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6/18/2006 12:06:00 PM← Technology Unit Lesson Plan
← Due to the affluent nature of the school at which I teach, students are expected to have access to a computer and the Internet at home. All students are expected to own or check out a graphing calculator from the library.
← Teacher: Ms. Camacho Ingersoll← Class: Math Analysis / Precalculus←
← Unit: Chapter 4 Trigonometry← Date: This unit is usually completed in December←
← ← Day 1
←
← Day 2 ← Day 3
←
← Day 4
←
← Day 5
← Topics
← 4.1 Radian & Degree Measure
← 4.2 Trig functions and the unit circle
← 4.3 Trig functions & right triangles
← 4.4 Trig functions at any angle
← Review 4.1-4.4
← Stan dards ←
1.0 Content: Students
understand the notion of
angle and how to
measure it, in both
degrees and radians.
1.0 Process: They can
convert between
degrees and radians.
2.0 Content: Students
know the definition of
sine and cosine as y-
and x- coordinates of
points on the unit circle.
5.0 Content: Students
know the definitions of
the tangent and
cotangent functions.
6.0 Content: Students
know the definitions of
the secant and cosecant
functions.
9.0 Process: Students
compute, by hand, the
values of the
trigonometric functions
at various standard
3.0 Content: Students know
the identity cos2 x+sin2 x = 1:
3.1 Process: Students
prove that this identity is
equivalent to the
Pythagorean Theorem (i.e.,
students can prove this
identity by using the
Pythagorean Theorem and,
conversely, they can prove
the Pythagorean Theorem
as a consequence of this
identity).
3.2 Process: Students
prove other trigonometric
identities and simplify others
by using the identity cos2
x+sin2 x = 1. For example,
7.0 Content: Students
know that the tangent of
the angle that a line
makes with the x- axis is
equal to the slope of the
line.
9.0 Process: Students
compute, by hand, the
values of the
trigonometric functions
at various standard
points.
12.0 Process: Students
use trigonometry to
determine unknown
sides or angles in right
triangles.
1.0 Content, 1.0 Process
2.0 Content
3.0 Content
3.1 & 3.2 Process
5.0 Content
6.0 Content
7.0 Content
9.0 Process
12.0 Process
19.0 Process
points. students use this identity to
prove that sec2 x = tan2 x +1.
12.0 Process: Students use
trigonometry to determine
unknown sides or angles in
right triangles.
19.0 Process: Students are
adept at using trigonometry
in a variety of applications
and word problems.
19.0 Process: Students
are adept at using
trigonometry in a variety
of applications and word
problems.
←
← Lecture Notes (Links to multimedia Resources)
← This lesson will
begin with an
introduction using the
link to Who should take
trig? trig?” This link is
also a great place for
students to review
because it provides
problems with answers
that follow. After the
brief intro, students will
take notes with Student
Success Organizer
Notes 4.1
← and learn basic
vocab and conversions:
← radian-degree,
← degree-radian,
← sketching
angles,
← complementary
& supplementary angles,
degree/minutes/seconds
← (DoM’S”) to
decimal form, decimal to
DoM’S”,
← and arc length.
← The day will
begin by answering any
HW Questions, followed
by notes on the unit
circle (use in slow
motion). Students will
define trig functions in
terms of x, y, & r that
are illustrated in the link.
Students will also learn
to evaluate trig functions
on using the graphing
calculator.
←
← Student
Success Organizer
Notes 4.2
←
←
The day will begin by
answering any HW
Questions, followed by a
Right Triangle PPT that
illustrates trig functions and
relationships, especially in
30-60-90 triangles
← 45-45-90 triangles .
← Student Success
Organizer Notes 4.3
← The day will
begin by answering any
HW Questions, followed
by a lesson illustrating
the sign change of trig
functions in different
quadrants using the
unit circle to illustrate
the movement and
change of sine and
cosine.
← Students will
work with trig functions
in terms of reference
angles.
← Student
Success Organizer
Notes 4.4
←
← The day will begin
by answering any HW
Questions, followed by a
PPT Right Triangle
Review .
The PPT reviews concepts
learned in 4.1-4.4, followed
by a speed quiz for
students to play a game
with three teams.
Students will also learn
about latitude and
longitude, uniform
circular motion,
angular speed .
←
← Independent practice (Internet Links)
← Student
Success Organizer
← Additional
Problems 4.1
← Student
Success Organizer
← Additional
Problems 4.2
← Student Success
Organizer
← Additional
Problems 4.3
← Student
Success Organizer
← Additional
Problems 4.4
← Homework
← 290 # 3-111 (3) ← 299 # 3-60 (3)
← ACE Practice
Quiz 4.1
← 308 # 3-69 (3)
← ACE Practice Quiz
4.2
← 318 # 5-95 (5)
← ACE Practice
Quiz 4.3
← 365 # 3-81 (3)
← ACE Practice Quiz
4.4
← AV, Internet materials required
← graphing
calculator w/ TV adapter
system &
← Internet w/
projector
← graphing
calculator w/ TV adapter
system;
← Internet w/
projector;
← email quiz
← graphing calculator
w/ TV adapter system;
← Internet w/ projector;
← PPT with projector;
← email quiz
← graphing
calculator w/ TV adapter
system;
← Internet w/
projector;
← email quiz
← graphing calculator
w/ TV adapter system;
← Internet w/
projector;
← PPT with projector
← email quiz
← Technology Enrichment
← Using a
computer and projector,
I can display the notes
on a white board and fill
in information and solve
problems without
recopying the problems.
Students can download
and print the Student
Success Organizer
(SSO) notes so they do
not have to copying to
do, saving time and
← Using a
computer and projector,
I can display the notes
on a white board and fill
in information and solve
problems without
recopying the problems.
Students can download
and print the Student
Success Organizer
(SSO) notes so they do
not have to copying to
do, saving time and
← Using a computer
and projector, I can display
the notes on a white board
and fill in information and
solve problems without
recopying the problems.
Students can download and
print the Student Success
Organizer (SSO) notes so
they do not have to copying
to do, saving time and
allowing them to focus more
on the lecture and not
← Using a
computer and projector,
I can display the notes
on a white board and fill
in information and solve
problems without
recopying the problems.
Students can download
and print the Student
Success Organizer
(SSO) notes so they do
not have to copying to
do, saving time and
← The Right Review
PPT will take students
through a brief review of
trigonometric relationships
in right triangles. The class
will divide into three teams
and play a speed quiz to
test their skills. There is
also a link to a video file on
the Internet in the ppt.
← The graphing
calculator TV adapter
allows students to see the
allowing them to focus
more on the lecture and
not copying notes.
← Using the
Internet, I will be able to
take students to sites
that can provide detailed
graphics and information
about trigonometric
concepts. The latitude
and longitude website
provides excellent 3D
graphics of the globe
and the relationship with
the degree. There is an
interactive portion of the
site that allows students
to determine the latitude
and longitude of a
particular location. The
links for the uniform
circular motion has
animated graphics that
illustrate uniform circular
motion and the angular
speed link shows the
student an interactive
allowing them to focus
more on the lecture and
not copying notes.
← Using the
Internet, I will be able to
take students to sites
that can provide detailed
graphics and information
about trigonometric
concepts. The unit circle
interactive graphic
provides an excellent
visual relationship
between the (x, y)
coordinates of a point
and the cosine and sine
segments on a unit
circle. The computer
generated graphics and
animations are much
more accurate than any
in class demonstration.
← The graphing
calculator TV adapter
allows students to see
the calculations that are
being performed so they
copying notes.
← The Right Triangle
PPT will take students
through the development of
the relationships in the
special right triangles step-
by-step with accurate
graphics with straight lines
and color.
← The graphing
calculator TV adapter allows
students to see the
calculations that are being
performed so they can follow
along and know the correct
information to enter into the
calculator, as well as see the
correct response. Students
will use a graphing calculator
to solve more advanced
problems.
← The textbook
website also allows students
to take a quiz, submit their
answers and receive instant
feedback. They can find out
the concepts they need to
allowing them to focus
more on the lecture and
not copying notes.
← Using the
Internet, I will be able to
take students to sites
that can provide detailed
graphics and information
about trigonometric
concepts. The unit circle
interactive graphic
provides an excellent
visual relationship
between the sign
change of cosine and
sine segments on a unit
circle. The computer
generated graphics and
animations are much
more accurate than any
in class demonstration.
← The graphing
calculator TV adapter
allows students to see
the calculations that are
being performed so they
can follow along and
calculations that are being
performed so they can
follow along and know the
correct information to enter
into the calculator, as well
as see the correct
response. Students will
use a graphing calculator to
solve more advanced
problems.
← The textbook
website also allows
students to take a quiz,
submit their answers and
receive instant feedback.
They can find out the
concepts they need to
strengthen. By email the
results to me, I can see
how the class is doing as a
whole and review
necessary concepts the
next day.
real-world application.
The computer generated
graphics and animations
are much more accurate
than any in class
demonstration.
← The graphing
calculator TV adapter
allows students to see
the calculations that are
being performed so they
can follow along and
know the correct
information to enter into
the calculator, as well as
see the correct
response. Students will
use a graphing
calculator to solve more
advanced problems.
can follow along and
know the correct
information to enter into
the calculator, as well as
see the correct
response. Students will
use a graphing
calculator to solve more
advanced problems.
← The textbook
website also allows
students to take a quiz,
submit their answers
and receive instant
feedback. They can find
out the concepts they
need to strengthen. By
email the results to me, I
can see how the class is
doing as a whole and
review necessary
concepts the next day.
strengthen. By email the
results to me, I can see how
the class is doing as a whole
and review necessary
concepts the next day.
know the correct
information to enter into
the calculator, as well as
see the correct
response. Students will
use a graphing
calculator to solve more
advanced problems.
← The textbook
website also allows
students to take a quiz,
submit their answers
and receive instant
feedback. They can find
out the concepts they
need to strengthen. By
email the results to me, I
can see how the class is
doing as a whole and
review necessary
concepts the next day.
← Assessment
← SSO & HW ← SSO, HW, QUIZ ← SSO, HW, QUIZ ← SSO, HW, QUIZ ← HW, QUIZ
← Points
← 3+4=7 ← 3+4+3=10 ← 3+4+3=10 ← 3+4+3=10 ← 4+3=7
← Teacher: Ms. Camacho Ingersoll← Class: Math Analysis / Precalculus←
← Unit: Chapter 4 Trigonometry← Date: This unit is usually completed in December←
← ← Day 6
←
← Day 7
←
← Day 8
←
← Day 9
←
← Day 10
←
← Topics
← Quiz 4.1-4.4
← 4.5 Graphs of Sine & Cosine Functions
← 4.6 Other Trig Graphs (Sec, Csc, Tan & Cot)
← 4.5-4.6 Review & Group Activity
← 4.7 Inverse Trig Functions
← Stan dards ←
1.0 Content, 1.0
Process
2.0 Content
3.0 Content, 3.1 & 3.2
Process
5.0 Content
6.0 Content
7.0 Content
9.0 Process
12.0 Process
19.0 Process
←
2.0 Content: Students
know the definition of
sine and cosine as y-
and x- coordinates of
points on the unit circle
and are familiar with the
graphs of the sine and
cosine functions.
4.0 Process: Students
graph functions of the
form f(t) = A sin (Bt + C )
or f(t) = A cos ( Bt + C)
and interpret A, B, and C
in terms of amplitude,
frequency, period, and
phase shift.
5.0 Content: Students
know the definitions of the
tangent and cotangent
functions.
5.0 Process: Students
can graph tangent and
cotangent functions.
6.0 Content: Students
know the definitions of the
secant and cosecant
functions.
6.0 Process: Students
can graph secant and
cosecant functions.
←
5.0 Content: Students
know the definitions of the
tangent and cotangent
functions.
5.0 Process: Students
can graph tangent and
cotangent functions.
6.0 Content: Students
know the definitions of the
secant and cosecant
functions.
6.0 Process: Students
can graph secant and
cosecant functions.
←
8.0 Content: Students
know the definitions of
the inverse trigonometric
functions.
9.0 Process: Students
compute, by hand, the
values of the
trigonometric functions
and the inverse
trigonometric functions at
various standard points.
←
← Lectu ← The day will The day will begin by The day will begin by The day will begin by ← The day will
re Notes (Links to multimedia Resources)
begin with a quick
review of any HW
Questions. Students will
take the 4.1-4.4 Quiz.
← Following the
quiz, there will be a brief
Review Graphing Calc
including
Setting windows,
Finding intercepts, and
finding maximum and
minimum values.
←
answering any HW
Questions. Students will
find out the answer to
the extra credit question
and see the rest of the
Tacoma Narrows
video. Students will
learn about waves and
graphing trig functions.
What is a wave?
Graphing sin waves
Sin transformation
Graphing cosine
waves
Graphing ppt
Student Success
Organizer Notes 4.5
answering any HW
Questions. Students will
continue the lesson on
graphing trig functions.
Graphing tangent
Graphing cotangent
Graphing secant
Graphing cosecant
Students will visually see
the relationship between
the following functions:
← sin/csc
← cos/sec
← tan/cot
periodic function
← Student Success
Organizer Notes 4.6
answering any HW
Questions. Students will
further extend the lesson
on waves and graphing
trig functions by looking at
the composition of
functions and waves
visually at the site Adding
Sine Waves .
Students will also
investigate the sound of
waves and combinations
of waves.
Consonance &
Dissonance
← Damping
Tacoma Narrows
collapse
begin by answering any
HW Questions. Students
will learn about inverse
trig functions and their
graphs.
← Inverse sine
← Inverse cosine
← Inverse tangent
←
← Student
Success Organizer
Notes 4.7
← Students will
learn about the
relationship of inverse trig
functions in different
quadrants.
← Students will use
the graphing calc to find
θ.
← Independent practice (Internet Links)
← Analyzing a
graph
← Ch 4 Tech.
Project
← Student
Success Organizer
← Additional
Problems 4.5
Student Success
Organizer
← Additional
Problems 4.6
← Roller coaster
graphing packet students
will complete together in
groups of 3-4.
Student Success
Organizer
← Additional
Problems 4.7
← Home ← Analyzing a ← 328 # 5-25 (5); ← 339 # 5-85a (5) ← Sound Wave ← 349 # 5-100 (5)
work graph
← Ch 4 Tech.
Project
← Start PPT
project
← 27-54 (3); 60-85
(5)
←
← Investigation Worksheet
← ACE Practice
Quiz 4.5
← ACE Practice
Quiz 4.6
← Finish SWI
Worksheet
← AV, Internet materials required
← graphing
calculator w/ TV adapter
system;
← Internet w/
projector;
← PPT with
projector
← graphing
calculator w/ TV adapter
system;
← Internet w/
projector;
← PPT with
projector
← graphing
calculator w/ TV adapter
system &
← Internet w/
projector
← graphing
calculator w/ TV adapter
system;
← Internet w/
projector; mobile laptop
lab w/ internet;
← email quiz
← graphing
calculator w/ TV adapter
system &
← Internet w/
projector
← Technology Enrichment
← Using the
Internet, I will be able to
take students to a
graphing calculator help
website that they can
revisit on their own if
they need further help.
← The graphing
calculator TV adapter
allows students to see
the calculations that are
being performed so they
can follow along and
know the correct
information to enter into
← Using a
computer and projector,
I can display the notes
on a white board and fill
in information and solve
problems without
recopying the problems.
Students can download
and print the Student
Success Organizer
(SSO) notes so they do
not have to copying to
do, saving time and
allowing them to focus
more on the lecture and
← Using a computer
and projector, I can display
the notes on a white board
and fill in information and
solve problems without
recopying the problems.
Students can download
and print the Student
Success Organizer (SSO)
notes so they do not have
to copying to do, saving
time and allowing them to
focus more on the lecture
and not copying notes.
← Using the Internet,
← Using a computer
I can show students the
websites they will be
visiting to complete the
class work and homework,
including video and audio
files. Students will use the
laptops to investigate
sound waves and
complete the roller coaster
packet and sound wave
investigation sheet. The
graphing calculator TV
adapter allows students to
see the calculations that
← Using a computer
and projector, I can
display the notes on a
white board and fill in
information and solve
problems without
recopying the problems.
Students can download
and print the Student
Success Organizer (SSO)
notes so they do not have
to copying to do, saving
time and allowing them to
focus more on the lecture
and not copying notes.
the calculator, as well as
see the correct
response. Students will
use a graphing
calculator to solve more
advanced problems.
After students have
reviewed graphing
calculator operations,
they will be able to
complete the textbook
website technology
project for chapter 4.
Students will need to
visit the website and
answer the graphing
calculator questions for
HW, bringing a printout
with their results.
← Students will
also receive instructions
on the PPT
presentations they will
need to complete by the
end of the chapter.
not copying notes.
← The Graphing
PPT will take students
through the properties of
the graphs of the sine
and cosine functions.
The interactive links
allow the user to control
the development the
graph and allow the user
to graph these functions
with transformations.
← The graphing
calculator TV adapter
allows students to see
the calculations that are
being performed so they
can follow along and
know the correct
information to enter into
the calculator, as well as
see the correct
response. Students will
use a graphing
calculator to solve more
advanced problems and
graph functions.
I will be able to take
students to sites that can
provide detailed graphics
and information about the
rest of the trig graphs and
show the visual
relationship between the
reciprocal functions.
← The graphing
calculator TV adapter
allows students to see the
calculations that are being
performed so they can
follow along and know the
correct information to enter
into the calculator, as well
as see the correct
response. Students will
use a graphing calculator
to solve more advanced
problems and graph
functions.
←
are being performed so
they can follow along and
know the correct
information to enter into
the calculator, as well as
see the correct response.
Students will use a
graphing calculator to
solve more advanced
problems and graph
functions. The textbook
website also allows
students to take a quiz,
submit their answers and
receive instant feedback.
They can find out the
concepts they need to
strengthen. By email the
results to me, I can see
how the class is doing as a
whole and review
necessary concepts the
next day.
← Using the
Internet, I will be able to
take students to sites that
can provide detailed
graphics and information
about inverse
trigonometric concepts.
The graphing calculator
TV adapter allows
students to see the
calculations that are
being performed so they
can follow along and
know the correct
information to enter into
the calculator, as well as
see the correct response.
Students will use a
graphing calculator to
solve more advanced
problems and graph
functions.
←
← Assessment
← Ch 4 Project ← SSO, HW ← SSO, HW ← Group WS, QUIZ
(2)
← HW, SWI
← Points
← 10 ← 3+4=7 ← 3+4=7 ← 10+3+3=16 ← 4+10
← Teacher: Ms. Camacho Ingersoll← Class: Math Analysis / Precalculus←
← Unit: Chapter 4 Trigonometry← Date: This unit is usually completed in December←
← ← Day 11
←
← Day 12
←
← Day 13
←
← Day 14
←
← Day 15
←
← Topics
← 4.8 Applications of Trigonometry
← Review Chapter 4
Chapter 4 Practice Test
← Chapter 4 Test← W/O Calculator
← Chapter 4 Test With Calculator
← Stan dards ←
12.0 Process: Students
use trigonometry to
determine unknown
sides or angles in right
triangles.
19.0 Process: Students
are adept at using
trigonometry in a variety
of applications and word
problems.
←
1.0 Content, 1.0
Process
2.0 Content
3.0 Content
3.1 & 3.2 Process
4.0 Process
5.0 Content, 5.0
Process
6.0 Content, 6.0
Process
8.0 Content
7.0 Content
9.0 Process
12.0 Process
19.0 Process
1.0 Content, 1.0 Process
2.0 Content
3.0 Content
3.1 & 3.2 Process
4.0 Process
5.0 Content, 5.0 Process
6.0 Content, 6.0 Process
8.0 Content
7.0 Content
9.0 Process
12.0 Process
19.0 Process
←
1.0 Content, 1.0 Process
2.0 Content
3.0 Content
3.1 & 3.2 Process
4.0 Process
5.0 Content, 5.0 Process
6.0 Content, 6.0 Process
8.0 Content
7.0 Content
9.0 Process
12.0 Process
19.0 Process
←
1.0 Content, 1.0
Process
2.0 Content
3.0 Content
3.1 & 3.2 Process
4.0 Process
5.0 Content, 5.0
Process
6.0 Content, 6.0
Process
8.0 Content
7.0 Content
9.0 Process
12.0 Process
← 19.0 Process
← Lecture Notes
← The day will
begin by answering any
The day will begin by
answering any HW
← The day will begin
by answering any HW
← Students will turn
in their packets which
← Students’
graphing calculator
(Links to multimedia Resources)
HW Questions.
Students will further
investigate Applications
of Trig with an
Application PPT along
with the
← Student
Success Organizer
Notes 4.8.
Questions. Questions. consist of their SSOs and
HW assignments.
memory will be cleared to
ensure no programs or
information is stored in
the calculator.
Calculators will also be
cleared following the test,
so no information is
transported from the
classroom.
← Independent practice (Internet Links)
← Student
Success Organizer
← Additional
Problems 4.8
←
← Students work in
groups of 2-4 on review
← CW 366 # 5-150
(5)
←
← Individual Chapter
Test in class 369 # 1-19
odd
← Review answers in
class
←
← Chapter 4 Test
← w/o calculator
← Chapter 4 Test
← w/ graphing
calculator
← Homework
← 359 # 16-40 all ← ACE Practice
Quiz 4.8
← ACE Practice
Quiz 4.7
← Finish 366 # 5-
150 (5)
← 369 # 2-20 even ← work on PPT
project
← work on PPT
project
← PPT project due
Monday
← AV, Internet materials required
← graphing
calculator w/ TV adapter
system;
← Internet w/
projector;
← PPT with
← graphing
calculator w/ TV adapter
system;
← Internet;
← email quiz
← graphing
calculator w/ TV adapter
system
← graphing
calculator
projector
← Technology Enrichment
← Using a
computer and projector,
I can display the notes
on a white board and fill
in information and solve
problems without
recopying the problems.
Students can download
and print the Student
Success Organizer
(SSO) notes so they do
not have to copying to
do, saving time and
allowing them to focus
more on the lecture and
not copying notes. I can
also show students a
site with information
about the real-world
applications of trig.
← The Application
PPT will take students
through a review of
solving right triangles
followed by word
problems where
students will use the
← The graphing
calculator TV adapter
allows students to see
the calculations that are
being performed so they
can follow along and
know the correct
information to enter into
the calculator, as well as
see the correct
response. Students will
use a graphing
calculator to solve more
advanced problems,
application problems
and graph functions.
← The textbook
website also allows
students to take a quiz,
submit their answers
and receive instant
feedback. They can find
out the concepts they
need to strengthen. By
email the results to me, I
can see how the class is
doing as a whole and
← The graphing
calculator TV adapter
allows students to see the
calculations that are being
performed so they can
follow along and know the
correct information to enter
into the calculator, as well
as see the correct
response. Students will
use a graphing calculator
to solve more advanced
problems, application
problems and graph
functions.
←
← Students will be
using a computer with PPT
to finish their projects.
←
← Students will use
a graphing calculator to
solve more advanced
problems and application
problems.
← Students will be
using a computer with
PPT to finish their
projects.
skills that have been
reviewed.
← The graphing
calculator TV adapter
allows students to see
the calculations that are
being performed so they
can follow along and
know the correct
information to enter into
the calculator, as well as
see the correct
response. Students will
use a graphing
calculator to solve more
advanced problems and
application problems.
review necessary
concepts the next day.
← Assessment
← SSO, HW ← HW, QUIZ (2) ← CW, HW ← Test ← Test, PPT
← Points
← 3+4=7 ← 4+3+3=10 ← 4+4=8 ← 65 ← 35+25=60