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- 1. Standard B Delivers Effective InstructionLesson Plan: Perimeter (audio recorded)Self Evaluation of Recorded LessonStudent Work Samples Demonstrating Growth o Student A o Student BReflective Essay on Student Work Samples
- 2. PerimeterGrade 4 MathMarch 16, 2011 (Wednesday)45 minutes 9:00 – 9:45Massachusetts Curriculum Framework:Mathematics – Measurement 4.M.4 Estimate and find area and perimeter of a rectangle, triangle, orirregular shape using diagrams, models and grids or by measuring.Objective:The goal of this lesson is for students to understand how to define and calculate perimeter of closedshapes. Another goal is for students to recognize some real world examples of when perimeter can beused.Expected Student Outcomes:At the completion of this lesson, students will be able to: Define that perimeter is the distance around a shape Calculate perimeter of polygons and irregular shapes Use perimeter to calculate the measure of a missing side of a shapeInstructional Procedures: I will introduce the topic of perimeter by asking students if they have ever heard the word or worked with perimeter. I will use what they say to build the definition of perimeter as the distance around a shape. I will then ask students if they can think of any real world examples where perimeter may be used. I will then hand out sheet Practice 20.4 to each student and set up the overhead projector to complete the sheet together as a class. I will use whole class discussion to arrive at answers and look at strategies while I fill everything in on the transparency of Practice 20.4. After doing a few problems together as a class, I will give students a few minutes to try some out on their own. I will bring the discussion back to whole class to check on progress and field answers. If there is time, students will practice problems independently from the textbook
- 3. The students will then break for music. After music, I will pick up wherever was left off and hand out homework (Lesson 28.2 sheet)Materials and Resources: Copy of Practice 20.4 sheet for each student Transparency of 20.4 and overhead projector Math textbooksAssessment of Student Achievement: In this lesson, I will assess what students already know by asking during the introduction if theyhave ever heard of or used perimeter. I will also be able to assess what they already know by listening toreal life examples that they give. During the lesson, I will be able to check for understanding by asking students not only whatthey are getting for answers, but how they arrived at answers and what their strategy was. I will be ableto walk around the room and see what kind of work they are showing on their sheet to check if they areunderstanding that to find perimeter you add all of the sides. I will know students are successful if theyare arriving at correct answers to the problems and are able to explain in words that perimeter meansthe distance around a shape. They will demonstrate this understanding through verbal answering ofquestions and written work on the sheet and textbook work.Student Evaluation: Student evaluation during this lesson is focused primarily on informal formative assessing. I willevaluate students by checking on their progress and understanding to know whether I will be able tomove on to area or spend more time with perimeter first. Perimeter will be formally evaluated on futurequizzes and tests. I will also use the homework on perimeter to evaluate where students need morehelp or if they are ready to move on.
- 4. Self Evaluation of Recorded Lesson - Perimeter Having to listen to myself on audio tape was a scary assignment. I was afraid of what Iactually sound like in front of a class. However, listening to and reflecting on the lesson was anincredibly valuable way to understand mistakes I made and where some of my strengths are. Irealized a few things that I would never had if I had not listened to myself teach. The recording begins with a review of a quiz on similarity, lines of symmetry, and turns,slides and reflections. I think it is important to sometimes review quizzes even though they arealready graded because quizzes are meant to be a learning experience. I did a good job at havingthe students explain and elaborate on answers. I think this helped the students who may havegotten something wrong but were not brave enough to ask for clarification in front of the wholeclass. I then tell the students to put away the quiz to take home and put their folders back in theirdesks. I realized that I have improved a bit on telling students exactly where to put things. Thiswas one of my weaker points when I first started the practicum. I assumed students were asorganized as I am. I then begin the introduction of the main lesson. I ask the students if anyone has heard ofperimeter or knows anything about it. I do this on purpose to give myself an idea of what thestudents already know. It is a quick informal assessment so that I know where my starting pointis. Most already have an awareness of what perimeter is. I then take some time to make real lifeconnections. I think this is so important because math should be taught in context. Studentsshould know why they are learning something and how it can be applied. The first studentexample of where they think perimeter can be used is when measuring a fence. This is the perfectperimeter example. I make it a point to emphasize what a great example this is. However, I thenstart mentioning area and how sometimes it can be confused with perimeter. I should not haveeven mentioned area yet, because I am already putting the idea of confusion in their heads.Another student mentions an example of her father using perimeter in construction. This isanother great real life example. The students then start to give examples that have to do withrugs, sheds and tiles. I try to encourage their examples and show how they are important forperimeter by stressing the word around, but I should have clarified that these examples may havebeen better suited for area. A final great student example of perimeter is the border around thebulletin board. I do a nice job of admitting my own mistake of not using perimeter to help me
- 5. plan to hang up the border. It is important for students to know everyone makes mistakes andthat is ok. I then transition to using the overhead and a worksheet to try out some perimeterproblems. While listening through this part of the lesson, I realized that I use questioningeffectively to get at student thinking and understanding. For example, one thing I say is, “Whywouldn’t it be a trapezoid?” I can hear myself thinking aloud, which is good modeling forstudents. Other examples of questioning I use are: “What am I supposed to do with this grid tofind perimeter?” “Do I count this tiny part? Is that important? Did I get everything?” “Can I put15 on the bottom of the rectangle? No? Why not? I think it could go there.” “45 feet is that myperimeter? No? Why not? Why would I do that?” Another effective strategy I heard myself using was not just telling students yes that’s theanswer and moving on. I search and probe for why that’s the answer. I poll students on what theygot for an answer and I then work out the problem to show strategies and demonstrate why ananswer is correct. For example, for one problem I field through the answers of 55, 40, and 30.“Did anyone else get 55? Who else got 30?” I then check for strategies. “What did you do? Howdid you get there?” Through this polling of answers and checking strategies, I realize that thestudents’ understanding is not great at this point so I do the problem together. “Let’s counttogether and see what we get.” For another problem, I field the answers of 10, 13 and 14. I againsee that the understanding is not where it should be so I do the problem together as a class. I alsomake it a point here to ask, “Do you see what you missed if you got 13?” This strategy is aneffective way to quickly informally assess students. I find this very useful and will continue toutilize it. After the problem with the varying answers of 10, 13 and 14, I do a good job of waitingto clarify any confusion before moving on, however I make a mistake. I should have doneanother similar problem to assess understanding again and reinforce how to do that type ofproblem, but I move on to a different problem that uses perimeter to find missing sides ofpolygons. I made this mistake because I was just following along with the worksheet. I shouldhave stepped away from the sheet and made up a similar problem to the one the studentsstruggled a bit with. Another mistake I noticed while listening was that I may have moved too quickly fromjust adding every single side to using multiplication to help with congruent sides. In my mind, it
- 6. should have been easy for students to see how multiplication and addition can be used together tofind perimeter. But, after listening to the lesson, I fear that I may have contributed to some of thelater confusion students had with area and perimeter by introducing multiplication here. It mayhave been clearer for students to strictly equate perimeter with addition and area withmultiplication. During this lesson, students already began confusing perimeter and area and wehad not even tackled area yet. For example, at one point, Meghan announces she is confused onsomething. I ask her to come up to the board and show me what she is confused about. She isalready doing area instead of perimeter. I then do a good job of refocusing as area beginscreeping in by asking, “What’s perimeter again?” and stressing that it means around the figure. Something about perimeter that I noticed I did well, but also made a mistake on wasemphasizing that units are important. I do not let a student get away with an answer of just 26. Iask 26 what to look for the unit of centimeters. However, one student suggests that perimeter ismeasured in square units. I take what he says and keep going with it for a bit until I realize thatit’s wrong. I try to then direct the students to use just units and not units squared, but I can hearthe uncertainty in my voice because I did get slightly confused on it. I should have quicklyreferenced the textbook to be confident and clear about it. Overall, I feel that there is a very good flow to the lesson. At one point, students whowere with the math specialist come back into the classroom and I seamlessly integrate them backin by asking a student to explain what we are doing, which was a nice review, and getting themto the problem we were working on. I also think there is a good flow with asking variousstudents to participate and having them build on each others’ answers. For example, I first askKate a question and when I see she is struggling, I ask Sean to build on what she said. Thisbuilds a community of learners by helping students create knowledge together. I also do a nicejob of switching back and forth between whole class and independent work. I introduce someproblems together and then have students try some on their own, but then I bring it back to wholeclass to check their understanding. I am able to answer their questions as the lesson goes andtailor what I am saying and doing to what the students are asking and what I see they needclarification on. I also try to keep a relaxed feel by saying things like “give everyone a second totry” and “we’ll see if we can get through 10 and 11 before music.” Keeping the atmosphererelaxed and flowing smoothly helps build a productive learning environment.
- 7. Reflective Essay: Student Work Samples Following student work was a great opportunity to see progression and changes instudents in just a short amount of time. For this reflection, I choose to follow Reading work oftwo students. One student (student A) was a struggling student. It was clear from the beginningof my time in the classroom that this student was not always eager to pay attention or to give onehundred percent effort. As I got to know the student, I became more aware that a lack of effortmay not be the only issue. This student needed more time than some to think and to arrive atanswers. This student also needed some reminders to stay on task and to focus in on the work.Student B however was the opposite. This student was someone who worked well independentlyand without much checking in from me. Student B would eagerly get right down to work onwhatever the task at hand was. At first, it seemed this student was always giving one hundredpercent effort. I choose these two students because I wanted to see how their differentapproaches to learning were reflected in their work. I tracked Student A’s progression through work with two novels that I taught. The firstsample is the student’s response to questions from Chapter 4 of Sadako and the Thousand PaperCranes. The student missed the mark on question four by just restating the question withoutanswering it. Getting question three wrong was a red flag to me that he did not understand whathappened in the chapter. Mitsue and Eiji were Sadako’s siblings and they were sad and upsetbecause Sadako was diagnosed with leukemia. Sadako getting sick was the major theme of thenovel, but he answered the question with a much less important detail from the chapter. Aftercorrecting this work, I talked to the student and made him aware that he really needed to try tofocus in on what was most important in the novel. The chapter five questions were self corrected.The student marked all of his answers with a great big C for correct. I asked him to look at it andI saw that he was still making some small errors, but he seemed to be getting at the themesbetter. By Chapter 6, the student’s answers were complete and thoughtful. This made me realizethat the student needed some time to work with the novel and digest all of the themes and ideas.After the novel was completed, I asked the students to write a letter to Sadako’s parents tellingthem three things they learned about their daughter and one lesson that she taught them. I wasexpecting Student A’s work to be just as thoughtful as his last response to Chapter 6, however, asthe sample shows, his writing was disorganized and did not focus on the most important detailsand themes of the novel. I was disappointed that the student’s progression did not continue. I
- 8. spoke with the student about the writing and it seemed as though he was just unfocused about itand did not take the assignment seriously. I should have spent more time with this particularstudent while planning the letter. It made me realize that seeing progression in a couple of piecesof work does not mean the progression will automatically continue. It was clear this studentneeded more help with focusing and planning. The next sample from Student A is a packet of work from the second novel I taught,Pearl Harbor is Burning. This time, the student received an A+ for the work. Throughout thenovel, his answers were complete, insightful and focused. I made sure to tell the student howproud of him I was and he was visibly proud of himself for his effort. I believe that after thestudent’s work with Sadako he realized he needed to approach this novel with a more seriousattitude. I checked in with him more often while he was working and helped him to organizesome of his thoughts. I also believe the student did well with this work because many of thequestions asked for personal connections and opinions. This helped the student make sense of thenovel. I learned that students approach literature differently and taking a personal approach maybe helpful for some. I was proud that I was able to help this student work towards such a greatgrade and understanding. The last sample from Student A is the test from Pearl Harbor isBurning, which solidified for me that he truly had made progress. Student B was an excellent student throughout my practicum time. I always expected hiswork to be well done. However, his first sample shows that even an excellent student sometimesloses focus and motivation. His answers are not written in complete sentences, which all studentsknew was the expectation, and he made a very weak connection in question one. This page waspart of the packet that the students completed while reading Pearl Harbor is Burning. The nextsample is another page from the packet where the student demonstrates his usual completesentences and focused answers. The student’s growth with these two samples is mainly afunction of his own self motivation. I made it clear to the students that I would be grading thepacket at the end of the novel and I expected that all answers be well thought out and writtencompletely. This student was able to self correct by knowing expectations. The next samples area graphic organizer and a paragraph that is well organized and planned. In contrast to Student A,this student understands how to organize ideas and how to include the most important details. Itwas effective to ask the students to first do a web. Even though this student is very capable, Iknow the paragraph would not have turned out as organized without the use of the web. Using
- 9. graphic organizers and webs is something that I will continue to do in my teaching. The lastsample is Student B’s Pearl Harbor is Burning Test where I did not take points off anywhere.The student demonstrated that he understood the text. Student B shows less significant growth than Student A because he is already at a higherlevel. However, I think it is important to acknowledge that students will not always be at onehundred percent at all times, as Student B demonstrated in the first sample. It is also important tochallenge students who are already at a higher level. There is always room for growth. As Ireflect back on these work samples, I would have liked to have differentiated the questions more.Each student answered the same questions, regardless of what level they were at. I realized thatusing novels to teach reading is an excellent way to differentiate because there are various pointsof entry for students. For the students such as Student B, I could have challenged them withquestions that asked for deeper connections and interpretations of the novels. For students suchas Student A, I could have used more of the personal connection questions to then build up totext comprehension questions. Following these two students showed me the importance ofeffective instruction being tailored to student needs.

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