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Illustrative Math-Media4Math Alignment

 

 

Illustrative Math Alignment: Grade 6 Unit 1

Reasoning to Find Area

Lesson 17: Squares and Cubes

Use the following Media4Math resources with this Illustrative Math lesson.

Thumbnail Image Title Body Curriculum Nodes
Video Definition 49--3D Geometry--Vertical Cross-Section of a Cube

Video Definition 49--3D Geometry--Vertical Cross-Section of a Cube

Vertical Cross-Section of a Cube

Topic

3D Geometry

Definition

A vertical cross-section of a cube is the intersection of the cube with a vertical plane, resulting in a square.

3-Dimensional Figures
Video Definition 49--3D Geometry--Vertical Cross-Section of a Cube--Spanish Audio

Video Definition 49--3D Geometry--Vertical Cross-Section of a Cube--Spanish Audio

Video Definition 49--3D Geometry--Vertical Cross-Section of a Cube--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 5--3D Geometry--Cone

Video Definition 5--3D Geometry--Cone

Cone

Topic

3D Geometry

Definition

A cone is a three-dimensional geometric shape with a circular base and a single vertex, called the apex, not in the plane of the circle.

Description

Cones are prevalent in both natural and man-made structures, such as traffic cones and volcanoes. In mathematics, cones are studied for their properties, including surface area and volume. The volume V of a cone is given by the formula

V = 1/3 πr2h

Cones
Video Definition 5--3D Geometry--Cone--Spanish Audio

Video Definition 5--3D Geometry--Cone--Spanish Audio

Video Definition 5--3D Geometry--Cone--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.

Cones
Video Definition 50--3D Geometry--Vertical Cross-Section of a Dodecahedron

Video Definition 50--3D Geometry--Vertical Cross-Section of a Dodecahedron

Vertical Cross-Section of a Dodecahedron

Topic

3D Geometry

Definition

A vertical cross-section of a dodecahedron is the intersection of the dodecahedron with a vertical plane, resulting in a polygon.

3-Dimensional Figures
Video Definition 50--3D Geometry--Vertical Cross-Section of a Dodecahedron--Spanish Audio

Video Definition 50--3D Geometry--Vertical Cross-Section of a Dodecahedron--Spanish Audio

Video Definition 50--3D Geometry--Vertical Cross-Section of a Dodecahedron--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 51--3D Geometry--Vertical Cross-Section of a Sphere

Video Definition 51--3D Geometry--Vertical Cross-Section of a Sphere

Vertical Cross-Section of a Sphere

Topic

3D Geometry

Definition

A vertical cross-section of a sphere is the intersection of the sphere with a vertical plane, resulting in a circle.

3-Dimensional Figures
Video Definition 51--3D Geometry--Vertical Cross-Section of a Sphere--Spanish Audio

Video Definition 51--3D Geometry--Vertical Cross-Section of a Sphere--Spanish Audio

Video Definition 51--3D Geometry--Vertical Cross-Section of a Sphere--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 52--3D Geometry--Vertical Cross-Section of a Tetrahedron

Video Definition 52--3D Geometry--Vertical Cross-Section of a Tetrahedron

Vertical Cross-Section of a Tetrahedron

Topic

3D Geometry

Definition

A vertical cross-section of a tetrahedron is the intersection of the tetrahedron with a vertical plane, resulting in a triangle or another polygon.

3-Dimensional Figures
Video Definition 52--3D Geometry--Vertical Cross-Section of a Tetrahedron--Spanish Audio

Video Definition 52--3D Geometry--Vertical Cross-Section of a Tetrahedron--Spanish Audio

Video Definition 52--3D Geometry--Vertical Cross-Section of a Tetrahedron--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 53--3D Geometry--Vertical Cross-Section of an Antiprism

Video Definition 53--3D Geometry--Vertical Cross-Section of an Antiprism

Vertical Cross-Section of an Antiprism

Topic

3D Geometry

Definition

A vertical cross-section of an antiprism is the intersection of the antiprism with a vertical plane, resulting in a polygon.

3-Dimensional Figures
Video Definition 53--3D Geometry--Vertical Cross-Section of an Antiprism--Spanish Audio

Video Definition 53--3D Geometry--Vertical Cross-Section of an Antiprism--Spanish Audio

Video Definition 53--3D Geometry--Vertical Cross-Section of an 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 54--3D Geometry--Vertical Cross-Section of an Icosahedron

Video Definition 54--3D Geometry--Vertical Cross-Section of an Icosahedron

Vertical Cross-Section of an Icosahedron

Topic

3D Geometry

Definition

A vertical cross-section of an icosahedron is the intersection of the icosahedron with a vertical plane, resulting in a polygon.

3-Dimensional Figures
Video Definition 54--3D Geometry--Vertical Cross-Section of an Icosahedron--Spanish Audio

Video Definition 54--3D Geometry--Vertical Cross-Section of an Icosahedron--Spanish Audio

Video Definition 54--3D Geometry--Vertical Cross-Section of an Icosahedron--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 55--3D Geometry--Vertical Cross-Sections of a Cone

Video Definition 55--3D Geometry--Vertical Cross-Sections of a Cone

Vertical Cross-Sections of a Cone

Topic

3D Geometry

Definition

Vertical cross-sections of a cone are the intersections of the cone with vertical planes, resulting in shapes like triangles or parabolas.

Cones
Video Definition 55--3D Geometry--Vertical Cross-Sections of a Cone--Spanish Audio

Video Definition 55--3D Geometry--Vertical Cross-Sections of a Cone--Spanish Audio

Video Definition 55--3D Geometry--Vertical Cross-Sections of a Cone--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.

Cones
Video Definition 56--3D Geometry--Vertical Cross-Sections of a Cylinder

Video Definition 56--3D Geometry--Vertical Cross-Sections of a Cylinder

Vertical Cross-Sections of a Cylinder

Topic

3D Geometry

Definition

Vertical cross-sections of a cylinder are the intersections of the cylinder with vertical planes, resulting in rectangles or ellipses.

Cylinders
Video Definition 56--3D Geometry--Vertical Cross-Sections of a Cylinder--Spanish Audio

Video Definition 56--3D Geometry--Vertical Cross-Sections of a Cylinder--Spanish Audio

Video Definition 56--3D Geometry--Vertical Cross-Sections of a Cylinder--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.

Cylinders
Video Definition 57--3D Geometry--Vertical Cross-Sections of a Square Pyramid

Video Definition 57--3D Geometry--Vertical Cross-Sections of a Square Pyramid

Vertical Cross-Sections of a Square Pyramid

Topic

3D Geometry

Definition

Vertical cross-sections of a square pyramid are the intersections of the pyramid with vertical planes, resulting in triangles or trapezoids.

Pyramids
Video Definition 57--3D Geometry--Vertical Cross-Sections of a Square Pyramid--Spanish Audio

Video Definition 57--3D Geometry--Vertical Cross-Sections of a Square Pyramid--Spanish Audio

Video Definition 57--3D Geometry--Vertical Cross-Sections of a Square Pyramid--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.

Pyramids
Video Definition 58--3D Geometry--Vertical Cross-Sections of a Triangular Prism

Video Definition 58--3D Geometry--Vertical Cross-Sections of a Triangular Prism

Vertical Cross-Sections of a Triangular Prism

Topic

3D Geometry

Definition

Vertical cross-sections of a triangular prism are the intersections of the prism with vertical planes, resulting in rectangles or triangles.

Triangular Prisms
Video Definition 58--3D Geometry--Vertical Cross-Sections of a Triangular Prism--Spanish Audio

Video Definition 58--3D Geometry--Vertical Cross-Sections of a Triangular Prism--Spanish Audio

Video Definition 58--3D Geometry--Vertical Cross-Sections of a Triangular Prism--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.

Triangular Prisms
Video Definition 59--3D Geometry--Volume

Video Definition 59--3D Geometry--Volume

Volume

Topic

3D Geometry

Definition

Volume is the amount of space occupied by a three-dimensional object.

Description

Volume is a fundamental concept in geometry, representing the amount of space a three-dimensional object occupies. It is essential for calculating the capacity of containers, the displacement of fluids, and the mass of objects. Understanding volume involves using formulas specific to each shape, such as 

V = l × w × h

 for a rectangular prism or 

V = 4/3 πr3

Volume
Video Definition 59--3D Geometry--Volume--Spanish Audio

Video Definition 59--3D Geometry--Volume--Spanish Audio

Video Definition 59--3D Geometry--Volume--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.

Volume
Video Definition 6--3D Geometry--Cross-sections of a Cube

Video Definition 6--3D Geometry--Cross-sections of a Cube

Cross-sections of a Cube

Topic

3D Geometry

Definition

Cross-sections of a cube are the intersections of a plane with the cube, resulting in various two-dimensional shapes.

Cubes
Video Definition 6--3D Geometry--Cross-sections of a Cube--Spanish Audio

Video Definition 6--3D Geometry--Cross-sections of a Cube--Spanish Audio

Video Definition 6--3D Geometry--Cross-sections of a Cube--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.

Cubes
Video Definition 7--3D Geometry--Cross-Sections of a Sphere

Video Definition 7--3D Geometry--Cross-Sections of a Sphere

Cross-Sections of a Sphere

Topic

3D Geometry

Definition

Cross-sections of a sphere are circular slices obtained by cutting the sphere with a plane.

Spheres
Video Definition 7--3D Geometry--Cross-Sections of a Sphere--Spanish Audio

Video Definition 7--3D Geometry--Cross-Sections of a Sphere--Spanish Audio

Video Definition 7--3D Geometry--Cross-Sections of a Sphere--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.

Spheres
Video Definition 8--3D Geometry--Cube

Video Definition 8--3D Geometry--Cube

Cube

Topic

3D Geometry

Definition

A cube is a three-dimensional geometric figure with six equal square faces.

Description

Cubes are fundamental in geometry due to their symmetry and simplicity. They are used in various applications, such as packaging and architecture, where efficient space utilization is essential. The volume V of a cube is calculated as 

V = a3

Cubes
Video Definition 8--3D Geometry--Cube--Spanish Audio

Video Definition 8--3D Geometry--Cube--Spanish Audio

Video Definition 8--3D Geometry--Cube--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.

Cubes
Video Definition 9--3D Geometry--Cylinder

Video Definition 9--3D Geometry--Cylinder

Cylinder

Topic

3D Geometry

Definition

A cylinder is a three-dimensional geometric shape with two parallel circular bases connected by a curved surface.

Description

Cylinders are common in everyday objects, such as cans and pipes. In mathematics, cylinders are studied for their properties, including surface area and volume. The volume V of a cylinder is given by the formula 

V = πr2h

Cylinders
Video Definition 9--3D Geometry--Cylinder--Spanish Audio

Video Definition 9--3D Geometry--Cylinder--Spanish Audio

Video Definition 9--3D Geometry--Cylinder--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.

Cylinders
Video Transcript: Desmos Geometry Exploration: Quadrilaterals with Parallel Sides

Video Transcript: Desmos Geometry Exploration: Quadrilaterals with Parallel Sides

Video Transcript: Desmos Geometry Exploration: Quadrilaterals with Parallel Sides

This is the transcript for the video entitled, Desmos Geometry Exploration: Quadrilaterals with Parallel Lines. In this video tutorial the basics of quadrilaterals are explored. Students are then shown how to construct quadrilaterals using the Desmos geometry tools.

Definition of a Quadrilateral
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 Transcript: Geometry Applications: Quadrilaterals, Segment 2: Squares and Rectangles

Video Transcript: Geometry Applications: Quadrilaterals, Segment 2: Squares and Rectangles

Video Transcript: Geometry Applications: Quadrilaterals, Segment 2: Squares and Rectangles

This is the transcript for the video of same title. Video contents: Frank Lloyd Wright's architectural masterpiece Falling Water is also a stunning assembly of quadrilateral shapes. Some of the rectangular forms in this building seem to defy gravity, as we explore the properties of squares and rectangles that allowed Frank Lloyd Wright to push the envelope of design and structure.

Applications of Quadrilaterals
Video Transcript: Geometry Applications: Transformations, Segment 2: 3D Translations

Video Transcript: Geometry Applications: Transformations, Segment 2: 3D Translations

Video Transcript: Geometry Applications: Transformations, Segment 2: 3D Translations

This is the transcript for the video of same title. Video contents: Cargo ships transport tons of merchandise from one country to another and accounts for most of the global economy. Loading and unloading these ships requires a great deal of organization and provides an ideal example of three-dimensional translations.

Applications of Transformations
Video Tutorial: Desmos Geometry Exploration: Quadrilateral with Parallel Sides

Video Tutorial: Desmos Geometry Exploration: Quadrilateral with Parallel Sides

Video Tutorial: Desmos Geometry Exploration: Quadrilateral with Parallel Sides

This is part of a collection of video tutorials on the topic of using the Desmos Geometry tools to explore geometric concepts.

Definition of a Quadrilateral
VIDEO: Geometry Applications: 3D Geometry

VIDEO: Geometry Applications: 3D Geometry

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
VIDEO: Geometry Applications: 3D Geometry, Segment 1: Introduction.

VIDEO: Geometry Applications: 3D Geometry, 1

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
VIDEO: Geometry Applications: 3D Geometry, Segment 2: Pyramids

VIDEO: Geometry Applications: 3D Geometry, 2

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
VIDEO: Geometry Applications: 3D Geometry, Segment 3: Cylinders

VIDEO: Geometry Applications: 3D Geometry, 3

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
VIDEO: Geometry Applications: Quadrilaterals, Segment 1: Introduction

VIDEO: Geometry Applications: Quadrilaterals, 1

VIDEO: Geometry Applications: Quadrilaterals, Segment 1: Introduction

Stonehenge is best known as a circular structure. But it’s the post and lintel construction used that is noteworthy, and this type of construction involves quadrilateral shapes. From the familiar door frames of houses to the majestic entryways of ancient temples, post and lintel construction provides a clear introduction to the nature of quadrilaterals. This segment also describes the key concepts developed throughout the program.

Applications of Quadrilaterals
VIDEO: Geometry Applications: Quadrilaterals, Segment 2: Squares and Rectangles

VIDEO: Geometry Applications: Quadrilaterals, 2

VIDEO: Geometry Applications: Quadrilaterals, Segment 2: Squares and Rectangles

Frank Lloyd Wright’s architectural masterpiece Falling Water is also a stunning assembly of quadrilateral shapes. Some of the rectangular forms in this building seem to defy gravity, as we explore the properties of squares and rectangles that allowed Frank Lloyd Wright to push the envelope of design and structure.

Applications of Quadrilaterals
Worksheet: 2D-3D Shapes

Worksheet: 2D-3D Shapes, Worksheet 4

Worksheet: 2D-3D Shapes, Worksheet 4

This is part of a collection of math worksheets on the topic of 2D and 3D geometry.

To see the complete worksheet collection on this topic, click on this link. Note: The download is a PDF file.

Related Resources

To see additional resources on this topic, click on the Related Resources tab.

Worksheet Library

To see the complete collection of Worksheets, click on this link.
3-Dimensional Figures
WorksheetThumbnail.jpg

Worksheet: Crossword Puzzle--Quadrilaterals

Worksheet: Crossword Puzzle--Quadrilaterals

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

To see the complete worksheet collection on this topic, click on this link. Note: The download is a PDF file.

Related Resources

To see additional resources on this topic, click on the Related Resources tab.

Worksheet Library

To see the complete collection of Worksheets, click on this link.
Definition of a Quadrilateral