Download Unit Title: Suggested Time

CMS Curriculum Guides 2011-2012
Course Title Geometry
Unit 7:
Circles and Other Conic Sections
Suggested Time: 12 days
Enduring understanding (Big Idea): Reasoning and Proof, Measurement, Coordinate Geometry, Modeling, Equivalence
Essential Questions:
(1) How can you prove relationships between angles and arcs in circles?
(2) When lines intersect a circle or within a circle, how do you find the
measures of resulting angles, arcs, and segments?
(3) How do you find the equation of a circle in the coordinate plane?
(4) How is each conic section formed by passing a plane through a cone?
(5) Given the equation of a circle, how can you identify the center and radius?
(6) How can you derive the equation for a parabola, given a focus and
directrix?
Common Core Standards
Textbook Alignment
G.C.2 Identify and describe
12-1 Tangent lines
relationships among inscribed angles, 12-2 Chords and Arcs (central
radii, and chords.
angles)
G.C.3 Construct the inscribed and
12-3 Inscribed Angles
circumscribed circles of a triangle
12-4 Angles Measures and
(unit 5), and prove properties of
angles for a quadrilateral inscribed Segment Lengths
in a circle.
G.C.4 (+) Construct a tangent line
from a point outside a given circle to
the circle.
1
Mathematical Practices
(1) Make sense of problems and persevere in solving them.
(2) Reason abstractly and quantitatively.
(3) Construct viable arguments and critique the reasoning of others.
(4) Model with mathematics.
(5) Use appropriate tools strategically.
(6) Attend to precision.
(7) Look for and make use of structure.
(8) Look for and express regularity in repeated reasoning.
Connection to 2003
Standards
2.03 Apply properties,
definitions, and theorems of
plane figures to solve
problems and write proofs:
(d) circles
12-1 Tangent lines
New CCSS
Additional Notes
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 where
the radius intersects the circle.
CMS Curriculum Guides 2011-2012
Course Title Geometry
Determine which conic section is
formed by passing a plane through a
cone.
(Not specifically stated in CCSS)
This standard is not covered in the
Pearson Geometry text. However,
online resources from chapter 10 of
the Pearson Algebra 2 text are used
as sources here.
Algebra 2
10-1 Exploring Conic Sections
G.GPE.2 Derive the equation of a
parabola given a focus and a
directrix.
This standard is not covered in the
Pearson Geometry text. However,
online resources from chapter 10 of
the Pearson Algebra 2 text are used
as sources here.
Algebra 2
10-2 Parabolas
G.GPE.1 Derive the equation of a
circle of given center and radius
using the Pythagorean Theorem;
complete the square to find the center
and radius of a circle given by an
equation.
G.GPE.4 Use coordinates to prove
simple geometric theorems
algebraically (i.e. ,prove or disprove
that the point (1, 3 ) lies on the
circle centered at the origin and
containing the point (0, 2))
Geometry
12-5 Circles in the Coordinate
Plane
Completing the square is not
covered in the Pearson Geometry
text. However, online resources
from chapter 10 of the Pearson
Algebra 2 text are used as sources
here.
Algebra 2
10-3 Circles
Prior Knowledge
Distance Formula, Pythagorean Theorem, Quadratic Functions
2
2.03 Apply properties,
definitions, and theorems of
plane figures to solve
problems and write proofs:
(d) circles
CMS Curriculum Guides 2011-2012
Course Title Geometry
Key Vocabulary
Chord
Inscribed angle
Intercepted arc
Point of tangency
Secant
Standard form of
equation of circle
Tangent to circle
conic sections
directrix
ellipse
focus
hyperbola
parabola
Additional Online Resources

Resources
Chapter 10 of Algebra 2 text - see online resources

Inquiry Activities
TI Activity http://www.pearsonsuccessnet.com/snpapp/iText/products/0-13-368863-101/media/Geometry/GE%20Chapter%2012/Teaching%20with%20TI%20Technology/GETI1203.p
df
TI Nspire
http://education.ti.com/calculators/timathnspired/US/Activities/Detail?sa=5025&t=5058&id=13470

Problem-Based Task
Equations – short task http://map.mathshell.org/materials/download.php?fileid=848
Rubric for Equations http://map.mathshell.org/materials/download.php?fileid=849
Pearson Algebra 2 Chapter 10: Adapt to include only circles and parabolas.
http://www.pearsonsuccessnet.com/snpapp/iText/products/0-13-368856-901/media/Algebra%202/A2%20Chapter%2010/Performance%20Tasks/A2PB10.pdf
See performance tasks for chapter 12 on pearsonsuccessnet.com

Projects
See projects for chapter 12 on pearsonsuccessnet.com
3