Illustrative Math Alignment: Grade 7 Unit 3

Measuring Circles

Lesson 2: Exploring Circles

Use the following Media4Math resources with this Illustrative Math lesson.

Title	Body	Curriculum Nodes
Worksheet: 2D Shapes, Worksheet 1	Worksheet: 2D Shapes, Worksheet 1 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.	Definition of a Circle and Definition of a Quadrilateral
Worksheet: Analyzing Shapes, Worksheet 1	Worksheet: Analyzing Shapes, Worksheet 1 This is part of a collection of math worksheets on the topic of analyzing shapes. 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 Circle, Definition of a Quadrilateral and Definition of a Triangle
Worksheet: Analyzing Shapes, Worksheet 3	Worksheet: Analyzing Shapes, Worksheet 3 This is part of a collection of math worksheets on the topic of analyzing shapes. 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 Circle
Worksheet: Identifying Shapes, Worksheet 1	Worksheet: Identifying Shapes, Worksheet 1 This is part of a collection of math worksheets on the topic of geometric shapes. 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 Circle, Definition of a Polygon and Definition of a Triangle
Worksheet: Identifying Shapes, Worksheet 1	Worksheet: Identifying Shapes, Worksheet 1 This is part of a collection of math worksheets on the topic of geometric shapes. 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 Circle, Definition of a Polygon and Definition of a Triangle
Worksheet: Identifying Shapes, Worksheet 1	Worksheet: Identifying Shapes, Worksheet 1 This is part of a collection of math worksheets on the topic of geometric shapes. 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 Circle, Definition of a Polygon and Definition of a Triangle
Worksheet: Identifying Shapes, Worksheet 1	Worksheet: Identifying Shapes, Worksheet 1 This is part of a collection of math worksheets on the topic of geometric shapes. 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 Circle, Definition of a Polygon and Definition of a Triangle
Worksheet: Identifying Shapes, Worksheet 2	Worksheet: Identifying Shapes, Worksheet 2 This is part of a collection of math worksheets on the topic of geometric shapes. 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 Circle, Definition of a Polygon and Definition of a Triangle
Worksheet: Identifying Shapes, Worksheet 2	Worksheet: Identifying Shapes, Worksheet 2 This is part of a collection of math worksheets on the topic of geometric shapes. 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 Circle, Definition of a Polygon and Definition of a Triangle
Worksheet: Identifying Shapes, Worksheet 2	Worksheet: Identifying Shapes, Worksheet 2 This is part of a collection of math worksheets on the topic of geometric shapes. 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 Circle, Definition of a Polygon and Definition of a Triangle
Worksheet: Identifying Shapes, Worksheet 2	Worksheet: Identifying Shapes, Worksheet 2 This is part of a collection of math worksheets on the topic of geometric shapes. 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 Circle, Definition of a Polygon and Definition of a Triangle
Worksheet: Identifying Shapes, Worksheet 3	Worksheet: Identifying Shapes, Worksheet 3 This is part of a collection of math worksheets on the topic of geometric shapes. 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 Circle, Definition of a Polygon and Definition of a Triangle
Worksheet: Identifying Shapes, Worksheet 3	Worksheet: Identifying Shapes, Worksheet 3 This is part of a collection of math worksheets on the topic of geometric shapes. 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 Circle, Definition of a Polygon and Definition of a Triangle
Worksheet: Identifying Shapes, Worksheet 3	Worksheet: Identifying Shapes, Worksheet 3 This is part of a collection of math worksheets on the topic of geometric shapes. 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 Circle, Definition of a Polygon and Definition of a Triangle
Worksheet: Identifying Shapes, Worksheet 3	Worksheet: Identifying Shapes, Worksheet 3 This is part of a collection of math worksheets on the topic of geometric shapes. 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 Circle, Definition of a Polygon and Definition of a Triangle
Worksheet: Identifying Shapes, Worksheet 4	Worksheet: Identifying Shapes, Worksheet 4 This is part of a collection of math worksheets on the topic of geometric shapes. 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 Circle, Definition of a Polygon and Definition of a Triangle
Worksheet: Identifying Shapes, Worksheet 4	Worksheet: Identifying Shapes, Worksheet 4 This is part of a collection of math worksheets on the topic of geometric shapes. 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 Circle, Definition of a Polygon and Definition of a Triangle
Worksheet: Identifying Shapes, Worksheet 4	Worksheet: Identifying Shapes, Worksheet 4 This is part of a collection of math worksheets on the topic of geometric shapes. 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 Circle, Definition of a Polygon and Definition of a Triangle
Worksheet: Identifying Shapes, Worksheet 4	Worksheet: Identifying Shapes, Worksheet 4 This is part of a collection of math worksheets on the topic of geometric shapes. 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 Circle, Definition of a Polygon and Definition of a Triangle
Math Clip Art--Geometry Concepts--Kite Shape 1	Math Clip Art--Kite Shape 1 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?"	Definition of a Circle, Definition of a Polygon and Definition of a Triangle
Math Clip Art--Geometry Concepts--Kite Shape 1	Math Clip Art--Kite Shape 1 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?"	Definition of a Circle, Definition of a Polygon and Definition of a Triangle
Math Clip Art--Geometry Concepts--Kite Shape 1	Math Clip Art--Kite Shape 1 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?"	Definition of a Circle, Definition of a Polygon and Definition of a Triangle
Math Clip Art--Geometry Concepts--Kite Shape 2	Math Clip Art--Kite Shape 2 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?"	Definition of a Circle, Definition of a Polygon and Definition of a Triangle
Math Clip Art--Geometry Concepts--Kite Shape 2	Math Clip Art--Kite Shape 2 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?"	Definition of a Circle, Definition of a Polygon and Definition of a Triangle
Math Clip Art--Geometry Concepts--Kite Shape 2	Math Clip Art--Kite Shape 2 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?"	Definition of a Circle, Definition of a Polygon and Definition of a Triangle
Math Clip Art--Geometry Concepts--Kite Shape 3	Math Clip Art--Kite Shape 3 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?"	Definition of a Circle, Definition of a Polygon and Definition of a Triangle
Math Clip Art--Geometry Concepts--Kite Shape 3	Math Clip Art--Kite Shape 3 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?"	Definition of a Circle, Definition of a Polygon and Definition of a Triangle
Math Clip Art--Geometry Concepts--Kite Shape 3	Math Clip Art--Kite Shape 3 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?"	Definition of a Circle, Definition of a Polygon and Definition of a Triangle
Definition--Geometry Basics--Inscribed Square	Inscribed Square 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.	Definition of a Circle
Definition--Geometry Basics--Inscribed Square	Inscribed Square 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.	Definition of a Circle
Definition--Geometry Basics--Inscribed Triangle	Inscribed Triangle 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.	Definition of a Circle
Definition--Geometry Basics--Inscribed Triangle	Inscribed Triangle 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.	Definition of a Circle
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--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	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--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--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--Geometry Basics--Inscribed Angle	Inscribed Angle 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.	Definition of a Circle
Definition--Geometry Basics--Inscribed Angle	Inscribed Angle 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.	Definition of a Circle
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
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
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
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
Definition--Circle Concepts--Inscribed Angle Theorem	Inscribed Angle Theorem Topic Circles Definition The inscribed angle theorem states that an inscribed angle is half the measure of the central angle that subtends the same arc.	Definition of a Circle
Definition--Circle Concepts--Inscribed Angle Theorem	Inscribed Angle Theorem Topic Circles Definition The inscribed angle theorem states that an inscribed angle is half the measure of the central angle that subtends the same arc.	Definition of a Circle
Definition--Circle Concepts--Inscribed Angle Theorem	Inscribed Angle Theorem Topic Circles Definition The inscribed angle theorem states that an inscribed angle is half the measure of the central angle that subtends the same arc.	Definition of a Circle
Definition--Circle Concepts--Tangent Line	Tangent Line Topic Circles Definition A tangent line is a straight line that touches a circle at exactly one point.	Definition of a Circle
Definition--Circle Concepts--Tangent Line	Tangent Line Topic Circles Definition A tangent line is a straight line that touches a circle at exactly one point.	Definition of a Circle
Definition--Circle Concepts--Tangent Line	Tangent Line Topic Circles Definition A tangent line is a straight line that touches a circle at exactly one point.	Definition of a Circle
Definition--Circle Concepts--Tangent Line	Tangent Line Topic Circles Definition A tangent line is a straight line that touches a circle at exactly one point.	Definition of a Circle

Illustrative Math Alignment: Grade 7 Unit 3

Measuring Circles

Lesson 2: Exploring Circles

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