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