Illustrative Math Alignment: Grade 7 Unit 3

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.

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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.

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.

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

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

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

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

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Worksheet Library

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

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

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

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

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This is part of a collection of math worksheets on the topic of analyzing shapes.

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This is part of a collection of math worksheets on the topic of analyzing shapes.

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This is part of a collection of math worksheets on the topic of geometric shapes.

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This is part of a collection of math worksheets on the topic of geometric shapes.

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This is part of a collection of math worksheets on the topic of geometric shapes.

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This is part of a collection of math worksheets on the topic of geometric shapes.

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This is part of a collection of math worksheets on the topic of geometric shapes.

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This is part of a collection of math worksheets on the topic of geometric shapes.

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This is part of a collection of math worksheets on the topic of geometric shapes.

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This is part of a collection of math worksheets on the topic of geometric shapes.

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This is part of a collection of math worksheets on the topic of geometric shapes.

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This is part of a collection of math worksheets on the topic of geometric shapes.

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This is part of a collection of math worksheets on the topic of geometric shapes.

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This is part of a collection of math worksheets on the topic of geometric shapes.

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This is part of a collection of math worksheets on the topic of geometric shapes.

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This is part of a collection of math worksheets on the topic of geometric shapes.

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This is part of a collection of math worksheets on the topic of geometric shapes.

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This is part of a collection of math worksheets on the topic of geometric shapes.

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Topic

Geometry Concepts

Description

This image features a kite shape, in this case a circular one. Ordinarily a kite is a quadrilateral with two pairs of adjacent equal-length sides. The diagonals intersect at right angles, and one diagonal bisects the other, creating a symmetrical shape.

Kite shapes are important in geometry for understanding properties like symmetry, area, and perimeter. They are used in various mathematical applications, including tiling and design.

Teacher's Script: "Examine this kite. What makes it a kite in the everyday understanding of it? Is it a kite in geometric terms?"

Topic

Geometry Concepts

Description

This image features a kite shape, in this case a circular one. Ordinarily a kite is a quadrilateral with two pairs of adjacent equal-length sides. The diagonals intersect at right angles, and one diagonal bisects the other, creating a symmetrical shape.

Kite shapes are important in geometry for understanding properties like symmetry, area, and perimeter. They are used in various mathematical applications, including tiling and design.

Teacher's Script: "Examine this kite. What makes it a kite in the everyday understanding of it? Is it a kite in geometric terms?"

Topic

Geometry Concepts

Description

This image features a kite shape, in this case a circular one. Ordinarily a kite is a quadrilateral with two pairs of adjacent equal-length sides. The diagonals intersect at right angles, and one diagonal bisects the other, creating a symmetrical shape.

Kite shapes are important in geometry for understanding properties like symmetry, area, and perimeter. They are used in various mathematical applications, including tiling and design.

Teacher's Script: "Examine this kite. What makes it a kite in the everyday understanding of it? Is it a kite in geometric terms?"

Topic

Geometry Concepts

Description

This image depicts another variation of a kite shape, in this case a circular shape. Geometrically, a kite is characterized by two pairs of adjacent equal-length sides and diagonals that intersect at right angles. This geometric configuration is symmetrical and unique.

Kite shapes are used to explore geometric properties such as symmetry, area, and perimeter. They are applicable in various fields, including mathematics, design, and architecture.

Teacher's Script: "Look at this kite. How is it a kite in the everyday sense? Is it a kite in a geometric sense?"

Topic

Geometry Concepts

Description

This image depicts another variation of a kite shape, in this case a circular shape. Geometrically, a kite is characterized by two pairs of adjacent equal-length sides and diagonals that intersect at right angles. This geometric configuration is symmetrical and unique.

Kite shapes are used to explore geometric properties such as symmetry, area, and perimeter. They are applicable in various fields, including mathematics, design, and architecture.

Teacher's Script: "Look at this kite. How is it a kite in the everyday sense? Is it a kite in a geometric sense?"

Topic

Geometry Concepts

Description

This image depicts another variation of a kite shape, in this case a circular shape. Geometrically, a kite is characterized by two pairs of adjacent equal-length sides and diagonals that intersect at right angles. This geometric configuration is symmetrical and unique.

Kite shapes are used to explore geometric properties such as symmetry, area, and perimeter. They are applicable in various fields, including mathematics, design, and architecture.

Teacher's Script: "Look at this kite. How is it a kite in the everyday sense? Is it a kite in a geometric sense?"

Topic

Geometry Concepts

Description

This image illustrates a circular kite shape. Geometrically, a kite is a a quadrilateral with two pairs of adjacent equal-length sides and diagonals that intersect at right angles. The symmetry and unique properties of kite shapes make them interesting geometric figures.

Kite shapes are used to explore properties such as symmetry, area, and perimeter. They are applicable in various mathematical contexts, including geometry and design.

Teacher's Script: "Observe this kite. How is a kite in the everyday sense of the word? Is it a kite in the geometric sense?"

Topic

Geometry Concepts

Description

This image illustrates a circular kite shape. Geometrically, a kite is a a quadrilateral with two pairs of adjacent equal-length sides and diagonals that intersect at right angles. The symmetry and unique properties of kite shapes make them interesting geometric figures.

Kite shapes are used to explore properties such as symmetry, area, and perimeter. They are applicable in various mathematical contexts, including geometry and design.

Teacher's Script: "Observe this kite. How is a kite in the everyday sense of the word? Is it a kite in the geometric sense?"

Topic

Geometry Concepts

Description

This image illustrates a circular kite shape. Geometrically, a kite is a a quadrilateral with two pairs of adjacent equal-length sides and diagonals that intersect at right angles. The symmetry and unique properties of kite shapes make them interesting geometric figures.

Kite shapes are used to explore properties such as symmetry, area, and perimeter. They are applicable in various mathematical contexts, including geometry and design.

Teacher's Script: "Observe this kite. How is a kite in the everyday sense of the word? Is it a kite in the geometric sense?"

Topic

Geometry Basics

Definition

A square whose vertices all touch a circle.

Description

Inscribed squares exemplify the relation between circles and polygons, highlighting how squares can fit perfectly within circles. This concept is key for understanding how shapes interact within each other geometrically. The side length of an inscribed square can be derived from the radius of the circumscribed circle by applying the formula s = r√2, where s is the side length and r is the radius. Recognizing inscribed shapes aids in broadening spatial awareness and reinforces connections between various geometric concepts, essential for advanced mathematics education.

Topic

Geometry Basics

Definition

A square whose vertices all touch a circle.

Description

Inscribed squares exemplify the relation between circles and polygons, highlighting how squares can fit perfectly within circles. This concept is key for understanding how shapes interact within each other geometrically. The side length of an inscribed square can be derived from the radius of the circumscribed circle by applying the formula s = r√2, where s is the side length and r is the radius. Recognizing inscribed shapes aids in broadening spatial awareness and reinforces connections between various geometric concepts, essential for advanced mathematics education.

Topic

Geometry Basics

Definition

A triangle drawn within another triangle, where each vertex touches the circumcircle.

Description

The inscribed triangle illustrates essential relationships between triangles and circles. Understanding this concept involves recognizing properties such as area calculations involving the circumcircle and relationships among various elements of triangles. The area can be found using the formula related to the circumradius and semi-perimeter, enhancing problem-solving skills and applying real-world considerations such as construction and design.

Topic

Geometry Basics

Definition

A triangle drawn within another triangle, where each vertex touches the circumcircle.

Description

The inscribed triangle illustrates essential relationships between triangles and circles. Understanding this concept involves recognizing properties such as area calculations involving the circumcircle and relationships among various elements of triangles. The area can be found using the formula related to the circumradius and semi-perimeter, enhancing problem-solving skills and applying real-world considerations such as construction and design.

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.

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.

Topic

Circles

Definition

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

Topic

Circles

Definition

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

Topic

Circles

Definition

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

Topic

Geometry Basics

Definition

An angle formed by two chords in a circle which have a common endpoint.

Description

The inscribed angle theorem states that an inscribed angle is half the measure of the central angle that subtends the same arc. This principle is vital for solving geometric problems related to circles and angles. For example, if the central angle measures 80 degrees, the inscribed angle will measure 40 degrees. Inscribed angles have significant applications in trigonometry and are fundamental in understanding circle theorems, showing interrelations between different angles in a circle and enhancing intuitive geometric reasoning skills among students.

Topic

Geometry Basics

Definition

An angle formed by two chords in a circle which have a common endpoint.

Description

The inscribed angle theorem states that an inscribed angle is half the measure of the central angle that subtends the same arc. This principle is vital for solving geometric problems related to circles and angles. For example, if the central angle measures 80 degrees, the inscribed angle will measure 40 degrees. Inscribed angles have significant applications in trigonometry and are fundamental in understanding circle theorems, showing interrelations between different angles in a circle and enhancing intuitive geometric reasoning skills among students.

Topic

Circles

Definition

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