grade 11 physics, year:arc63158/documents/word_documents/... · web view2.0 content: students know...

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.


know the definition of

sine and cosine as y-

and x- coordinates of

points on the unit circle.


know the definitions of

the tangent and

cotangent functions.



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:


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).


prove other trigonometric

identities and simplify others

by using the identity cos2

x+sin2 x = 1. For example,


know that the tangent of

the angle that a line

makes with the x- axis is

equal to the slope of the

line.



values of the


at various standard

points.


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

http://www.cde.ca.gov/be/st/ss/mthtrig.asp


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.


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


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.

http://college.hmco.com/mathematics/larson/precalculus/6e/students/sso.html


http://webhome.broward.edu/~mperes/unitcirc/unitcircle2.html

http://mathworld.wolfram.com/Quadrant.html



http://mathworld.wolfram.com/RightTriangle.html

http://mathworld.wolfram.com/RightTriangle.html







http://aleph0.clarku.edu/~djoyce/java/trig/who.html

http://aleph0.clarku.edu/~djoyce/java/trig/who.html

Students will also learn

about latitude and

longitude, uniform

circular motion,

angular speed .

←

http://www.ies.co.jp/math/java/trig/kanran/kanran.html

http://mathworld.wolfram.com/UniformCircularMotion.html

http://mathworld.wolfram.com/UniformCircularMotion.html

http://www.sciencecourseware.org/eec/Earthquake/EpicenterMagnitude/Tutorials/LL.swf

http://www.sciencecourseware.org/eec/Earthquake/EpicenterMagnitude/Tutorials/LL.swf

← 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


system;

← Internet w/

projector;

← email quiz

← graphing calculator

w/ TV adapter system;

← Internet w/ projector;

← PPT with projector;

← email quiz

← graphing


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





problems without




Success Organizer



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


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





problems without




Success Organizer



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

http://college.hmco.com/cgi-bin/SaCGI.cgi/ace1app.cgi?FNC=AcePresent__Apresent_html___mathematics_larson_precalculus_6e_04-04
















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



not copying notes.

← Using the





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


allows students to see

the calculations that are

being performed so they

copying notes.

← The Right Triangle


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



not copying notes.

← Using the





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





can follow along and


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






know the correct

information to enter into

the calculator, as well as

see the correct


use a graphing

calculator to solve more

advanced problems.


know the correct



see the correct


use a graphing


advanced problems.

← The textbook

website also allows


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.


results to me, I can see how

the class is doing as a whole

and review necessary


know the correct



see the correct


use a graphing


advanced problems.

← The textbook

website also allows



and receive instant







review necessary


← 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



← ← 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

←


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.


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.


know the definitions of the

tangent and cotangent

functions.


can graph tangent and




secant and cosecant

functions.


can graph secant and

cosecant functions.

←



tangent and cotangent

functions.


can graph tangent and




secant and cosecant

functions.


can graph secant and

cosecant functions.

←



the inverse trigonometric

functions.



values of the


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


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


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


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


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.


← 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)

http://www.sfu.ca/sonic-studio/handbook/index.html

http://college.hmco.com/mathematics/larson/precalculus/6e/students/chapter_projects.html



http://www.nsa.gov/teachers/hs/preclc02.pdf







http://mathworld.wolfram.com/Quadrant.html



http://mathworld.wolfram.com/InverseTangent.html

http://mathworld.wolfram.com/InverseCosine.html

http://mathworld.wolfram.com/InverseSine.html

http://en.wikipedia.org/wiki/Tacoma_Narrows_Bridge#Cause_of_collapse

http://encarta.msn.com/media_461550807_761561057_-1_1/Collapse_of_the_Tacoma_Narrows_Bridge.html

http://www.kettering.edu/~drussell/Demos/SHO/damp.html

http://www.mindspring.com/~scottr/zmusic/

http://www.mindspring.com/~scottr/zmusic/

http://www.ling.udel.edu/idsardi/253/sinewave/

http://www.ling.udel.edu/idsardi/253/sinewave/



http://encarta.msn.com/media_461518028_761572350_-1_1/Figure_5_Periodic_Functions.html

http://encarta.msn.com/media_461524602_761572350_-1_1/Tangent_and_Cotangent.html

http://encarta.msn.com/media_461524600_761572350_-1_1/Cosine_and_Secant.html

http://encarta.msn.com/media_461524599_761572350_-1_1/Sine_and_Cosecant.html

http://mathworld.wolfram.com/Cosecant.html

http://mathworld.wolfram.com/Secant.html

http://mathworld.wolfram.com/Cotangent.html

http://www.ies.co.jp/math/java/trig/graphTanX/graphTanX.html



http://www.ies.co.jp/math/java/trig/graphCosX/graphCosX.html

http://www.ies.co.jp/math/java/trig/graphCosX/graphCosX.html

http://www.ies.co.jp/math/java/trig/ABCsinX/ABCsinX.html

http://www.ies.co.jp/math/java/trig/graphSinX/graphSinX.html

http://www.kettering.edu/~drussell/Demos/waves-intro/waves-intro.html

http://encarta.msn.com/media_461550807_761561057_-1_1/Collapse_of_the_Tacoma_Narrows_Bridge.html

http://college.hmco.com/mathematics/larson/precalculus/6e/students/tech_guide/ti83.pdf

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


← graphing


system;

← Internet w/

projector;

← PPT with

projector

← graphing


system;

← Internet w/

projector;

← PPT with

projector

← graphing


system &

← Internet w/

projector

← graphing


system;

← Internet w/

projector; mobile laptop

lab w/ internet;

← email quiz

← graphing


system &

← Internet w/

projector


← Using the


take students to a

graphing calculator help

website that they can

revisit on their own if

they need further help.

← The graphing






know the correct


← Using a





problems without




Success Organizer



do, saving time and




and projector, I can display

the notes on a white board

and fill in information and

solve problems without




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,


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


and projector, I can

display the notes on a

white board and fill in

information and solve

problems without




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.










see the correct


use a graphing


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


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






know the correct



see the correct


use a graphing


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








as see the correct


use a graphing calculator


problems and graph

functions.

←

are being performed so

they can follow along and

know the correct



see the correct response.

Students will use a

graphing calculator to

solve more advanced

problems and graph

functions. The textbook

website also allows


submit their answers and

receive instant feedback.

They can find out the

concepts they need to


results to me, I can see

how the class is doing as a

whole and review

necessary concepts the

next day.

← Using the


take students to sites that

can provide detailed


about inverse

trigonometric concepts.

The graphing calculator

TV adapter allows

students to see the

calculations that are



know the correct



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



← ← 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 ←


use trigonometry to

determine unknown

sides or angles in right

triangles.


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


2.0 Content

3.0 Content

3.1 & 3.2 Process

4.0 Process



8.0 Content

7.0 Content

9.0 Process

12.0 Process

19.0 Process

←


2.0 Content

3.0 Content

3.1 & 3.2 Process

4.0 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


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.


← 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


← graphing


system;

← Internet w/

projector;

← PPT with

← graphing


system;

← Internet;

← email quiz

← graphing


system

← graphing

calculator







http://aleph0.clarku.edu/~djoyce/java/trig/apps.html

http://aleph0.clarku.edu/~djoyce/java/trig/apps.html

projector


← Using a





problems without




Success Organizer



do, saving time and



not copying notes. I can

also show students a

site with information

about the real-world

applications of trig.

← The Application


through a review of

solving right triangles

followed by word

problems where

students will use the

← The graphing






know the correct



see the correct


use a graphing


advanced problems,

application problems

and graph functions.

← The textbook

website also allows



and receive instant







← The graphing








as see the correct


use a graphing calculator


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






know the correct



see the correct


use a graphing


advanced problems and

application problems.

review necessary


← 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

grade 11 physics, year:arc63158/documents/word_documents/... · web view2.0 content: students know...

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