1. Podcast: How to assemble your TWS planning document for submission on Dec. 9, 2013 Recorded by Dr. Janet Painter, Nov. 26, 2013 Methods - EDU 420 /416/ 628 Fall 2013

2. Teacher Work Sample EE 3: Planning/Implementation PhaseHailey Garrou Spring 2012 Dr. Janet Painter 3. Garrou 18Table of Contents Description of Setting 3-6Rationale/Relationship to Standards 7-8 Unit Goals/Lesson Outcomes 9 Assessment Plan 10-18 Pre-Assessment 13-15 Post-Assessment 16-18 Teaching Plans/Materials 19-34 All lesson plans are attached as separate TaskStream files (not in this document). Unit Plan Outline 19 Lesson 1: 3.1 Radian Measure 20 Lesson 2: 3.1 Radian Measure (continued) 21 Lesson 3: 3.2 Applications of Radian Measure 22 Lesson 4: 3.1-3.2 Review and Quiz 23 Lesson 5: 3.3 Circular Functions of Real Numbers 24 Lesson 6: 3.3 Circular Functions of Real Numbers (continued) 25 Lesson 7: Chapter 3 Review 26 Lesson 8: Chapter 3 Test 27 Lesson 9: 4.1 Graphs of the Sine and Cosine Functions 28 Lesson 10: 4.2 Translations of the Graphs of the Sine and Cosine Functions 29 Lesson 11: 4.1-4.2 Modeling Activity 30 Lesson 12: 4.1-4.2 Review and Quiz 31 Lesson 13: 4.3 Graphs of the Other Circular Functions 32 Lesson 14: Chapter 4 Review 33 Lesson 15: Chapter 4 Test 34 Samples of Student Work 35-47 Appendices/References 48 4. Garrou 18Description of Setting My student teaching placement is at St. Stephens High School. The school is located at 3205 34th Street Drive NE in Hickory, North Carolina and is one of seven high schools in the Catawba County School District. The principal at St. Stephens is Mrs. DeAnna Taylor, and my cooperating teacher is Mrs. Barbara Faulkner. The school consists of one main building with three long hallways that are connected by two additional hallways running the opposite direction. All of the academic classrooms, as well as offices, the newly renovated cafeteria, and the media center, are housed within this building. In addition to the main building, St. Stephens has a football stadium (including an outdoor track), tennis courts, baseball and softball fields, and a theater, affectionately known as the tractor shed. The mission of St. Stephens High School is to teach, learn, and lead for the future. St. Stephens has also adopted three core beliefs, which are:Creating and maintaining positive relationships with students is essential to academic success. All students will graduate with 21st century skills. Serving our students by partnering with all stakeholders in a meaningful educational process is paramount to academic success.These beliefs form the basis of the schools educational philosophy and help to create a positive learning environment that is conducive to student success. St. Stephens operates on a semester system. The first semester begins on August 25, 2011 and ends on January 20, 2012. The second semester begins on January 25, 2012 and ends on June 8, 2012. The school day begins at 8:05 AM and ends at 3:10 AM. The daily schedule contains four blocks, each of which are around 90 minutes, with a five-minute break between 5. Garrou 18classes. There is an additional Enrichment Period every day from 11:08 to 11:38 AM. During this time, students may choose from a list of enrichment activities in which they are interested (e.g. band, chorus, theater, yearbook), or they may use this time as a study hall to work on homework or get help from their teachers. There are four lunches scheduled during third period, from 11:43 AM to 1:40 PM. Each class is assigned to one of the four lunches (usually based on department), and each lunch lasts for 27 minutes. 1,199 students attend St. Stephens High School. This is significantly higher than both the district average (893) and the state average (792). Of these 1,199 students, 612 are male and 587 are female. St. Stephens is a fairly diverse school, serving a 30% minority population. 840 students are white, 162 are Hispanic (the schools largest minority population), 88 are black, 70 are Asian, 3 are American Indian, and 36 are multiracial. The percentage breakdown for each of these ethnicities is shown in the chart below. These percentages are similarEthnicities in SSHS Student Populationto the Catawba County SchoolsAmerican Multiracial 3% Indian 0%averages. According to 2009-2010Asian 6%data, 72.98% of students in Catawba County are white, 9.61% are HispanicBlack 7%(somewhat lower than the St. Stephens average), 5.63% areHispanic 14%black, 7.29% are Asian, 0.28% are American Indian, and 4.22% are multiracial.White 70% 6. Garrou 18 The school serves an area of relatively low socioeconomic wealth, with 486 students qualifying for free or reduced lunch. St. Stephens currently employs 75 teachers, along with 6 teacher assistantsand several other support staff. The student-to-teacher ratio is around 16 to 1. 94% of teachers at St. Stephens are fully licensed and 97% are highly qualified. Both of these numbers are within two percentage points of the district and state averages. My Pre-Calculus class contains 20 students, a relatively small number for a school the size of St. Stephens. This is most likely a result of Pre-Calculus being a higher-level math class, as most of the basic math classes have closer to 30 students. In my class, there are 10 juniors and 10 seniors. The breakdown by gender is Ethnicities in Pre-Calculus Class almost as evenly split, with 9 male students and 11 female students. The ethnicity Asian 5%breakdown of the class is represented in the chart below. The makeup of the class is 85%Hispanic 10%white (17 students), 10% Hispanic (2students), and 5% Asian (1 student). These percentages are roughly similar to the schools overall population, although the percentage of Caucasian students in my classWhite 85%is slightly higher than that of the school.For the 2010-2011 school year, St. Stephens met 17 of their 19 target goals, so they did notmake AYP. However, they did receive School of Distinction status. Students at St. Stephens performed very well on their EOC tests. Their scores were first in Catawba County for Algebra 7. Garrou 18 II; second in Catawba County for Algebra I, Biology, Physical Science, and U.S. History; and third in Catawba County for Civics and English I. Additionally, St. Stephens had a graduation rate of81.87% last year. As a part St. Stephens 2009-2012 School Improvement Plan, two SMART goals were developed. The first goal is that 85% of students enrolled in EOC classes will score proficient on the EOC exam, as measured by ABC performance indicators. The second goal is that the Graduation Cohort rate for St. Stephens High School will be 85%. St. Stephens hopes to achieve both of these goals by June of 2012. 8. Garrou 18Rationale for Unit My unit plan will be taught in my Pre-Calculus class, and the topic of it will be radianmeasure and circular functions. This unit covers Chapters 3 and 4 in the textbook. Chapter 3 deals with radian measure and the circular functions, and Chapter 4 covers graphs of the circular functions. This unit corresponds to Objective 2.02 from the North Carolina Standard Course of Study curriculum for Pre-Calculus. This objective states that students will be able to use trigonometric and inverse trigonometric functions to model and solve problems [and] justify results. This unit also corresponds to the Trigonometric Functions domain in the Common Core Standards for Functions. This unit is a critically important part of any course involving trigonometry because it forms the foundation for dealing with trigonometric functions in all higher-level mathematics courses. The textbook prefaces Chapter 3 with the explanation, In most work involving applications of trigonometry, angles are measured in degrees. In more advanced work in mathematics, the use of radian measure of angles is preferred. Radian measure allows us to treat the trigonometric functions as functions with domains of real numbers, rather than angles.It may be initially unclear to students why the use of radian measure is necessary. However, as the unit progresses and eventually builds up to the use of trigonometric functions in modeling contexts, it will become increasingly clear. As the textbook states, using degrees as the domain for trigonometric functions is adequate for most cases when we want to model something that involves angles. However, periodic functions (functions that increase and decrease in a predictable pattern) have many practical applications that do not involve angles. For instance, hours of daylight, monthly average temperatures, tidal patterns, phases of the moon, etc. can all be modeled with periodic functions. Data of this nature does not always involve angles, so in 9. Garrou 18 order to use a trigonometric function to model this data, we must have a system that creates a real number domain for trigonometric functions. Radian measure creates this system. Whentrigonometric functions have domains of real numbers instead of angles, they are called circular functions. The practical value of this unit is incredible. We will discuss extensively the many applications of periodic functions and practice creating models for periodic data. Practically any data that increases and decreases in a predictable pattern can be modeled with a trigonometric function. During the unit, students will complete an activity in which they must collect data on sunrise and sunset times for a particular city and use this data to create a model of the hours of daylight for that city. This model can then be used to predict the daylights hours for any day of the year in that city. Also during this unit, students will do a Think-Pair-Share in which they discuss how trigonometric functions can be applied to real-life situations. My hope is that by the end of the unit, students will be able to see both the mathematical and the practical significance of this material. 10. Garrou 18Unit Goals 1.Students will be able to convert angle measures from degrees to radians and from radiansto degrees. 2.Students will be able to evaluate trigonometric functions of any angle and solve forunknown variables in trigonometric equations. 3.Students will be able to calculate arc length and area of a sector of a circle, given aspecified radius and central angle. 4.Students will be able to identify the period, amplitude, horizontal shift (anddirection), and vertical shift (and direction) of a given circular function.5.Students will be able to graph circular functions over a specified interval and identifyimportant characteristics of the graph, such as domain, range, xintercepts, maximums/minimums, asymptotes, etc. 6.Students will be able to create a trigonometric model for a set of periodic data. 11. Garrou 18Assessment Plan I designed a pre- and post-test for my unit, which covers chapters 3 and 4 on radianmeasure and circular functions. Originally, my plan was to make the pre-test different from the posttest, but after discussing it with my cooperating teacher, I decided that the pre- and post-assessments needed to be identical. This is simply proper statistical practice. If you are going to assess student growth between the pre-test and post-test, you must eliminate the possibility that any difference in scores could have been caused by asking different questions. Therefore, I decided to use the same assessment for both the pre- and post-test. I designed the assessment, based on the goals and objectives that I have set for the unit. The concepts that I hope students will learn during the course of the unit are listed in the table below. I kept in mind that the post-test would be a cumulative test for Chapters 3 and 4, in addition to the separate chapter tests. Since the students will have just taken the Chapter 4 Test, I do not want them to see this as yet another test, so I have decided to present it as a cumulative review of Chapters 3 and 4. I went through the two separate chapter tests and divided them into the seven main concepts listed in the table below. Then I designed a few key questions that I thought captured the essence of these skills to include in the pre- and post-assessment. Again, since the students will have just been tested on Chapter 4 when they take the post-test, I did not want to go overboard with the amount of questions, so I tried to include as few questions as possible. The assessment is only 12 items, which seems very short, but several items contain multiple parts. By the time the students complete the post-assessment, I will already have gathered a great deal of assessment data from guided practice, homework, worksheets, projects, quizzes, chapter tests, and various types of formative assessment, so it is not at all necessary that I give the students anoverly lengthy assessment. I believe 12 questions will be more than sufficient for me to assess student growth. 12. Garrou 18 Designing the pre-test was a difficult task for me because I did not want to present the students with questions I knew they would not be able to answer. However, I soon realized that forthis particular unit, there is no way to avoid this. The concept of radian measure is entirely new to students, so I do not anticipate that they will be able to answer many of the questions on the pre-test. This is not necessarily a bad thing; it just means that there will be a great deal of room for growth. Some of the students might figure out that they can use their calculators to help them answer a few of the questions, which is perfectly fine, but they will have to know to change the calculator to radian mode. They may be able to use the calculator to evaluate some of the trigonometric equations and to help them graph trigonometric functions, but because they will not yet understand the concept of radian measure, correct answers on these questions will not indicate that a student has mastered the corresponding skills. I decided to ease students nerves by calling the pre-assessment a presurvey and by assuring them that the only purpose of this is for me to see what they already know. I will explain that they are not expected to know any of this yet, but they should do their best and see if they can make an educated guess on any of the questions. After the students have completed the pre- and post-assessments, I will compare the data and use the results to assess the growth students have made over the course of the unit. The following chart shows the concepts and skills I will be assessing, the corresponding NC Standard Course of Study objectives, the lessons in which I will teach each skill/concept, and the accompanying item(s) on the pre- and post-test. 13. Garrou 18 Standards MatrixSkill/Concept AssessedNC SCOS ObjectiveLessonItems on Pre/Post-TestConverting between degrees and radians2.02 (a)3.11, 2Evaluating/solving trigonometric equations2.02 (a)3.33, 4, 5Calculating arc length and area of a sector2.02 (a)3.26, 7Identifying period, amplitude, horizontal shift, and vertical shift of trigonometric functions2.02 (a,b)4.1, 4.2, 4.38, 9Graphing trigonometric equations2.02 (a,b)4.1, 4.2, 4.310, 11Creating a trigonometric model for a set of data2.02 (a,b)4.1, 4.212 14. Garrou 18 15. Garrou 18 16. Garrou 18 17. Garrou 18 18. Garrou 18 19. Garrou 18 20. Garrou 19Unit Plan Outline Class: Pre-Calculus Approximate Dates: February 21 March 21, 2012 Chapters: 3-4 Unit Title: Radian Measure and Circular Functions Link:https://w.taskstream.com/Unit/View/549E3CD102A1D2DD1DF73AFC2A932C2E Radian Measure and Circular FunctionsChapter 3: Radian Measure and Circular Functions o 3.1 Radian Measure o 3.2 Applications of Radian Measure o 3.1-3.2 Review and Quiz o 3.3 Circular Functions of Real Numbers oChapter 3 Review o Chapter 3 Test Chapter 4: Graphs of Circular Functions o 4.1 Graphs of the Sine and Cosine Functions o 4.2 Translations of the Graphs of the Sine and Cosine Functions o 4.1-4.2 Modeling Activity o 4.1-4.2 Review and Quizo 4.3 Graphs of the Other Circular Functions o Chapter 4 Review o Chapter 4 Test 21. Garrou 47Lessons Lesson 1 (3.1: RadianMeasure)https://w.taskstream.com/Lesson/View/ED4A65581F44758EBEB190C768A8 265D Today was the first day of my unit plan, so I administered the pre-test I designed for the unit. As I expected, the students did not know how to answer any of the questions, so they got very frustrated at first. This unit hinges on the concept of radian measure, which is entirely new to these students. The students in my Pre-Calculus class are pretty strong math students, so they were not too happy that I was asking them questions they did not know how to answer. I told them that I did not expect them to know how to answer any of the questions at this point. I only wanted to see what they already know so I do not spend a lot of time re-teaching material they have already mastered. When I started the lesson, it was hard for me to tell whether or not they were getting it because they are so quiet and polite. As I mentioned earlier, radian measure is very different from anything we have covered previously in the class. It is one of those tricky concepts that either really makes sense to students or really does not, which makes it challenging to teach. I am planning togive the students a warm-up tomorrow with some problems similar to those I assigned for homework so I can assess whether or not they understood the homework problems. Today in class, I gave the students some guided practice problems to work on, and I was circulating, I quickly realized that there was some confusion about a certain type of problem. The problems showed students an angle and asked them to identify which whole number radian measure would accompany that angle. I realized that I had not clearly distinguished between whole number radians and radians with pi in them, so I clarified this concept with the class and did afew problems with them, which seemed to help. 22. To get the URL for your lessons, go to the Lesson Builder on TaskStream, select the lesson, then generate a URL (see area circled in red in the example page below). A pop-up box will appear with the URL in it and you can copy and paste it into your Word document. 23. Garrou 47 Lesson 2 (3.1: Radian Measure continued)https://w.taskstream.com/Lesson/View/AD90A0CB3946B10D60BCC5DF1591 D0C2 I am glad that I decided to split lesson 3.1 into two sections and spend two days teaching it. This foundation is absolutely critical for students to understand radian measure and be able to use it fluently. One thing I did today that worked really well was to show the class an online applet that allows you to drag a dot around the circumference of a circle, changing the measure of the central angle. As the angle changes, the applet shows the angle measure in both degrees and radians so students can see the comparison. I really think that seeing this visual representation helped tieeverything together for some of the students. I could almost see the light bulbs coming on for a few students, which was very encouraging for me. If I were to re-teach this lesson, I think I would show the applet earlier in the lesson, rather than as a summative activity because it was so helpful. I had a slightly embarrassing moment today when I was working out an example problem. Instead of writing 120, I wrote 210, which of course, thoroughly confused all the students. I did not even notice my mistake until Mrs. Faulkner pointed it out to me later. I wasmortified! I know that teachers make mistakes all the time, but I could not believe that none of the students had corrected my error. I asked them why they did not say anything, and they said that they did not want to be wrong, but I think that they were also afraid of hurting my feelings. I laughed it off and told them to let me know the next time I make a silly mistake. In a way, I think this helped lighten the mood of the class and made the entire atmosphere less serious. When I did go back and correct my mistake, I heard several students say, Oh, that makes so much more sense! Oh well. At least I showed them that I am only human and that I make mistakes too! 24. Garrou 47 Lesson 3 (3.2: Applications of Radian Measure)https://w.taskstream.com/Lesson/View/53677F4AD12864E611A63DF46C1A 5007 Todays lesson was on finding the length of an arc and the area of a sector, which is pretty simply because all you have to do is plug numbers into a formula. In order to make it more challenging, I wanted to guide them into deriving the formula for the area of a sector. I first asked the students to give me the general formula for the area of a circle with radius r. Then I asked them to tell me how they would calculate the area of half a circle, a third of a circle, and a fourth of a circle. For each sector, I asked them to give me the measure of the central angle (in radians) that wouldform that sector. Then we looked for a relationship between the angle measure and the area of the sector. It took a bit of probing, but they eventually discovered that you need to multiply the central angle and by 1/2 r2. Of course, I could have just given them this formula and saved a lot of time, but I thought there was some value in showing them how the formula was derived. Pre-Calculus is an honors weighted class, so these students need to move beyond simply memorizing a formula to a deeper understanding of why the formula works. I also discovered today that I need to hold myself to these higher expectations, as well. I am so used to teaching foundations level classes in which you have to explicitly explain every detail that I forget how much my Pre-Cal students are capable of. I could tell by their faces that some of them were very bored by todays lesson because it was so easy for them. When I was planning these lessons last semester, I did not yet know who my students would be, so it was hard for me to plan how much I should explain and how much I should let them discover on their own. I think that in the future, I want to opt for a more discovery-based approach in this class whenever possible, because Ithink these students are smart enough and curious enough to be able to handle that kind of instruction. 25. Garrou 47 Lesson 4 (3.1-3.2 Review and Quiz)https://w.taskstream.com/Lesson/View/76ECE17F903E1354430F8A96F51559 86 Today I played a game with the students to help them review lessons 3.1 and 3.2 before they take a quiz on that material. I had planned to play trashketball with them, but I realized when I got to school that I had forgotten to bring my little basketball with me. I looked around this morning, trying to find a small ball to use for the game, but I could not find one. The only thing I could find that I thought would be safe to throw was a bunny stuffed animal that Mrs. Morrison had brought to decorate for Easter. So, instead of playing trashketball, we had to playtrashketbunny. It was silly, but it gave us all a good laugh, and I still think the students had fun. We spent longer on the review game than I anticipated, which is not necessarily a bad thing. It just means that I will have to wait and give them the quiz tomorrow. It is probably good that it worked out this way, actually, because I have discovered that several of the students in this class work very slowly, so they may need an entire class period to take the quiz. I would much rather they work slowly and accurately than work quickly and make careless mistakes. However, it issometimes frustrating because I know how much material we need to cover in such a short amount of time. In retrospect, I think it would have worked better for the purposes of the game if I had given them time to work through the entire sheet before playing the game, rather than stopping them after each question. I think that is something I will try in the future because I feel like we wasted a lot of time in transition today. Overall, I think the review went fairly well, though. The students seem prepared for their quiz, so I hope the grades will be good. This quiz will be the first grade (other than homework) that I have taken in this unit, so I want it to be a good one. 26. Garrou 47 Lesson 5 (3.3: Circular Functions of Real Numbers)https://w.taskstream.com/Lesson/View/CC15C520406D1045432A1445DEA0 BE3A I am not completely happy with todays lesson, although I cannot pinpoint exactly why. I think it just feels so backwards to me to teach the unit circle this late in the chapter. When I was planning these lessons last semester, I thought it was strange that the book we are using does not introduce the unit circle until section 3.3, but I decided to just go with the books order, rather than moving things around too much. I think that if I were to re-teach this unit, I would go with my instincts and introduce the unit circle in 3.1. It just makes so much more sense to me to do it that way. Whenstudents see the unit circle, they begin to understand where the sine and cosine values for each of the angle measures come from. It just helps to tie everything together. When I was teaching section 3.3 today, it felt like I was going backwards and teaching material I have already covered. In a way, I have already covered it. I explained to the students that circular functions are slightly different from trigonometric functions because they are functions of arc length, rather than angle measure. However, at this point, it is hard for students to understandthe necessity of changing the domain from angle measures to real numbers, because they have not yet seen how circular functions can be used in modeling contexts. Thus, this subtle difference was basically lost on them, and they probably felt like I was just re-teaching what I had already taught them in lesson 3.1. One aspect of todays lesson that the students really liked was the unit circle chart I gave them to fill out. This chart allows students to fill in the sine, cosine, tangent, secant, cosecant, and cotangent values for each angle measure. It is a great study guide, and I could tell they liked having a way to organize all that information. I told them that this chart would be a great study tool as they become more comfortable with using radian measure. 27. Garrou 47 Lesson 6 (3.3: Circular Functions of Real Numbers continued)https://w.taskstream.com/Lesson/View/827C5B0EF0D76E975A52DD426D3 34B29 I started todays lesson by giving everyone a blank unit circle, just to see how much they could fill in on their own. As soon as I said the dreaded words, without using your notes, I heard a chorus of groans and complaints, but I stood firm. They need to understand how important this material is and how they need to be able to recall it at the drop of a hat. I assured them that I did not intent to take a grade on this (yet), but that I did want to see how much they remembered from yesterday. I also told them that when they take the Chapter 3 Test in a few days, the only thing I will give them is a blank unit circle. They can fill it in if they want to use it, but they have to know it. When I looked at the unit circles they filled in at the beginning of class, I had mixed opinions. Some students were only able to fill in the degree measures, whereas some students were able to fill in almost the entire thing. I think that for some students, it just clicks more quickly than it does for others. Unfortunately, the only way to get a better grasp on the unit circle is to practice using it, which we will do quite a bit. For this reason, I am glad that I decided to split 3.3 into two sectionsand teach it over a two-day period because it allows the students more time to practice using the unit circle. Unfortunately, when I videotaped my lesson today, I forgot to erase the video of yesterdays lesson from the camera. The camera only has about 2 hours of internal memory, so I was only able to videotape about 30 minutes of todays lesson before the camera ran out of memory and stopped recording. I did not realize it had stopped until after the class was over, so I did not get the last hour of todays class on film. It was not an earth-shattering lesson by any means, but I do wish that I had gotten it all on film. At least I got a little bit of it before the camera shut off. 28. Garrou 47 Lesson 7 (Chapter 3 Review)https://w.taskstream.com/Lesson/View/D7F7C3193431A595CC2D8426BFC6 B416 Yesterday afternoon, I had the greatest idea! I was thinking about how I could help my students study the unit circle for their Chapter 3 Test, and I thought that it would be really great if there were some way they could cover up all the radian measures and coordinates so only the degree measures were visible. Then they could somehow spin the circle around and view the radians and coordinates for only one point at a time so they could check themselves. I had an image in my mind of some sort of unit circle spinner, so I went home and played around with it until I came up withsomething I really liked (see attachment in Chapter 3 Review lesson plan). I made some templates, and during todays class, I walked the students through making their own until circle spinner to use as a study guide. I think they really liked them! When they were working on the review worksheet, I saw several of the students actually using their spinners to help them with the questions, which was very encouraging for me. You know you have a keeper when you see students actually using the tool they have created. I showed it to Mrs. Morrison, the other Pre-Calculus teacher, and she loved it, so I gave her copies of my templates. I was a little disappointed because, since we spent so much time making the spinners, we did not get to play the review game that I had planned for today. It was a really neat, logic-based game that Mrs. Faulkner told me about, and I think these students would have really enjoyed it, but I am glad that I chose to spend that time creating the study tool instead of playing the game. I think that it was a more valuable use of our time because they will be able to use the spinners to help them study tonight. I will just save the game for another time. I think one of my biggest challenges asa beginning teacher has been learning to manage my time, but I think I am improving with practice. 90 minutes goes by much more quickly than I realized! 29. Garrou 47 Lesson 8 (Chapter 3 Test)https://w.taskstream.com/Lesson/View/4DA1F34622A72F9859ADA41EF54780E 9 Today my class took the Chapter 3 Test, and I am very impressed with the grades. The grades ranged from a 75 to 103.5, and the class average was an 89.9. There were 6 As, 8 Bs, 2 Cs, and only 1 D. Three students were absent and need to make up the test. I had conflicted feelings about whether or not to give the students the formulas for arc length and area of a sector on the test. I asked Mrs. Faulkner what she would do, and we eventually decided to go ahead and give them the formulas. I thought about what my goals were for the unit, and I decided that I am moreinterested in their ability to accurately use the formulas, rather than their ability to memorize them, and Mrs. Faulkner agreed. I looked through the tests to see if there were any types of questions that were consistently missed, and I did not notice any that stood out. I was however, very impressed that many students got the extra credit question correct. This is the extra credit question that I gave them: Miss Garrous class is having a pizza party. There is a medium pizza with a 8-inch radius that is cut into 8slices and a large pizza with a 10-inch radius that is cut into 12 slices. If you want the largest slice of pizza, should you choose a slice of the medium pizza or the large pizza? The students had to know that they needed to treat each slice of pizza as a sector and find its area. In order to do this, they also needed to determine the central angle by dividing 360 into the appropriate number of slices, and then converting this degree measure into radians. Overall, it was a very complex question, so I was quite impressed that so many of them got it right. Perhaps it was because the question seemed relevant to them. If that is not a real-life application, then I dont know what is! 30. Garrou 47 Lessons 9 (4.1: Graphs of the Sine and Cosine Functions)https://w.taskstream.com/Lesson/View/D4A521B397D885B8FFC4570AA2C0 EA6C After teaching only one lesson, I can already tell that I have not allotted enough time for Chapter 4. I forgot how difficult graphing trig functions can be, and I believe I have underestimated how long it will take us to cover this chapter. Today I only got through about 2/3 of section 4.1, so I will need to spend another day on this section, which I anticipated. However, I did not anticipate half of my class being absent tomorrow because of the ACT. Rather than finishing this section with only half the class, I have decided to rewrite my plans for tomorrow and just review. Iwill continue section 4.1 the following day when the rest of the class returns. Today, we learned how to graph the functions y = sin x and y = cos x, and we also learned how to change the amplitude of those functions. I showed the students a really neat applet that I found on a website called Interactive Mathematics. It shows how you can change the radius of a circle to increase or decrease the height of a periodic function. I think that seeing this visual allowed the students to see the connection between the equation and its graph. I had hoped that wewould also get to look at how to change the period of a graph today, but I spent more time going over the Chapter 3 Test than I anticipated, so we did not have a chance to get that far in the notes. I had to alter the homework assignment at the last minute since I was not able to cover as much material as I had planned. I hope that the problems I gave them for homework were applicable and not too challenging, based on the examples we did in class today. My hope is that tomorrow I can do an exploration activity with the students who are there. Rather than just telling them the rule for how to change the period of a function, I would like for them to graph a few equations, and then make their own conjectures about how the equation is related to the period of a function. 31. Garrou 47 Lesson 10 (4.2: Translations of the Graphs of the Sine and Cosine Functions)https://w.taskstream.com/Lesson/View/628F50075287D52E168604DAB3F6 AD86 I discovered today that, as much as I like using the School Pad to teach, it is very difficult to use it to graph trig functions. For some reason, after I plot all my points and try to connect them, the graph looks terrible! I would like to have a little more control over my pen as I am drawing the graph, so I think that tomorrow I will start using the board to graph these functions. Todays lesson was sort of mediocre, in my opinion. I thought they would catch on quickly because the rules for translating periodic functions are very similar to the rules for translating quadratic functions, which they learned in Algebra II. The students seemed to understand todays lesson while we were going through the notes, but when I gave them some guided practice problems to do, and they started trying to apply the rules of transformations, they quickly became confused. I think they just became overwhelmed by the amount of information. I know that it is a lot to take in, but I did not anticipate that they would have this much trouble graphing. I think I am going to have to spend a few extra days reviewing before we do the modeling activity and the quiz. I talked to Mrs. Faulkner after todays lesson, and she said that she teaches graphing differently than I do. I taught them to create a table of values, plot a few key points, and connect them to form the graph. Mrs. Faulkner said that she teaches them to graph the original function(y = sin x or y = cos x) and then draw each transformation of the graph. In some ways, I like this approach better because I think it is more comprehensive, but at the same time, I feel like there are fewer opportunities for error if you create a table of values. I probably will not teach my class thisalternative method, just because I do not want to confuse them, but if I were to teach this unit again, I would consider trying Mrs. Faulkners method. 32. Garrou 47 Lesson 11 (4.1-4.2 Modeling Activity)https://w.taskstream.com/Lesson/View/F05753CB583C3F5B77E43AE659C5 7C9F I really enjoyed todays lesson because I got to do a really interesting modeling activity with my class. I took the students to the computer lab and had them choose any city in the world and download a table of sunrise and sunset times for that city. It was really interesting because some of the students had a special connection to the cities they chose. Then I took them back to the classroom and walked them through the process of creating an equation that would model the hours of daylight for that city on any given day of the year.One aspect of todays lesson that I did not anticipate was how much trouble the students had converting the days of year into an integer between 1 and 365. For instance, March 15thwould be day 74 because 31 (Jan.) + 28 (Feb.) + 15 (Mar.) = 74. I asked them to do this for the 1st and 15th days of each month. For some reason, several of the students were very confused by this, and I could not really figure out why. I think I was eventually able to explain it so it made sense to them, but of all the components of this activity, I definitely did not anticipate that being the part they would have the most trouble with. When they had come up with a model for their set of data, I asked each group to use that model to predict the number of daylight hours for their chosen city on July 4th and December 25th. Then I asked them to go back to the original data to find the actual number of daylight hours on those days, and see how close their predictions were. When I looked at the papers they turned in, I was shocked by how accurate some of the models were. Some of the predicted values differed from the actual values by only a tenth of an hour! That is only 6 minutes! It is truly amazing how applicable periodic functions can be, and I am glad that I was able to demonstrate that for my students today. This is definitely an activity that I would do again. 33. Garrou 47 Lesson 12 (4.1-4.2 Review and Quiz)https://w.taskstream.com/Lesson/View/3915367A92CC1AD57340D6AC2F4DA83 2 Yesterday we reviewed sections 4.1 and 4.2 in order to prepare the class for a quiz. We did not have time to take the quiz yesterday because we spent a lot of time reviewing, so I decided to wait and give it today. For the review, I had students split up into groups of 3 and gave each group a function to graph. They had to graph the original function and the new function on the same graph so they could compare the changes between the two equations. When all the groups were finished, they presented their graphs to the class and explained howthe graph changed, as well as the aspects of the equation that corresponded to that change. I tried to take a more hands-off approach and put the responsibility of explaining the graphs on the students, although I did ask a few probing questions and clarified some misconceptions. Overall, I was quite pleased with their performance, although I can tell they have not had much experience doing these sorts of presentations in a math class. They seemed very shy and unsure of themselves, even though most of the groups did a great job. I did discover one source of confusion today. The students kept asking me, How do you know which x-values to use in your table of values? I tried to explain to them that it depends on the period and the phase shift, and that figuring out which points will work best is something that comes with practice. I also told them that, if in doubt, it is better to have too many points that too few. I was also very impressed with the quizzes when I graded them. I was prepared for the worst, since the students seemed to be having such difficulty with these sections, but I was pleasantly surprised. Most of the students made in A-B range, and I only noticed minor errors in theirgraphs. There was only one problem that seemed to cause a lot of difficulty, and it was, admittedly, a difficult problem, so I may just count it as extra credit. 34. Garrou 47 Lesson 13 (4.3: Graphs of the Other Circular Functions)https://w.taskstream.com/Lesson/View/D170887277CDFC797A857257D58 759CE Todays lesson went fairly well. It is much easier to teach students how to graph secant, cosecant, tangent, and cotangent since they already know how to graph sine and cosine. I told them at the beginning of class that they have already learned the hard part because they can use the sine and cosine functions as a guide for graphing the other four. I was a little disappointed because I did not get a chance to go through as many of the examples as I had hoped to do in class. The problem with this chapter is that examples take so long to do. Each problem takes about 5-10minutes, so if I have to go over 5 homework problems, then by the time I am finished, half the class is already over. I was able to get through all of the notes, though, so they should have enough information to be able to do the homework problems. However, I anticipate that they may have some questions I need to address at the beginning of class tomorrow. One thing I did not anticipate is that they would have so much difficulty figuring out where to put the asymptotes. For tangent and cotangent, finding the asymptotes is pretty straightforward because there is a nice rule to tell you where they are. However, for secant and cosecant, finding the asymptotes is a little more tricky. The easiest thing to do is just to graph the reciprocal function (sine or cosine), see where is crosses the x-axis, and draw an asymptote anywhere there is an x-intercept. I was also a little frustrated today because there were several students with their heads down, and I kept having to ask them to wake up. This is an upper-level math class, so I guess I just expected these students to be a little more self-motivated. They may have a rude awakening in a fewdays when they take the Chapter 4 Test and realize that they do not know how to graph some of the equations because they did not pay attention in class. 35. Garrou 47 Lesson 14 (Chapter 4 Review)https://w.taskstream.com/Lesson/View/60B22EE3B5E7BB7EFC1577FA7772 5C05 Todays lesson definitely did not go as planned. When the students came in today, I realized that they had a lot more questions on the 4.3 homework than I anticipated. We spent about half the class going over several of the homework problems in great detail because I wanted to be sure they were comfortable with section 4.3 before we began reviewing for the Chapter 4 Test. Then I decided to do the Create-a-Function activity that I had planned. I asked students to find a partner, and then I had each pair draw several pieces of a function that they had to put togetherinto one large function, and then graph it. Overall, I was quite pleased with the results of this activity. I was able to walk around and help groups that were struggling, but most of the groups seemed to be doing fine. My only regret with this activity was that I wish we had time to repeat the activity several times so that each group had the opportunity to practice graphing several different types of functions. I have found that I really enjoy doing groupwork activities with this class because it allows them to open up a little more. Normally, they are so quiet and reserved that it is difficult for me to tell whether or not they understand the material. When they work in partners or small groups, I am actually able to do more formative assessment because they are all actively participating. It is also nice because they are a little more mature than my Geometry classes, so they can handle a less structured activity. Doing groupwork in my Geometry classes is always stressful for me because it seems to devolve into crowd-control. Unfortunately, we did not even have a chance to start on the Chapter 4 Review worksheet today, so I am going to have to spend another day reviewing before we take the Chapter 4 Test. I am willing to do this, though, if it means they will be more prepared for the test. 36. Garrou 47 Lesson 15 (Chapter 4 Test)https://w.taskstream.com/Lesson/View/25ACBC1E19F65B4BF6BF4344CCF727C 7 Today I gave my students the Chapter 4 Test, which means that we are officially finished with this unit. I have started grading the Chapter 4 Tests, and so far, the grades really are not bad. I have, however, been a little disappointed that so many students are missing parts of the last question. The last question of the test asks students to create a sine model for a set of periodic data. This is similar to the modeling activity that we did with the daylight hours, and there was also a very similar question on the Chapter 4 Review, which I went over in great detail yesterday. In myopinion, being able to apply their knowledge of periodic functions to create a model for a set of data is one of the most important and one of the most practical goals of this unit, so I am a little disappointed that my students do not seem to have mastered this skill. Other than the last question, most of the tests have been pretty good - not as good as the Chapter 3 Tests, but still not bad. There are a few students, however, who I can tell did not put forth their best effort in this chapter. These are the students who consistently fell asleep in class, did not do the homework, and did not pay attention when I went over example problems. I think there is a bit of senior-itis going around, and a few of my students seem to have caught it. What frustrates me is that I know they are very smart students and could do incredibly well in the class if they would just put forth a little bit of effort. I hope that they find the motivation they need to work harder and finish out the year strong. I have enjoyed teaching this unit, even though I know the students are ready to be finished with it. I feel as though I definitely underestimated the amount of time it would take to coverChapter 4, especially, but I am satisfied that I maintained high expectations for my students and covered the material in great detail. 37. Garrou 47Samples of Student Work 38. Garrou 47 39. Garrou 47 40. Garrou 47 41. Garrou 47 42. Garrou 47 43. Garrou 47 44. Garrou 47 45. Garrou 47 46. Garrou 47 47. Garrou 47 48. Garrou 47 49. Garrou 47 50. Garrou 48Appendices/ReferencesTextbook: Lial, M.L., Hornsby, J., Schneider, D.I. (2001). Trigonometry (7th Edition). Pearson-AddisonWesley.Website: Interactive Mathematics. http://www.intmath.com/**For all other appendices (worksheets, tests, etc.) see attached lesson plans in TaskStream. 51. Once the lessons within the TWS unit have been taught, and once the TWS is ready for submission for licensure purposes, it will be divided among two places (two different evidences): EE 3 Planning/Implementation Phase and EE5 Assessment/ Impact on Student Learning. You created the beginning of EE3 during your methods class, you finish EE3 and complete EE5 also once you have taught the lessons. To create the EE5, you will display and analyze the data from your pre and post tests/assessments and you will write a narrative about the results. You will include the same description of the setting (DOS) you used for EE3 because the same state reviewers who look at EE 3 may not also see EE5. Thus your EE5 will include the DOS to provide context. To see what an EE5 looks like as well as other evidences, go to the TWS Resource File on TaskStream at this URL: https://www.taskstream.com/ts/painter1/TWSResourceFile 52. Reminders Save your work several places! Check your lessons on TaskStream to be sure they are complete, have all attachments in their most current version, and that any links/URLs work. Proofread your document before submitting. Check all links to be sure they work and connect to the correct plan or place. Upload your TWS planning document before you come to the exam on Dec. 9, 2013 which starts at 8:00 a.m. in Rhyne 116.See you on Dec. 3 for our last class. Please complete the course evaluation online by the deadline. You should have received emails alerting you to the opening of that opportunity. Your feedback is important and valued.