Illustrative Math-Media4Math Alignment

 

 

Illustrative Math Alignment: Grade 8 Unit 3

Functions and Volume

Lesson 12: How Much Will Fit?

Use the following Media4Math resources with this Illustrative Math lesson.

Thumbnail Image Title Body Curriculum Topic
Collection Holiday Themed Resource Collection: Math in the News  

This is a collection of Holiday-Themed issues of Math in the News.

 

Data Analysis, Applications of Exponential and Logarithmic Functions, Surface Area and Volume
Math in the News Math in the News Collection: Applications of Surface Area and Volume

Overview

This is a collection of issues of Math in the News that deal with applications of Surface Area and Volume.

 

 

 
Surface Area and Volume
Math in the News Math in the News Collection: Applications of 3D Geometry

Overview

This is a collection of issues of Math in the News that deal with applications of 3D geometry.

 

 

 
3-Dimensional Figures and Applications of 3D Geometry
Math in the News Math in the News Collection: Business Math

Overview

This is a collection of issues of Math in the News that deal with business applications.

 

 

 
Applications of Exponential and Logarithmic Functions, Data Analysis and Volume
Math in the News Math in the News Collection: Applications of Data Analysis

Overview

This is a collection of Math in the News stories that focus on the topic of Data Analysis.

 

 

 
Data Analysis, Data Gathering, Probability, Percents and Ratios and Rates
Math Examples Math Examples Collection: Calculating Mass and Volume

Overview

This collection aggregates all the math examples around the topic of Calculating Mass and Volume. There are a total of 10 Math Examples. This collection of resources is made up of downloadable PNG images that you can easily incorporate into your lesson plans.

 

To learn more about Media4Math's Math Examples, click on this video link.

 

Mass and Volume
Math Videos Math Video Collection: 3D Geometry Animations

Overview

This collection aggregates all the math videos and resources in this series: 3D Geometry Animations. There are a total of 10 resources. This collection of resources is made up of downloadable MP4, transcripts, and other resources files that you can easily incorporate into a presentation.

 

3-Dimensional Figures, Cubes, Cones, Triangular Prisms, Pyramids, Cylinders and Rectangular Prisms
Math Videos Math Video Collection: Geometry Applications Video Series: Surface Area and Volume

Overview

This collection aggregates all the math videos and resources in this series: Geometry Applications Video Series: Surface Area and Volume. There are a total of 12 resources. This collection of resources is made up of downloadable MP4, transcripts, and other resources files that you can easily incorporate into a presentation.

 

Applications of Surface Area and Volume, Surface Area and Volume
Math Examples Math Examples Collection: Volumes of Cubes

Overview

This collection aggregates all the math examples around the topic of Volumes of Cubes. There are a total of 8 Math Examples. This collection of resources is made up of downloadable PNG images that you can easily incorporate into your lesson plans.

 

Volume
Math Examples Math Examples Collection: Volume

Overview

This collection of math examples on the topic of Volume provides students with an in-depth exploration of volume concepts through a variety of visual models. Covering a range of skills and increasing in complexity, this collection helps students master foundational and advanced topics in volume. From calculating the volume of basic geometric shapes to applying volume formulas to complex objects, these examples build confidence and enhance comprehension by breaking down challenging concepts visually.

Volume
Math Examples Math Examples Collection: Perfect Squares and Cubes--Area and Volume

Overview

Explore an in-depth collection of math examples on perfect squares and cubes, ideal for mastering polynomial concepts. This Media4Math collection features a progression of examples that build from foundational to more advanced polynomial skills, helping students gain confidence as they move through increasingly complex exercises. Each example incorporates visual models, which are particularly useful for simplifying abstract concepts like polynomial expansion and factorization, making the learning process more accessible.

Variable Expressions
Math Examples Math Examples Collection: Modeling Volume

Overview

This collection of math examples on the topic of Volume provides a comprehensive approach to understanding and mastering volume calculations. These examples increase in complexity and cover a range of essential skills, from basic volume calculations of simple shapes to more advanced composite figures. Using visual models, these examples simplify complex concepts, helping students grasp the intricacies of volume calculation through clear, engaging representations.

Volume
Math Videos Math Video Collection: Geometry Applications Video Series: 3D Geometry

Overview

This collection aggregates all the math videos and resources in this series: Geometry Applications Video Series: 3D Geometry. There are a total of 18 resources. This collection of resources is made up of downloadable MP4, transcripts, and other resources files that you can easily incorporate into a presentation.

 

3-Dimensional Figures, Applications of 3D Geometry, Pyramids, Cylinders, Rectangular Prisms and Triangular Prisms
VIDEO: 3D Geometry Animation: Antiprism VIDEO: 3D Geometry Animation: Antiprism VIDEO: 3D Geometry Animation: Antiprism

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.

— CLICK THE PREVIEW BUTTON TO SEE THE VIDEO ANIMATION —

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 Triangular Prisms
VIDEO: 3D Geometry Animation: Cone VIDEO: 3D Geometry Animation: Cone VIDEO: 3D Geometry Animation: Cone

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.

— CLICK THE PREVIEW BUTTON TO SEE THE VIDEO ANIMATION —

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 Cones
VIDEO: 3D Geometry Animation: Cube VIDEO: 3D Geometry Animation: Cube VIDEO: 3D Geometry Animation: Cube

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.

— CLICK THE PREVIEW BUTTON TO SEE THE VIDEO ANIMATION —

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 Cubes
VIDEO: 3D Geometry Animation: Cylinder VIDEO: 3D Geometry Animation: Cylinder 3D Geometry Animation: Cylinder

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.

— CLICK THE PREVIEW BUTTON TO SEE THE VIDEO ANIMATION —

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 Cylinders
VIDEO: 3D Geometry Animation: Octahedron VIDEO: 3D Geometry Animation: Octahedron VIDEO: 3D Geometry Animation: Octahedron

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.

— CLICK THE PREVIEW BUTTON TO SEE THE VIDEO ANIMATION —

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
VIDEO: 3D Geometry Animation: Pyramid VIDEO: 3D Geometry Animation: Pyramid VIDEO: 3D Geometry Animation: Pyramid

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.

— CLICK THE PREVIEW BUTTON TO SEE THE VIDEO ANIMATION —

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 Pyramids
VIDEO: 3D Geometry Animation: Rectangular Prism VIDEO: 3D Geometry Animation: Rectangular Prism VIDEO: 3D Geometry Animation: Rectangular Prism

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.

— CLICK THE PREVIEW BUTTON TO SEE THE VIDEO ANIMATION —

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 Rectangular Prisms
VIDEO: 3D Geometry Animation: Tetrahedron VIDEO: 3D Geometry Animation: Tetrahedron VIDEO: 3D Geometry Animation: Tetrahedron

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.

— CLICK THE PREVIEW BUTTON TO SEE THE VIDEO ANIMATION —

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
VIDEO: 3D Geometry Animation: Triangular Prism VIDEO: 3D Geometry Animation: Triangular Prism VIDEO: 3D Geometry Animation: Triangular Prism

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.

— CLICK THE PREVIEW BUTTON TO SEE THE VIDEO ANIMATION —

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
Closed Captioned Video: Algebra Applications: Rational Functions, Segment 1: Submarines Closed Captioned Video: Algebra Applications: Rational Functions, 1 Closed Captioned Video: Algebra Applications: Rational Functions, 1

Topic

Rational Functions

Description

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

This video provides a detailed explanation of explains submarine pressure and volume relationships using rational functions, illustrating depth impacts on vessel integrity and scuba safety. and its significance in understanding rational functions.

Rational Expressions and Rational Functions and Equations
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, 2

Topic

Rational Functions

Description

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

This video provides a detailed explanation of examines surface area to volume ratios in animals using rational functions, connecting these ratios to evolutionary adaptations in different climates and its significance in understanding rational functions.

Rational Expressions and Rational Functions and Equations
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

Topic

3D Geometry

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, 1

Topic

3D Geometry

Description

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.

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, 2

Topic

3D Geometry

Description

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.

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, 3

Topic

3D Geometry

Description

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.

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

Topic

Area and Volume

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, 1

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.

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, 1

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.

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, 2

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.

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, 3

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.

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.)

Your browser does not support the video tag.

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: 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
Math Example--Polynomial Concepts-- Perfect Squares and Cubes--Example 1 Math Example--Polynomial Concepts-- Perfect Squares and Cubes--Example 1 Math Example--Polynomial Concepts-- Perfect Squares and Cubes--Example 1

Topic

Polynomials

Description

An example showing how to find the side lengths of a square given its area, A = x2+ 2x + 1.

Example 1: Given the area A = x2+ 2x + 1, find the side lengths. Solution: Express the area as a perfect square, (x + 1)2, so the side lengths are x + 1.

Polynomials involve expressions with variables raised to powers, and these examples specifically address perfect squares and cubes. Each example in this collection explores how to derive side lengths or volumes using factorization, demonstrating the practical applications of polynomial expressions.

Variable Expressions
Math Example--Polynomial Concepts-- Perfect Squares and Cubes--Example 2 Math Example--Polynomial Concepts-- Perfect Squares and Cubes--Example 2 Math Example--Polynomial Concepts-- Perfect Squares and Cubes--Example 2

Topic

Polynomials

Description

Another example of finding the side lengths of a square with area A = x2+ 4x + 4.

Example 2: Given A = x2+ 4x + 4, find the side lengths. Solution: Factor as (x + 2)2, so the side lengths are x + 2.

Polynomials involve expressions with variables raised to powers, and these examples specifically address perfect squares and cubes. Each example in this collection explores how to derive side lengths or volumes using factorization, demonstrating the practical applications of polynomial expressions.

Variable Expressions
Math Example--Polynomial Concepts-- Perfect Squares and Cubes--Example 3 Math Example--Polynomial Concepts-- Perfect Squares and Cubes--Example 3 Math Example--Polynomial Concepts-- Perfect Squares and Cubes--Example 3

Topic

Polynomials

Description

Shows how to determine the side lengths of a square with area A = x2 - 2x + 1.

Example 3: For A = x2 - 2x + 1, the solution expresses it as (x - 1)2, making the side lengths x - 1.

Polynomials involve expressions with variables raised to powers, and these examples specifically address perfect squares and cubes. Each example in this collection explores how to derive side lengths or volumes using factorization, demonstrating the practical applications of polynomial expressions.

Variable Expressions