Download Domain: Standards for Math Practice

Progressive Mathematics Initiative
www.njctl.org
Mathematics Curriculum
Unit Plan # 7
Title: Circles
Subject: Geometry
Length of Time: 3.5 weeks
Unit Summary: The unit explores parts of a circle and the relationships between intersecting lines and
circles.
Learning Targets
PARCC
Major Clusters;
Supporting Clusters;
Additional Clusters + Additional Standard
Conceptual Category: Geometry Domain: Circles
Cluster: Understand and apply theorems about circles.
Standard#:
Standard:
Prove that all circles are similar.
G-C.1
G-C.2
Identify and describe relationships among inscribed angles, radii, and chords.
G-C.3
Construct the inscribed and circumscribed circles of a triangle, and prove properties of
angles for a quadrilateral inscribed in a circle.
Construct a tangent line from a point outside a given circle to the circle.
+G-C.4
Cluster: Find arc lengths and areas of sectors
Derive using similarity the fact that the length of the arc intercepted by an angle is
proportional to the radius, and define the radian measure of the angle as the constant of
proportionality; derive the formula for the area of a sector.
Domain: Standards for Math Practice
G-C.5
Standard#:
Standard:
MP1
Making sense of problems and persevere in solving them.
MP2
Reason abstractly and quantitatively.
MP3
Construct viable arguments and critique the reasoning of others.
MP4
Model with mathematics.
MP5
Use appropriate tools strategically.
MP6
Attend to precision.
MP7
Look for and make use of structure.
MP8
Look for and express regularity in repeated reasoning.
Unit Essential Question:
Unit Enduring Understandings:
 Do “how” and “where” a line(s)
 Tangent lines intersect a circle at a single point.
intersect a circle make a difference?
 The angle measure of an angle that intersects a circle is
related to the measure of the arc intersected.
 The power of a point depends on where the lines intersect
in relationship to the circle.
 There is a relationship between central angles and arcs of
a circle
 There is relationship between a chord, its distance from
the center of a circle, and the radius of the circle.
Unit Objectives:
 Students will be able to identify the parts of a circle.
 Students will be able to find the measure of angles given angles with vertices at the center, inside
the circle, on the circle, or outside the circle.
 Students will be able to calculate the length of an arc in a circle.
 Students will be able to calculate the measurement of angles and arcs in radians.
Geometry – Circles
~1~
NJCTL.org

Students will be able to calculate the lengths of tangents, secant segments, and chords depending
on the location of the intersection.
Evidence of Learning
Formative Assessments:
 SMART Response questions used throughout the unit.
 4 Quizzes
Summative Assessment:
 Unit Test
Lesson Plan
Topics
Topic #1: Parts of a Circle
Topic #2: Central Angles & Arcs
Topic #3: Arc Length & Radians
Quiz 1:Parts of a Circle
Topic #4: Chords, Inscribed Angles, and Triangles
Lab #1: Properties of Chords
Lab #2: Inscribed Angles
Quiz #2: Chords, Inscribed Angles & Triangles
Topic #5: Tangents & Secants
Lab #3: Tangent Lines
Quiz 3: Tangents & Secants
Topic #6: Segments and Circles
Quiz 4: Segments and Circles
Topic #7: Review and Unit Test
Curriculum Resources:
 www.njctl.org/courses/math/geometry/
Lesson Components
21st Century Skills
 Financial, Economic, Business, and Entrepreneurial Literacy
21st Century Themes
 Critical Thinking and Problem Solving
 Communication and Collaboration
 Life and Career Skills
Geometry – Circles
~2~
1
1.5
2
0.5
4
0.5
4
0.5
1
0.5
2
NJCTL.org