Orange Public Schools CCSS Curriculum
CONTENT AREA: Mathematics
#
Course: Geometry UNIT #: 5
STUDENT LEARNING OBJECTIVES
1
2
3
Construct tangent line from a point outside a given
circle to the circle and describe the relationship of
the angle formed by the radius of a circle and the
line that is tangent to the point where the radius
intersects the circle.
Construct the inscribed and circumscribed circles of
a triangle and prove properties of angles for a
quadrilateral inscribed in a circle. Find the angle
measures in degrees.
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.
UNIT NAME: Circles
CORRESPONDING
CCSS
# of Classes
G.C.4, G.C.2
3
G.C.3
4-5
G.GPE.1
6-7
Major Content Supporting Content Additional Content Identified by PARCC Model Content Frameworks
Code #
G.C.2
G.C.3
G.C.4
G.GPE.1
Common Core State Standards
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 where the radius intersects the circle.
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.
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.
Orange Public Schools CCSS Curriculum
CONTENT AREA: Mathematics
Course: Geometry UNIT #: 5
UNIT NAME: Circles
Justification
Students will eventually build up to a standard that requires them to write an equation, and understand the relationship
between that equation and the graph of the circle in a coordinate setting. These are both big ideas of Algebra 1 & 2 and
will prepare students better for their next course. A review of algebra 1 topics will most likely be necessary to teach SLO
3, which will also serve as an essential “refresher” before students go off on Summer Break and attempt a course that
has content they haven’t seen in over a year (Algebra). Also, The equation of a circle relates to the graph of a parabola
(which they have seen in Algebra 1 and will see again in Algebra 2). This allows some classes (i.e. honors) to make
connections between prior, present, and future content in Mathematics.
Standard G.GPE.1 is building off prior content, such as similarity and Pythagorean’s theorem. This is effective for making
connections in mathematics for students as well as spiraling in topics that achievement data has shown to be weaker
areas for our students.
It follows a sequence that is more cohesive and coherent. We ended Unit 4 teaching circle standards, so it makes sense
(to our students and us as teachers) to continue teaching properties of circles, as opposed to jumping to a new topic and
not allowing our students to develop any deep understanding of circles.
The Unit 5 standards are levels of learning that are diverse in type and rigor. There is no one emphasis on a type of
learning (i.e. proofs, proofs, and more proofs). Instead students will be expected to do the following: construct,
describe, find, show, prove, derive, etc.
Having only 3 SLO’s with ~14 classes allows some extra time to properly scaffold/build up to the more challenging
standards. SLO 3 will require some review of Algebra 1 material and SLO 2 will most likely be challenging for our
students (it requires them to “prove”). Therefore we can slow down the pace around those SLO’s are provide lessons
that will attempt to fill in gaps between where our students need to be and where they really are.
Resources
Carnegie Chapters 11, 12, 13
Explorations in Core Math Section 12. 1 (SLO 1)
Explorations in Core Math Section 12. 4 (SLO 2)
Explorations in Core Math Section 12. 5 (SLO 1)
Explorations in Core Math Section 12. 7 (SLO 3)
Explorations in Core Math Section 12. 2 and 12.3 (CCSS G.C.2, which is from Unit 4 but may serve as review material)