neagoy, it goes on to examine similarities and differences among rational functions and numbers. Finally, it takes a look at rational functions graphs and ends with a delightful example merging Euclidean and analytic geometry, thanks to the TI-Nspire technology. Concepts explored: functions, rational expressions, rational functions, asymptotes Note: The download for this resources is the Promethean Flipchart.

To access the full video [Algebra Nspirations: Rational Functions and Expressions]: https://media4math.com/library/algebra-nspirations-rational-functions-and-expressions

Rational Functions and Equations
Promethean Flipchart: Geometry Applications: 3D Geometry 1

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

Applications of 3D Geometry
Promethean Flipchart: Geometry Applications: 3D Geometry 2

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

 

Applications of 3D Geometry
Quizlet Flash Cards: Composite Functions Quizlet Flash Cards: Composite Functions Quizlet Flash Cards: Composite Functions

What Are Composite Functions?

Modeling Functions

Composite Functions
Quizlet Flash Cards: Evaluating Functions Quizlet Flash Cards: Evaluating Functions Description

In this set of Quizlet flash cards test understanding of functions.

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Quizlet Library

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Relations and Functions
Quizlet Flash Cards: Identifying Functions Quizlet Flash Cards: Identifying Functions Description

In this set of Quizlet flash cards test understanding of functions.

Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards.

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Quizlet Library

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Relations and Functions
QuizletFlashCards.jpg Quizlet Flash Cards: Point-Slope Form

In this set of Quizlet flash cards test understanding of the point-slope form.

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Point-Slope Form
QuizletFlashCards.jpg Quizlet Flash Cards: Slope-Intercept Form

In this set of Quizlet flash cards test understanding of the slope-intercept form.

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Slope-Intercept Form
Test Prep Interactive Quiz--Linear Functions Test Prep Interactive Quiz--Linear Functions Test Prep Interactive Quiz--Linear Functions

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ary">click on this link.

Graphs of Linear Functions, Slope and Slope-Intercept Form
TI-84 Tutorial: Linear Functions TI-84 Tutorial: Linear Functions TI-84 Tutorial: Linear Functions

In this TI-84 tutorial we show how to graph linear functions and trace their coordinates. Note: The download is a PPT file.

Graphs of Linear Functions
Video Definition 1--3D Geometry--Antiprism Video Definition 1--3D Geometry--Antiprism Antiprism

Topic

3D Geometry

Definition

An antiprism is a polyhedron composed of two parallel copies of some particular polygon, connected by an alternating band of triangles.

3-Dimensional Figures
Video Definition 1--3D Geometry--Antiprism--Spanish Audio Video Definition 1--3D Geometry--Antiprism--Spanish Audio Video Definition 1--3D Geometry--Antiprism--Spanish Audio

This is part of a collection of math video definitions related to the topic of 3D Geometry. These videos have Spanish audio. Note: The download is an MP4 video.

3-Dimensional Figures
Video Definition 10--3D Geometry--Dodecahedron Video Definition 10--3D Geometry--Dodecahedron Dodecahedron

Topic

3D Geometry

Definition

A dodecahedron is a three-dimensional geometric shape with twelve flat faces, each a regular pentagon.

Description

Dodecahedrons are part of the family of Platonic solids, known for their symmetry and aesthetic appeal. They are used in various fields, including molecular chemistry and architecture, where symmetry plays a crucial role. Understanding dodecahedrons is important in math education as it introduces students to complex geometric shapes and their properties. Teachers can use models and diagrams to demonstrate the symmetry and structure of dodecahedrons, fostering an appreciation for geometric beauty and complexity.

3-Dimensional Figures