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Curriculum Map for:
Time
Frame /
Content
MRS21/22 M2
Essential Question(s)
and ENGAGENY Links
Final Draft
Skills
Module 2: Trigonometry
Common Core Standards
Sample Lesson Link,
Projects and Assessments
Topic A
25
days
1
1
1
1
In this topic, students
develop an understanding
of the six basic
trigonometric functions
Lesson 1: Ferris
Wheels—Tracking the
Height of a Passenger
Car [Periodic
Functions]
2
2
2
2
2
Lesson 2: The Height
and Co-Height
Functions of a Ferris
Wheel [Periodic
Functions and Graphs]
3
3
3
3
3
Lesson 3: The Motion
of the Moon, Sun, and
Stars—Motivating
Mathematics [Unit
Circle, Sine/Cosine]
Sample Lessons Module 2
Objectives: Students apply geometric concepts
in modeling situations. Specifically, they find
distances between points of a circle and a given
line to represent the height above the ground of a
passenger car on a Ferris wheel as it is rotated a
number of degrees about the origin from an initial
reference point. Students sketch the graph of a
nonlinear relationship between variables
F-TF.A.1-F-TF.A.9
F-IF.C.7e
F-TF.B.5
S-ID.B.6a
F-TF.C.8
All Modules
Assessments Link
Differentiation/ Resources/
Strategies
Objectives: Students model and graph two
functions given by the location of a passenger car
on a Ferris wheel as it is rotated a number of
degrees about the origin from an initial reference
position.
Objectives: Students explore the historical
context of trigonometry as motion of celestial
bodies in a presumed circular arc. Students
describe the position of an object along a line of
sight in the context of circular motion. Students
understand the naming of the quadrants and why
counterclockwise motion is deemed the positive
direction of turning in mathematics.
Regents
Mixed Reviews
4
4
4
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4
Lesson 4: From Circleometry to
Trigonometry [Sine
and Cosine Function
Values]
Objectives: Students will define sine and cosine
as functions for degrees of rotation of the ray
formed by the positive -axis up to one full turn.
Students use special triangles to geometrically
determine the values of sine and cosine for 30°,
45°, 60°, and 90° degrees.
5
5
5
5
5
Lesson 5: Extending
the Domain of Sine and
Cosine to All Real
Numbers [Reference
Angles]
Objectives: Students will define sine and cosine
as functions for all real numbers measured in
degrees. Students will evaluate the sine and cosine
functions at multiples of 30° and 45°.
F-TF.A.1-F-TF.A.9
F-IF.C.7e
F-TF.B.5
S-ID.B.6a
F-TF.C.8
Sample Lessons Module 2
All Modules
Assessments Link
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6
6
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7
Lesson 6: Why Call It
Tangent? [Tangent
Function Values]
Lesson 7: Secant and
the Co-Functions
[Reciprocal Trig
Functions]
Objectives: Students define the tangent function
and understand the historic reason for its name.
Students use special triangles to determine
geometrically the values of the tangent function
for 30°, 45°, and 60°.
Objectives: Students define the secant function
and the co-functions in terms of points on the unit
circle. They relate these names for these functions
to the geometric relationships among lines,
angles, and right triangles in a unit circle diagram.
Students use reciprocal relationships to relate the
trigonometric functions and use these
relationships to evaluate trigonometric functions
for multiples of 30°, 45°, and 60° degrees.
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Regents
Mixed Reviews
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8
8
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8
Lesson 8: Graphing the
Sine and Cosine
Functions
Objectives: Students graph the sine and cosine
functions and analyze the shape of these curves.
For the sine and cosine functions, students sketch
graphs showing key features, which include
intercepts; intervals where the function is
increasing, decreasing, positive, or negative;
relative maxima and minima; symmetries; end
behavior; and periodicity.
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9
9
9
9
Lesson 9: Awkward!
Who Chose the
Number 360, Anyway?
[Radians]
Objectives: Students explore horizontal scalings
of the graph of y =sin(x). Students convert
between degrees and radians.
10
10
10
10
Lesson 10: Basic
Trigonometric
Identities from Graphs
[Translation Identities]
Objectives: Students observe identities from
graphs of sine and cosine basic trigonometric
identities and relate those identities to periodicity,
even and odd properties, intercepts, end behavior,
and the fact that cosine is a horizontal translation
of sine.
use trigonometric
functions to model
periodic phenomena
Lesson 11:
Transforming the
Graph of the Sine
Function [Trig Graphs]
Objectives: Students formalize the periodicity,
frequency, phase shift, midline, and amplitude of
a general sinusoidal function by understanding
how the parameters A, w, h, and k in the formula
f(x) = Asin(w(x-h))+k
are used to transform the graph of the sine
function, and how variations in these constants
change the shape and position of the graph of the
sine function.
Students learn the relationship among the
constant A, w, h, and k in the formula f(x) =
Asin(w(x-h))+k
and the properties of the sine graph.
12
12
12
12
12
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12
Lesson 12: Ferris
Wheels—Using
Trigonometric
Functions to Model
Cyclical Behavior
[Graphs, including
word problems related
to the graph]
Sample Lessons Module 2
All Modules
Assessments Link
Regents
Mixed Reviews
Topic B: Students will
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11
F-TF.A.1-F-TF.A.9
F-IF.C.7e
F-TF.B.5
S-ID.B.6a
F-TF.C.8
Objectives: Students review how changing the
parameters A, ω, h, and k in f(x) = A sin(ω(x - h))
+ k affects the graph of the sine function.
Students examine the example of the Ferris wheel,
using height, distance from the ground, period,
and so on, to write a function of the height of the
passenger cars in terms of the sine function: f(x) =
A sin(ω(x - h)) + k.
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13
13
13
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13
Lesson 13: Tides,
Sound Waves, and
Stock Markets
[Creating a
graph/equation to
model a set of data]
14
14
Lesson 14: Graphing
the Tangent Function
Objectives: Students model cyclical phenomena
from biological and physical science using
trigonometric functions. Students understand that
some periodic behavior is too complicated to be
modeled by simple trigonometric functions.
Objectives: Students graph the tangent function.
Students use the unit circle to express the values
of the tangent function for π - x, π + x, and 2π - x
in terms of tan(x), where x is any real number in
the domain of the tangent function.
F-TF.A.1-F-TF.A.9
F-IF.C.7e
F-TF.B.5
S-ID.B.6a
F-TF.C.8
Sample Lessons Module 2
All Modules
Assessments Link
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15
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15
Lesson 15: What Is a
Trigonometric
Identity? [Pythagorean
Identities]
Objectives: Students prove the Pythagorean
identity sin2(x) + cos2(x) = 1. Students extend
trigonometric identities to the real line, with
attention to domain and range. Students use the
Pythagorean identity to find sin(θ), cos(θ), or
tan(θ), given sin(θ), cos(θ), or tan(θ) and the
quadrant of the terminal ray of the rotation.
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16
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Lesson 16: Proving
Trigonometric
Identities
Objectives: Students prove simple identities
involving the sine function, cosine function, and
secant function.
Students recognize features of proofs of identities
17
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Lesson 17:
Trigonometric Identity
Proofs [Sin/Cos/Tan of
(a – b) and (a + b)]
Objectives: Students see derivations and proofs
of the addition and subtraction formulas for sine
and cosine.Students prove some simple
trigonometric identities.
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Regents
Mixed Reviews