Download Geometry Unit 9 Plan (July 2015)

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Transcript
Geometry Unit 9 Plan – 21 Periods
Unit of Study: Unit Circle Geometry Unit 9
Standard(s) to be Assessed
HSG-CO.A.1 Know precise definitions of angle
and circle based on the undefined notion of
distance around a circular arc.
HSG-C.B.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.
HSG-C.B.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.
HSF-TF.A.1 (supporting standard) Understand
radian measure of an angle as the length of the
arc on the unit circle subtended by the angle.
HSF-TF.A.2 (supporting standard) Explain how
the unit circle in the coordinate plane enables
the extension of trigonometric functions to all
real numbers, interpreted as radian measures of
angles traversed counterclockwise around the
unit circle.
HSG-C.B.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.
HSG-GPE.A.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.
Page 1 of 2
Learning Target to be
Assessed
Pre/Post Angle
Relationships
Assessment
Item #s
Unit
Common
Assessment
Item #s
LT1: Know the definitions of
angle and circle based on
distance around an arc.
1
LT2: Derive and calculate the
length of an arc.
2, 3, 4
LT3: Define and determine
radian measure.
LT4: Derive the formula for
area of a sector and use the
formula to calculate the area
of a sector.
LT5: Derive the equation of a
circle and apply the equation
of a circle by recognizing its
relationship to the center and
radius, points on the circle,
and graph.
5, 6
32
7, 8, 9
10, 11, 12, 13,
14
Geometry Unit 9 Plan – 21 Periods
HSG-GPE.B.4
Use coordinate to prove simple geometric
theorems algebraically. For example, prove or
disprove that a figure defined by four given
points in the coordinate plane is a rectangle;
prove or disprove that the point (1, √3) lies on
the circle centered at the origin and containing
the point (0, 2).
LT6: Use coordinates to show
that a point lies on a circle.
15
Note: HSG-C.A.l Prove that all circles are similar—This standard is not assessed in the district common assessment but
should be addressed in instruction as possibly a demonstration.
Instructional Information for Unit Circle Geometry Unit 9 (13 periods)
Big Idea: Radian measure is an equivalent expression of degree measure; the unit circle relates right triangles and the
equation circles.
Essential Question: Why do we use radian measure?
Resources:
Formative Assessment Lessons: http://map.mathshell.org/materials/lessons.php

Circles I
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