Illustrative Math-Media4Math Alignment

 

 

Illustrative Math Alignment: Grade 7 Unit 3

Measuring Circles

Lesson 11: Stained-Glass Windows

Use the following Media4Math resources with this Illustrative Math lesson.

Thumbnail Image Title Body Curriculum Nodes
Math Clip Art--Venn Diagram 1 Math Clip Art--Venn Diagram 1 Math Clip Art--Venn Diagram 1

This is part of a collection of math clip art images that show Venn Diagrams.

Applications of Circles
Formulas--Area of a Semi-Circle Formulas--Area of a Semi-Circle Formulas--Area of a Semi-Circle

The formula for: Area of a Semi-Circle.

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

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Area and Circumference
Formulas--Circumference of a Circle Formulas--Circumference of a Circle Formulas--Circumference of a Circle

The formula for the Circumference of a Circle.

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.

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Area and Circumference
Math Clip Art--Geometry Concepts--Circle Illustrations--Circle Math Clip Art--Geometry Concepts--Circle Illustrations--Circle Math Clip Art--Circle Illustrations--Circle

Topic

Geometry Concepts

Description

This clip art illustrates a basic circle, which is a fundamental shape in geometry. A circle is defined as the set of all points in a plane that are equidistant from a central point. This image serves as a visual representation of this concept, showcasing the perfect symmetry and continuous curvature that characterize circles.

Definition of a Circle
Math Clip Art--Geometry Concepts--Circle Illustrations--Circle Centered at Origin of Coordinate Grid Math Clip Art--Geometry Concepts--Circle Illustrations--Circle Centered at Origin of Coordinate Grid Math Clip Art--Circle Illustrations--Circle Centered at Origin of Coordinate Grid

Topic

Geometry Concepts

Description

This clip art depicts a circle centered at the origin (0,0) of a coordinate grid. It illustrates the relationship between circles and the Cartesian coordinate system, a fundamental concept in analytic geometry. The image shows how a circle's position can be defined in relation to the x and y axes.

Definition of a Circle
Math Clip Art--Geometry Concepts--Circle Illustrations--Circle Centered at Origin of Coordinate Grid--with Radius Labeled Math Clip Art--Geometry Concepts--Circle Illustrations--Circle Centered at Origin of Coordinate Grid--with Radius Labeled Math Clip Art--Circle Illustrations--Circle Centered at Origin of Coordinate Grid--with Radius Labeled

Topic

Geometry Concepts

Description

This clip art shows a circle centered at the origin of a coordinate grid with its radius clearly labeled. This illustration is crucial for understanding the relationship between a circle's radius and its equation in the coordinate plane. The labeled radius helps visualize how the distance from the center to any point on the circle remains constant, which is the defining property of a circle.

Definition of a Circle
Math Clip Art--Geometry Concepts--Circle Illustrations--Circle Centered in Q1 Math Clip Art--Geometry Concepts--Circle Illustrations--Circle Centered in Q1 Math Clip Art--Circle Illustrations--Circle Centered in Q1

Topic

Geometry Concepts

Description

This clip art illustrates a circle centered in the first quadrant (Q1) of the coordinate plane. This representation is crucial for understanding how the position of a circle's center affects its equation and properties. In Q1, both x and y coordinates of the center are positive, which influences the circle's equation and its intersection with the axes.

Definition of a Circle
Math Clip Art--Geometry Concepts--Circle Illustrations--Circle Centered in Q2 Math Clip Art--Geometry Concepts--Circle Illustrations--Circle Centered in Q2 Math Clip Art--Circle Illustrations--Circle Centered in Q2

Topic

Geometry Concepts

Description

This clip art shows a circle centered in the second quadrant (Q2) of the coordinate plane. In Q2, the x-coordinate of the center is negative while the y-coordinate is positive. This positioning is crucial for understanding how the location of a circle's center affects its equation and its relationship with the coordinate axes.

Definition of a Circle
Math Clip Art--Geometry Concepts--Circle Illustrations--Circle Centered in Q3 Math Clip Art--Geometry Concepts--Circle Illustrations--Circle Centered in Q3 Math Clip Art--Circle Illustrations--Circle Centered in Q3

Topic

Geometry Concepts

Description

This clip art depicts a circle centered in the third quadrant (Q3) of the coordinate plane. In Q3, both the x and y coordinates of the center are negative. This positioning is essential for understanding how the location of a circle's center influences its equation and its interactions with the coordinate axes.

Definition of a Circle
Math Clip Art--Geometry Concepts--Circle Illustrations--Circle Centered in Q4 Math Clip Art--Geometry Concepts--Circle Illustrations--Circle Centered in Q4

Topic

Geometry Concepts

Description

This clip art illustrates a circle centered in the fourth quadrant (Q4) of the coordinate plane. In Q4, the x-coordinate of the center is positive while the y-coordinate is negative. This positioning is crucial for understanding how the location of a circle's center affects its equation and its relationship with the coordinate axes.

Definition of a Circle
Math Clip Art--Statistics and Probability--Circle Graph Math Clip Art--Statistics and Probability--Circle Graph Math Clip Art--Statistics and Probability--Circle Graph

This is part of a collection of math clip art images that show different statistical graphs and concepts, along with some probability concepts.

Data Analysis
Math Clip Art--Geometry Concepts--Circle Illustrations--Unit Circle Math Clip Art--Geometry Concepts--Circle Illustrations--Unit Circle Math Clip Art--Geometry Concepts--Circle Illustrations--Unit Circle

This is part of a collection of math clip art images about selected topics in Geometry. Also look at our Geometry Basics math clip art collection.

Definition of a Circle and Applications of Coordinate Geometry
Math Clip Art--Geometry Concepts--Circle Illustrations--Unit Circle Math Clip Art--Geometry Concepts--Circle Illustrations--Unit Circle Math Clip Art--Geometry Concepts--Circle Illustrations--Unit Circle

This is part of a collection of math clip art images about selected topics in Geometry. Also look at our Geometry Basics math clip art collection.

Definition of a Circle and Applications of Coordinate Geometry
Formulas--Area of a Sector of a Circle Formulas--Area of a Sector of a Circle Formulas--Area of a Sector of a Circle

The formula for: Area of a Sector of a Circle.

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.

Area and Circumference
Math Clip Art--Venn Diagram 2 Math Clip Art--Venn Diagram 2 Math Clip Art--Venn Diagram 2

This is part of a collection of math clip art images that show Venn Diagrams.

Applications of Circles
Video Transcript: Geometry Applications: Circles Video Transcript: Geometry Applications: Circles Video Transcript: Geometry Applications: Circles

This is the transcript for the video of same title. Video contents: In this program we explore the properties of circles. We do this in the context of two real-world applications. In the first, we look at the design of the Roman Coliseum and explore how circular shapes could have been used to design this elliptical structure. In the second application we look at the Roman Pantheon, specifically its spherical dome, to see how the properties of chords and secants help clarify its unique design.

Applications of Circles
Video Transcript: Geometry Applications: Circles, Segment 1: The Basics of Circles Video Transcript: Geometry Applications: Circles, Segment 1: The Basics of Circles Video Transcript: Geometry Applications: Circles, Segment 1: The Basics of Circles

This is the transcript for the video of same title. Video contents: We visit Chaco Canyon in New Mexico to explore the circular kivas and in the process discover how circular buildings have been used to study the heavens.

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.

Applications of Circles
Video Transcript: Geometry Applications: Circles, Segment 2: Circles and Arcs Video Transcript: Geometry Applications: Circles, Segment 2: Circles and Arcs Video Transcript: Geometry Applications: Circles, Segment 2: Circles and Arcs

This is the transcript for the video of same title. Video contents: The Roman Coliseum is a large elliptical structure. Yet, the Romans likely used circular arcs to build it. This segment explores the properties of circles and shows how arcs can be used to create elliptical shapes.

Applications of Circles
Video Transcript: Geometry Applications: Circles, Segment 3: Chords and Inscribed Angles Video Transcript: Geometry Applications: Circles, Segment 3: Chords and Inscribed Angles Video Transcript: Geometry Applications: Circles, Segment 3: Chords and Inscribed Angles

This is the transcript for the video of same title. Video contents: The Roman Pantheon is a domed structure that shows a keen awareness of the position of the sun throughout the year. The source of light from the top of the dome allows for the exploration of chords, inscribed angles, central angles, and intercepted arcs.

Applications of Circles
Geometry Applications Teachers Guide: Circles Geometry Applications Teachers Guide: Circles Geometry Applications Teachers Guide: Circles

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

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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Applications of Circles
WorksheetThumbnail.jpg Worksheet: Crossword Puzzle--Circles Worksheet: Crossword Puzzle--Circles

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.

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Worksheet Library

To see the complete collection of Worksheets, click on this link.
Definition of a Circle
Worksheet: TI-Nspire Mini-Tutorial: Circumscribing a circle about a triangle Worksheet: TI-Nspire Mini-Tutorial: Circumscribing a circle about a triangle Worksheet: TI-Nspire Mini-Tutorial: Circumscribing a circle about a triangle

This is part of a collection of math worksheets on the use of the TI-Nspire graphing calculator. Each worksheet supports a companion TI-Nspire Mini-Tutorial video. It provides all the keystrokes for the activity.

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

Related Resources

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Worksheet Library

To see the complete collection of Worksheets, click on this link.
Geometric Constructions with Triangles
Definition--Geometry Basics--Circle Inscribed In a Triangle Definition--Geometry Basics--Circle Inscribed In a Triangle Circle Inscribed In a Triangle

Topic

Geometry Basics

Definition

A circle that is tangent to all three sides of a triangle.

Description

A circle inscribed in a triangle is a circle that is tangent to all three sides of the triangle. This concept is important in understanding the properties of triangles and their relationship with circles. For example, the radius of the inscribed circle can be used to calculate the area of the triangle using the formula Area = 1/2 × perimeter × radius. Understanding inscribed circles helps in solving problems related to triangle geometry and optimization.

Definition of a Circle
Definition--Circle Concepts--Circle Inscribed in a Square Definition--Circle Concepts--Circle Inscribed in a Square Circle Inscribed in a Square

Topic

Circles

Definition

A circle inscribed in a square touches all four sides of the square at exactly one point each.

Definition of a Circle
Definition--Circle Concepts--Circumscribed Angle Definition--Circle Concepts--Circumscribed Angle Circumscribed Angle

Topic

Circles

Definition

A circumscribed angle is an angle formed outside a circle by two intersecting tangents.

Definition of a Circle
Math Clip Art--Applications of Direct Variations--Circles 9 Math Clip Art--Applications of Direct Variations--Circles 9 Math Clip Art--Applications of Direct Variations--Circles 9

This is a collection of clip art images that show an application of direction variations in the context of circles.

Ratios and Rates and Proportions
Definition--Circle Concepts--Circular Arc Definition--Circle Concepts--Circular Arc Circular Arc

Topic

Circles

Definition

A circular arc is a portion of the circumference of a circle.

Description

Circular arcs are segments of a circle's circumference, used extensively in design, architecture, and engineering to create curved structures and paths. The length of an arc is determined by the central angle and the circle's radius, calculated using the formula 

L = rθ

Definition of a Circle
VIDEO: Geometry Applications: Circles, Segment 1: The Basics of Circles. VIDEO: Geometry Applications: Circles, 1 VIDEO: Geometry Applications: Circles, 1

Topic

Circles

Description

This segment discusses the geometry of circles and their cultural and astronomical significance. It introduces concepts such as the center, radius, diameter, chords, and arcs, emphasizing their applications in ancient structures like Pueblo Bonito and Stonehenge. Key vocabulary includes equinox, solstice, radius, and chord. Applications include tracking celestial events and designing circular structures for ceremonial or observational purposes.

Applications of Circles
VIDEO: Geometry Applications: Circles, Segment 2: Circles and Arcs. VIDEO: Geometry Applications: Circles, 2 VIDEO: Geometry Applications: Circles, 2

Topic

Circles

Description

This segment explores the geometric complexities of the Roman Colosseum and its elliptical structure. It differentiates between circular and elliptical geometries, explaining terms like ellipse, foci, and perimeter. The video applies these concepts to analyze the construction techniques of the Colosseum, showcasing the Romans’ use of circular arcs to approximate an ellipse.

Applications of Circles and Definition of a Circle
VIDEO: Geometry Applications: Circles, Segment 2: Circles and Arcs. VIDEO: Geometry Applications: Circles, 2 VIDEO: Geometry Applications: Circles, 2

Topic

Circles

Description

This segment explores the geometric complexities of the Roman Colosseum and its elliptical structure. It differentiates between circular and elliptical geometries, explaining terms like ellipse, foci, and perimeter. The video applies these concepts to analyze the construction techniques of the Colosseum, showcasing the Romans’ use of circular arcs to approximate an ellipse.

Applications of Circles and Definition of a Circle
VIDEO: Geometry Applications: Circles, Segment 3: Chords and Inscribed Angles VIDEO: Geometry Applications: Circles, 3 VIDEO: Geometry Applications: Circles, 3

Topic

Circles

Description

Focusing on the Pantheon, this segment introduces chords, inscribed angles, and intercepted arcs, connecting them to architectural features. he video uses the oculus as a practical example, demonstrating how light patterns and angles relate to geometric principles. Applications include understanding light dynamics and their symbolic representation in architecture.

Applications of Circles and Definition of a Circle
VIDEO: Geometry Applications: Circles, Segment 3: Chords and Inscribed Angles VIDEO: Geometry Applications: Circles, 3 VIDEO: Geometry Applications: Circles, 3

Topic

Circles

Description

Focusing on the Pantheon, this segment introduces chords, inscribed angles, and intercepted arcs, connecting them to architectural features. he video uses the oculus as a practical example, demonstrating how light patterns and angles relate to geometric principles. Applications include understanding light dynamics and their symbolic representation in architecture.

Applications of Circles and Definition of a Circle
Interactive Math Game--Memory Game, Circles Interactive Math Game--Memory Game: Circles Interactive Math Game--Memory Game: Circles

Use this math game to review circles. This is a Memory-style game in which students must remember the location of pairs of identical images.

This is part of a collection of math games and interactives. To see the complete collection of the games, click on this link. Note: The download is the teacher's guide.

Related Resources

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Definition of a Circle
Interactive Crossword Puzzle--Circles Interactive Crossword Puzzle--Circles Interactive Crossword Puzzle--Circles

This interactive crossword puzzle tests knowledge of key terms on the topic of circles.

This is part of a collection of math games and interactives. To see the complete collection of the games, click on this link. Note: The download is the teacher's guide.

Related Resources

To see additional resources on this topic, click on the Related Resources tab.
Definition of a Circle
Math in the News: Issue 88--Examining the Polar Vortex Math in the News: Issue 88--Examining the Polar Vortex Math in the News: Issue 88--Examining the Polar Vortex

January 2014. In this issue of Math in the News we examine the Polar Vortex. We examine the physics of the cyclonic winds that make up the Polar Vortex and under what conditions the current expansion of Arctic weather affects a large part of the United States.

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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Applications of Circles
Promethean Flipchart: Geometry Applications: Circles 1

The Roman Coliseum is a large elliptical structure. Yet, the Romans likely used circular arcs to build it. This segment explores the properties of circles and shows how arcs can be used to create elliptical shapes. Note: The download for this resources is the Promethean Flipchart.

To access the full video [Geometry Applications: Circles, Segment 2: Circles and Arcs]: https://www.media4math.com/library/geometry-applications-circles-segment-2-circles-and-arcs

This video includes a video transcript: https://media4math.com/library/video-transcript-geometry-applications-circles-segment-2-circles-and-arcs

Applications of Circles
Promethean Flipchart: Geometry Applications: Circles 2

The Roman Pantheon is a domed structure that shows a keen awareness of the position of the sun throughout the year. The source of light from the top of the dome allows for the exploration of chords, inscribed angles, central angles, and intercepted arcs. Note: The download for this resources is the Promethean Flipchart.

To access the full video [Geometry Applications: Circles, Segment 3: Chords and Inscribed Angles]: https://media4math.com/library/geometry-applications-circles-segment-3-chords-and-inscribed-angles

This video includes a Video Transcript: https://www.media4math.com/library/video-transcript-geometry-applications-circles-segment-3-chords-and-inscribed-angles

Applications of Circles
Google Earth Voyager Story: Circular Structures, Part 1 Google Earth Voyager Story: Circular Structures, Part 1 Google Earth Voyager Story: Circular Structures, Part 1

Topic

Geometric Models

Applications of Circles
Google Earth Voyager Story: Circular Structures, Part 2 Google Earth Voyager Story: Circular Structures, Part 2 Google Earth Voyager Story: Circular Structures, Part 2

Topic

Geometric Models

Applications of Circles and Cylinders
VIDEO: Geometry Applications: Circles VIDEO: Geometry Applications: Circles VIDEO: Geometry Applications: Circles

Topic

Circles

Applications of Circles
Definition--Circle Concepts--Arc Length Definition--Circle Concepts--Arc Length Arc Length

Topic

Circles

Definition

An arc length is the distance along the curved line making up the arc.

Description

The arc length is a crucial concept in geometry, particularly when dealing with circles. It is calculated using the formula 

L = rθ

Definition of a Circle
Definition--Circle Concepts--Center of a Circle Definition--Circle Concepts--Center of a Circle Center of a Circle

Topic

Circles

Definition

The center of a circle is the point equidistant from all points on the circle.

Description

The center of a circle is a pivotal concept in geometry, serving as the reference point from which the radius is measured. It is crucial in defining the circle's position in a plane and is used in various applications such as navigation, where the center can represent a central point of rotation or balance. In mathematical terms, the center is often denoted as the point (h , k) in the Cartesian coordinate system, where all points on the circle satisfy the equation 

Definition of a Circle
Definition--Circle Concepts--Chord Definition--Circle Concepts--Chord Chord

Topic

Circles

Definition

A chord is a line segment with both endpoints on the circle.

Definition of a Circle
Definition--Circle Concepts--Circle Definition--Circle Concepts--Circle Circle

Topic

Circles

Definition

A circle is a set of all points in a plane equidistant from a given point, the center.

Description

The circle is one of the most fundamental shapes in geometry, characterized by its symmetry and uniformity. It is used extensively in various fields, including engineering, design, and astronomy, where its properties are applied to create wheels, gears, and orbits. Mathematically, a circle is defined by its center and radius, and its equation in a plane is 

(x − h)2 + (y − k)2 = r2 

Definition of a Circle
Definition--Charts and Graphs--Circle Graph Definition--Charts and Graphs--Circle Graph Definition--Charts and Graphs--Circle Graph

This is a collection of definitions related to the concept of charts, graphs, and data displays.

Data Analysis
Definition--Circle Concepts--Diameter Definition--Circle Concepts--Diameter Diameter

Topic

Circles

Definition

The diameter of a circle is a line segment that passes through the center and has its endpoints on the circle, calculated as D = 2πr.

Description

The diameter is a fundamental concept in geometry, representing the longest distance across a circle. It is widely used in fields such as engineering, design, and manufacturing, where precise measurements of circular objects are required. The formula 

D = 2πr

Definition of a Circle
Definition--Circle Concepts--Radius of a Circle Definition--Circle Concepts--Radius of a Circle Radius of a Circle

Topic

Circles

Definition

The radius of a circle is a line segment from the center to any point on the circle.

Definition of a Circle
Definition--Circle Concepts--Secant to a Circle Definition--Circle Concepts--Secant to a Circle Secant to a Circle

Topic

Circles

Definition

A secant is a line that intersects a circle at two points.

Description

Secants are significant in geometry, representing lines that intersect a circle at two distinct points. These lines are used in various applications, such as in design and architecture, where precise measurements of angles and distances are essential. In mathematics, secants are explored in the context of circle theorems, providing insights into the properties of lines and circles. In education, understanding secants helps students develop geometric reasoning and problem-solving skills, which are essential for advanced studies in geometry and trigonometry.

Definition of a Circle
Definition--Circle Concepts--Sector Definition--Circle Concepts--Sector Sector

Topic

Circles

Definition

A sector is a portion of a circle enclosed by two radii and the arc between them.

Description

Sectors are fundamental in the study of circles, representing a portion of the circle's area. These shapes are used in various applications, such as in design and architecture, where precise measurements of angles and areas are essential. The area of a sector is calculated using the formula 

A = 1/2r2θ

Definition of a Circle
Formulas--Area of a Circle Formulas--Area of a Circle Formulas--Area of a Circle

The formula for the Area of a Circle.

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.

Area and Circumference