Download Module 15 - Lake County Schools

2016-2017 Curriculum Blueprint
Grade: 9-12
Course: Geometry
6 days
Module 15: Angles and Segments in Circles
Learning Goal
The student is expected to identify and
describe relationships among inscribed angles,
radii, and chords. The student is also expected
to construct inscribed and circumscribed
triangles and prove properties of inscribed
rectangles.
Essential Questions
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3.
How can you determine the measure of central and
inscribed angles of a circle?
What are the key theorems related to special segments in
circles, such as tangents, chords, and radii?
What relationships exist among angles and segments within
circles?
Approximate Time:
Unit Overview
In this unit students will learn about central and inscribed angles,
chords, secants, tangent lines, and arcs. They will work with
segment lengths in circles and angles formed by intersecting lines
of a circle. Students will also explore the formulas for
circumference and area of a circle, area of a sector and the
equation of a circle.
Vertical Progression
MAFS.8.G.B.7, MAFS.8.G.B.8 In eighth grade students use The Pythagorean Theorem to solve for the unknown side in a right triangle and use it to find the distance between two
points.
Module Focus Standards
Module Topics
Essential Vocabulary
Test Specifications for Geometry (Reference sheet located at end)
High School Flip Book
MAFS.912.G-C.1.2 (DOK 2) Identify and describe relationships among
inscribed angles, radii, and chords. Include the relationship between central,
inscribed, and circumscribed angles; inscribed angles on a diameter are right
angles; the radius of a circle is perpendicular to the tangent Identify inscribed
angles, radii, chords, central angles, circumscribed angles, diameter, and
tangent. (conceptual)
 Recognize that inscribed angles on a diameter are right angles.
 Recognize that radius of a circle is perpendicular to the radius at the point
of tangency.
 Examine the relationship between central, inscribed, and circumscribed
angles by applying theorems about their measures.
Central Angles and Inscribed Angles (G-C.1.2)
Resources:
Lesson 15.1 (HMH book)
Module 5 Lesson 4 – Engage NY
Circles and Their Relationships Among Central
Angles, Arcs, and Chords (p. 15) - Georgia
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Formative Assessments:
Circles with Angles - CPALMS
Inscribed Angle on Diameter - CPALMS
Higher Order Question Stems
MAFS.912.G-C.1.3 (DOK 2) Construct the inscribed and circumscribed circles
of a triangle, and prove properties of angles for a quadrilateral inscribed in a
circle. (conceptual, procedural)
 Define inscribed and circumscribed circles of a triangle.
 Recall midpoint and bisector definitions.
 Define a point of concurrency.
 Prove properties of angles for a quadrilateral inscribed in a circle.
 Students may use geometric simulation software to make geometric
constructions.
Angles in Inscribed Quadrilaterals (G-C.1.3, GC.4.13)
Resources:
Lesson 15.2 (HMH Book)
Module 5 Lesson 3 – Engage NY
Investigating Angle Relationships in Circles Part 2
(p. 48) - Georgia
Formative Assessments:
Module 1 Lesson 4 Exit Ticket – Engage NY
Inscribed Quadrilaterals – CPALMS
chord
central angle
inscribed angle
inscribed polygon
point of tangency
secant segment
central secant segment
tangent segment
 What properties could we use to find a
solution?
 What evidence will support your solution?
 How has you model served its purpose?
Writing Connections
 Compare and contrast two strategies used to
solve the problem.
 Compare two arguments and determine
correct or flawed logic.
 Interpret the result of a mathematical
situation.
2016-2017 Curriculum Blueprint
Grade: 9-12
Course: Geometry
6 days
Module 15: Angles and Segments in Circles
MAFS.912.G-CO.4.13 (DOK 2) Construct an equilateral triangle, a square, and
a regular hexagon inscribed in a circle. (procedural)
 Construct an equilateral triangle, square, and regular hexagon inscribed in
a circle.
Mathematical Practice Standards
Link to Mathematical Practice Standards Rubric
MAFS.912.MP.2.1 Reason abstractly and quantitatively.
MAFS.912.MP.3.1 Construct viable arguments and critique the reasoning of
others.
MAFS.912.MP.4.1 Model with mathematics.
Link to Webb’s DOK Guide
Tangents and Circumscribed Angles (G-C.A.2)
Resources:
Lesson 15.3 (HMH Book)
Module 5 Lesson 11 - Engage NY
Chords, Secants, and Tangents (p. 56) - Georgia
Off on a Tangent - CPALMS
Formative Assessments:
Tangent Line and Radius - CPALMS
Module 5 Lesson 11 Exit Ticket – Engage NY
Constructing a Tangent Line - CPALMS
Segment Relationships in Circles (G-C.1.2)
Resources:
Lesson 15.4 (HMH Book)
Module 5 Lesson 16 – Engage NY
Chords, Secants, and Tangents (p. 56) - Georgia
Formative Assessments:
RTI Workbook (HMH pg. 113)
Module 5 Lesson 16 Exit Ticket – Engage NY
Angle Relationships in Circles (G-C.1.2)
Resources:
Lesson 15.5 (HMH Book)
Module 5 Lesson 14 – Engage NY
Chords, Secants, and Tangents (p. 56) - Georgia
Formative Assessments:
RTI Workbook (HMH pg. 114)
Module 5 Lesson 14 Exit Ticket – Engage NY
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