Download Curriculum 2.0 Geometry Unit Five MCPS © 2014 Page 1 of 2 C2.0

Curriculum 2.0 Geometry
Unit Five
C2.0 Geometry Unit 5 Instructional Focus: Circles
Topic
Instructional Foci
Students prove basic theorems about circles, including that a tangent line is perpendicular to a radius, the inscribed angle
theorem, and theorems about chords, secants, and tangents as they relate to segment lengths and angle measures. They study
relationships among segments on chords, secants, and tangents as an application of similarity.
Days
Standards:
G-C.1 Prove that all circles are similar.
Topic 1: Circles and Angles
G-C.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 where the radius intersects the circle.
G-C.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral
inscribed in a circle.
G-C.4 (+) Construct a tangent line from a point outside a given circle to the circle.
approx.
14-15
The (+) standards indicate those which are unique to the C2.0 Honors Geometry course. They will not be assessed on
PARCC, but are included in items on the C2.0 Honors Geometry final exam.
Sample Learning Tasks (SLTs):
SLT 1: Prove that all circles are similar by using dilations and relationships between parts of a circle.
SLT 2: Identify and describe relationships among angles, radii, and chords.
SLT 3: Determine relationships between radii, chords, and tangents.
SLT 4: Determine missing measurements by using the relationships among central angles, inscribed angles, and the arcs
they intercept.
SLT 5: Determine missing measurements by using the relationships among central angles, inscribed angles, circumscribed
angles, other angles, and the arcs they intercept.
SLT 6: Determine missing measurements by using the relationships among central angles, inscribed angles, circumscribed
angles, other angles, and the arcs they intercept.
SLT 7: Determine missing measurements by using the relationships among central angles, inscribed angles, circumscribed
angles, other angles, and the arcs they intercept.
SLT 8: Using definitions, properties, and theorems, prove properties of angles for polygons inscribed in a circle.
MCPS © 2014
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Curriculum 2.0 Geometry
Topic 2: Arc Length and Area
Topic 1: Circles and
Angles (Continued)
Topic
Unit Five
Instructional Foci
SLT 9: Construct the circumcenter of a triangle to circumscribe a circle about a triangle.
SLT 10: Construct the incenter of a triangle to inscribe a circle within a triangle.
SLT 11: Use points of concurrency to solve real world problems.
SLT 12: Use points of concurrency to solve real world problems.
Days
Formatives:
Unit 5 T1 Formative Assessment #1 – This formative assessment is designed to assess student understanding after SLT 8.
Unit 5 T1 Formative Assessment #2 – This formative assessment is designed to assess student understanding after SLT 12.
Students apply their understandings regarding similarity of all circles to determine the proportional relationship between arc
length and radii of circles (i.e., radian measure). They move flexibly and efficiently between degree measure and radian
measure of corresponding central angles and the measure of their intercepted arcs. When computing the arc length, the area
of a sector, and the area of a segment in a circle, students are able to demonstrate the use of multiple paths to determine the
correct length or area.
Standards:
G-C.5 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.
approx.
Sample Learning Tasks (SLTs):
SLT 13: Derive the constant of proportionality between arc length & radii (radian measure).
SLT 14: Derive the constant of proportionality between arc length & radii (radian measure).
SLT 15: Find the arc length of a circle.
SLT 16: Using similarity, derive the formula for the area of a sector.
SLT 17: Find the area of a sector and segment in a circle.
SLT 18: Find the area of a sector and segment in a circle.
7-8
Formative:
Unit 5 T2 Formative Assessment #1 – This formative assessment is designed to assess student understanding after SLT 18.
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