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Illustrative Math-Media4Math Alignment

 

 

Illustrative Math Alignment: Grade 8 Unit 3

Functions and Volume

Lesson 22: Volume As a Function of . . .

Use the following Media4Math resources with this Illustrative Math lesson.

Thumbnail Image Title Body Curriculum Topic
Math Example--Volume Concepts--Exploring Volumes of Cubes: Example 1 Math Example--Volume Concepts--Exploring Volumes of Cubes: Example 1 Math Example--Volume Concepts--Exploring Volumes of Cubes: Example 1

This is part of a collection of math examples that focus on volume.

Volume
Math Example--Volume Concepts--Exploring Volumes of Cubes: Example 2 Math Example--Volume Concepts--Exploring Volumes of Cubes: Example 2 Math Example--Volume Concepts--Exploring Volumes of Cubes: Example 2

This is part of a collection of math examples that focus on volume.

Volume
Math Example--Volume Concepts--Exploring Volumes of Cubes: Example 3 Math Example--Volume Concepts--Exploring Volumes of Cubes: Example 3 Math Example--Volume Concepts--Exploring Volumes of Cubes: Example 3

This is part of a collection of math examples that focus on volume.

Volume
Math Example--Volume Concepts--Exploring Volumes of Cubes: Example 4 Math Example--Volume Concepts--Exploring Volumes of Cubes: Example 4 Math Example--Volume Concepts--Exploring Volumes of Cubes: Example 4

This is part of a collection of math examples that focus on volume.

Volume
Math Example--Volume Concepts--Exploring Volumes of Cubes: Example 5 Math Example--Volume Concepts--Exploring Volumes of Cubes: Example 5 Math Example--Volume Concepts--Exploring Volumes of Cubes: Example 5

This is part of a collection of math examples that focus on volume.

Volume
Math Example--Volume Concepts--Exploring Volumes of Cubes: Example 6 Math Example--Volume Concepts--Exploring Volumes of Cubes: Example 6 Math Example--Volume Concepts--Exploring Volumes of Cubes: Example 6

This is part of a collection of math examples that focus on volume.

Volume
Math Example--Volume Concepts--Exploring Volumes of Cubes: Example 7 Math Example--Volume Concepts--Exploring Volumes of Cubes: Example 7 Math Example--Volume Concepts--Exploring Volumes of Cubes: Example 7

This is part of a collection of math examples that focus on volume.

Volume
Math Example--Volume Concepts--Exploring Volumes of Cubes: Example 8 Math Example--Volume Concepts--Exploring Volumes of Cubes: Example 8 Math Example--Volume Concepts--Exploring Volumes of Cubes: Example 8

This is part of a collection of math examples that focus on volume.

Volume
Math Example--Volume Concepts--Modeling Volume--Example 1 Math Example--Volume Concepts--Modeling Volume--Example 1 Math Example--Volume Concepts--Modeling Volume--Example 1

Topic

Volume

Description

The image shows a rectangular prism made up of 3 unit cubes arranged in a single row. The example asks for the volume of the figure, and the solution involves counting the number of unit cubes. Example 1: The figure consists of 3 unit cubes. The caption reads: "Count the number of unit cubes to find the volume. 3 unit cubes means that the volume is 3."

Volume
Math Example--Volume Concepts--Modeling Volume--Example 2 Math Example--Volume Concepts--Modeling Volume--Example 2 Math Example--Volume Concepts--Modeling Volume--Example 2

Topic

Volume

Description

The image shows a figure made up of 4 unit cubes, with one cube stacked on top of another, forming an L-shape. The example asks for the volume, and the solution involves counting the cubes. Example 2: The figure consists of 4 unit cubes. The caption reads: "Count the number of unit cubes to find the volume. 4 unit cubes means that the volume is 4."

Volume
Math Example--Volume Concepts--Modeling Volume--Example 3 Math Example--Volume Concepts--Modeling Volume--Example 3 Math Example--Volume Concepts--Modeling Volume--Example 3

Topic

Volume

Description

The image shows a figure made up of 5 unit cubes arranged in an irregular shape, with one cube raised above others. The example asks for the volume, and the solution involves counting the number of unit cubes. Example 3: The figure consists of 5 unit cubes. The caption reads: "Count the number of unit cubes to find the volume. 5 unit cubes means that the volume is 5."

Volume
Math Example--Volume Concepts--Modeling Volume--Example 4 Math Example--Volume Concepts--Modeling Volume--Example 4 Math Example--Volume Concepts--Modeling Volume--Example 4

Topic

Fractions

Description

The image shows a rectangular prism made up of 6 unit cubes arranged in two layers (a top and bottom row). The example asks for the volume, and the solution involves counting all the cubes in both layers. Example 4: The figure consists of 6 unit cubes. The caption reads: "Count the number of unit cubes to find the volume. 6 unit cubes means that the volume is 6."

Volume
Math Example--Volume Concepts--Modeling Volume--Example 5 Math Example--Volume Concepts--Modeling Volume--Example 5 Math Example--Volume Concepts--Modeling Volume--Example 5

Topic

Fractions

Description

The image shows a 3D figure made up of unit cubes. The figure is stacked in a staggered manner, with some cubes placed directly on top of others. Below the figure, there is a breakdown showing the individual cubes counted to determine the volume. Example 5: The caption asks for the volume of the figure, which is made up of unit cubes. The solution involves counting the cubes to find the volume.

Volume
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.

Related Resources

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

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.

Related Resources

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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 20--Heat Wave! Math in the News: Issue 20--Heat Wave! Math in the News: Issue 20--Heat Wave!

8/1/11. In this issue we look at the physics of air pressure and the forces that give rise to heat waves.

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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Data Analysis
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.

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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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.

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 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.

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 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.

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 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.

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 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.

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 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.

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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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.

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 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.

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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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.

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
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.

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

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Quizlet Library

To see the complete Quizlet Flash Card Library, click on this Link to see the collection.

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.

Related Resources

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Quizlet Library

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Relations and Functions
Video Transcript: Algebra Applications: Rational Functions, Segment 2: Biology Video Transcript: Algebra Applications: Rational Functions, Segment 2: Biology Video Transcript: Algebra Applications: Rational Functions, Segment 2: Biology

This is the transcript for the video of same title. Video contents: 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
Video Transcript: Algebra Nspirations: Functions and Relations, Part 2 Video Transcript: Algebra Nspirations: Functions and Relations, 2 Video Transcript: Algebra Nspirations: Functions and Relations, Part 2

This is the transcript for the video of same title. Video contents: In this Investigation we look at functions.

This is part of a collection of video transcript from the Algebra Nspirations video series. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript Library

To see the complete collection of video transcriptsy, click on this link.

Applications of Functions and Relations and Relations and Functions
Video Transcript: Geometry Applications--Volume of a Pyramid Video Transcript: Geometry Applications--Volume of a Pyramid Video Transcript: Geometry Applications--Volume of a Pyramid

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

This is part of a collection of video transcript from the Geometry Applications video series. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript Library

To see the complete collection of video transcriptsy, click on this link.

Video Library

To see the complete collection of videos in the Video Library, click on this link.

Pyramids
Video Transcript: Geometry Applications: 3D Geometry Video Transcript: Geometry Applications: 3D Geometry Video Transcript: Geometry Applications: 3D Geometry

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.

3-Dimensional Figures and Applications of 3D Geometry
Video Transcript: Geometry Applications: 3D Geometry, Segment 1: Introduction Video Transcript: Geometry Applications: 3D Geometry, Segment 1: Introduction Video Transcript: Geometry Applications: 3D Geometry, Segment 1: Introduction

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.

This is part of a collection of video transcript from the Geometry Applications video series. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript Library

To see the complete collection of video transcriptsy, click on this link.

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

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.

3-Dimensional Figures and Applications of 3D Geometry
Video Transcript: Geometry Applications: 3D Geometry, Segment 3: Cylinders Video Transcript: Geometry Applications: 3D Geometry, Segment 3: Cylinders Video Transcript: Geometry Applications: 3D Geometry, Segment 3: Cylinders

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.

3-Dimensional Figures and Applications of 3D Geometry
Video Tutorial: Multiple Representations of Functions Video Tutorial: Multiple Representations of Functions Video Tutorial: Multiple Representations of Functions

This video looks at multiple representations of functions, including symbolic, tabular, and graphic. Examples of linear, quadratic, polynomial, and exponential functions are shown.

Relations and Functions
VIDEO: 3D Geometry Animation: Antiprism Folding Out into Two Pyramids VIDEO: 3D Geometry Animation: Antiprisms 2 VIDEO: 3D Geometry Animation: Antiprism Folding Out into Two Pyramids

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