Standard B

Delivers Effective Instruction

Lesson Plan: Perimeter (audio recorded)

Self Evaluation of Recorded Lesson

Student Work Samples Demonstrating Growth

o Student A

o Student B

Reflective Essay on Student Work Samples

Perimeter

Grade 4 Math

March 16, 2011 (Wednesday)

45 minutes 9:00 – 9:45

Massachusetts Curriculum Framework:

Mathematics – Measurement 4.M.4 Estimate and find area and perimeter of a rectangle, triangle, or

irregular 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 closed

shapes. Another goal is for students to recognize some real world examples of when perimeter can be

used.

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 shape

Instructional 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

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 textbooks

Assessment of Student Achievement:

In this lesson, I will assess what students already know by asking during the introduction if they

have ever heard of or used perimeter. I will also be able to assess what they already know by listening to

real life examples that they give.

During the lesson, I will be able to check for understanding by asking students not only what

they are getting for answers, but how they arrived at answers and what their strategy was. I will be able

to walk around the room and see what kind of work they are showing on their sheet to check if they are

understanding that to find perimeter you add all of the sides. I will know students are successful if they

are arriving at correct answers to the problems and are able to explain in words that perimeter means

the distance around a shape. They will demonstrate this understanding through verbal answering of

questions and written work on the sheet and textbook work.

Student Evaluation:

Student evaluation during this lesson is focused primarily on informal formative assessing. I will

evaluate students by checking on their progress and understanding to know whether I will be able to

move on to area or spend more time with perimeter first. Perimeter will be formally evaluated on future

quizzes and tests. I will also use the homework on perimeter to evaluate where students need more

help or if they are ready to move on.

Self Evaluation of Recorded Lesson - Perimeter

Having to listen to myself on audio tape was a scary assignment. I was afraid of what I

actually sound like in front of a class. However, listening to and reflecting on the lesson was an

incredibly valuable way to understand mistakes I made and where some of my strengths are. I

realized 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 are

already graded because quizzes are meant to be a learning experience. I did a good job at having

the students explain and elaborate on answers. I think this helped the students who may have

gotten something wrong but were not brave enough to ask for clarification in front of the whole

class. I then tell the students to put away the quiz to take home and put their folders back in their

desks. I realized that I have improved a bit on telling students exactly where to put things. This

was one of my weaker points when I first started the practicum. I assumed students were as

organized as I am.

I then begin the introduction of the main lesson. I ask the students if anyone has heard of

perimeter or knows anything about it. I do this on purpose to give myself an idea of what the

students already know. It is a quick informal assessment so that I know where my starting point

is. Most already have an awareness of what perimeter is. I then take some time to make real life

connections. I think this is so important because math should be taught in context. Students

should know why they are learning something and how it can be applied. The first student

example of where they think perimeter can be used is when measuring a fence. This is the perfect

perimeter example. I make it a point to emphasize what a great example this is. However, I then

start mentioning area and how sometimes it can be confused with perimeter. I should not have

even 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 is

another great real life example. The students then start to give examples that have to do with

rugs, sheds and tiles. I try to encourage their examples and show how they are important for

perimeter by stressing the word around, but I should have clarified that these examples may have

been better suited for area. A final great student example of perimeter is the border around the

bulletin board. I do a nice job of admitting my own mistake of not using perimeter to help me

plan to hang up the border. It is important for students to know everyone makes mistakes and

that is ok.

I then transition to using the overhead and a worksheet to try out some perimeter

problems. While listening through this part of the lesson, I realized that I use questioning

effectively to get at student thinking and understanding. For example, one thing I say is, “Why

wouldn’t it be a trapezoid?” I can hear myself thinking aloud, which is good modeling for

students. Other examples of questioning I use are: “What am I supposed to do with this grid to

find perimeter?” “Do I count this tiny part? Is that important? Did I get everything?” “Can I put

15 on the bottom of the rectangle? No? Why not? I think it could go there.” “45 feet is that my

perimeter? No? Why not? Why would I do that?”

Another effective strategy I heard myself using was not just telling students yes that’s the

answer and moving on. I search and probe for why that’s the answer. I poll students on what they

got for an answer and I then work out the problem to show strategies and demonstrate why an

answer 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? How

did you get there?” Through this polling of answers and checking strategies, I realize that the

students’ understanding is not great at this point so I do the problem together. “Let’s count

together and see what we get.” For another problem, I field the answers of 10, 13 and 14. I again

see that the understanding is not where it should be so I do the problem together as a class. I also

make it a point here to ask, “Do you see what you missed if you got 13?” This strategy is an

effective way to quickly informally assess students. I find this very useful and will continue to

utilize it.

After the problem with the varying answers of 10, 13 and 14, I do a good job of waiting

to clarify any confusion before moving on, however I make a mistake. I should have done

another similar problem to assess understanding again and reinforce how to do that type of

problem, but I move on to a different problem that uses perimeter to find missing sides of

polygons. I made this mistake because I was just following along with the worksheet. I should

have stepped away from the sheet and made up a similar problem to the one the students

struggled a bit with.

Another mistake I noticed while listening was that I may have moved too quickly from

just adding every single side to using multiplication to help with congruent sides. In my mind, it

should have been easy for students to see how multiplication and addition can be used together to

find perimeter. But, after listening to the lesson, I fear that I may have contributed to some of the

later confusion students had with area and perimeter by introducing multiplication here. It may

have been clearer for students to strictly equate perimeter with addition and area with

multiplication. During this lesson, students already began confusing perimeter and area and we

had not even tackled area yet. For example, at one point, Meghan announces she is confused on

something. I ask her to come up to the board and show me what she is confused about. She is

already doing area instead of perimeter. I then do a good job of refocusing as area begins

creeping 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 was

emphasizing that units are important. I do not let a student get away with an answer of just 26. I

ask 26 what to look for the unit of centimeters. However, one student suggests that perimeter is

measured in square units. I take what he says and keep going with it for a bit until I realize that

it’s wrong. I try to then direct the students to use just units and not units squared, but I can hear

the uncertainty in my voice because I did get slightly confused on it. I should have quickly

referenced 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 who

were with the math specialist come back into the classroom and I seamlessly integrate them back

in by asking a student to explain what we are doing, which was a nice review, and getting them

to the problem we were working on. I also think there is a good flow with asking various

students to participate and having them build on each others’ answers. For example, I first ask

Kate a question and when I see she is struggling, I ask Sean to build on what she said. This

builds a community of learners by helping students create knowledge together. I also do a nice

job of switching back and forth between whole class and independent work. I introduce some

problems together and then have students try some on their own, but then I bring it back to whole

class to check their understanding. I am able to answer their questions as the lesson goes and

tailor what I am saying and doing to what the students are asking and what I see they need

clarification on. I also try to keep a relaxed feel by saying things like “give everyone a second to

try” and “we’ll see if we can get through 10 and 11 before music.” Keeping the atmosphere

relaxed and flowing smoothly helps build a productive learning environment.

Reflective Essay: Student Work Samples

Following student work was a great opportunity to see progression and changes in

students in just a short amount of time. For this reflection, I choose to follow Reading work of

two students. One student (student A) was a struggling student. It was clear from the beginning

of my time in the classroom that this student was not always eager to pay attention or to give one

hundred percent effort. As I got to know the student, I became more aware that a lack of effort

may not be the only issue. This student needed more time than some to think and to arrive at

answers. 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 independently

and without much checking in from me. Student B would eagerly get right down to work on

whatever the task at hand was. At first, it seemed this student was always giving one hundred

percent effort. I choose these two students because I wanted to see how their different

approaches to learning were reflected in their work.

I tracked Student A’s progression through work with two novels that I taught. The first

sample is the student’s response to questions from Chapter 4 of Sadako and the Thousand Paper

Cranes. The student missed the mark on question four by just restating the question without

answering it. Getting question three wrong was a red flag to me that he did not understand what

happened in the chapter. Mitsue and Eiji were Sadako’s siblings and they were sad and upset

because Sadako was diagnosed with leukemia. Sadako getting sick was the major theme of the

novel, but he answered the question with a much less important detail from the chapter. After

correcting this work, I talked to the student and made him aware that he really needed to try to

focus 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 and

I saw that he was still making some small errors, but he seemed to be getting at the themes

better. By Chapter 6, the student’s answers were complete and thoughtful. This made me realize

that 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 telling

them three things they learned about their daughter and one lesson that she taught them. I was

expecting Student A’s work to be just as thoughtful as his last response to Chapter 6, however, as

the sample shows, his writing was disorganized and did not focus on the most important details

and themes of the novel. I was disappointed that the student’s progression did not continue. I

spoke with the student about the writing and it seemed as though he was just unfocused about it

and did not take the assignment seriously. I should have spent more time with this particular

student while planning the letter. It made me realize that seeing progression in a couple of pieces

of work does not mean the progression will automatically continue. It was clear this student

needed 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 the

novel, his answers were complete, insightful and focused. I made sure to tell the student how

proud of him I was and he was visibly proud of himself for his effort. I believe that after the

student’s work with Sadako he realized he needed to approach this novel with a more serious

attitude. I checked in with him more often while he was working and helped him to organize

some of his thoughts. I also believe the student did well with this work because many of the

questions asked for personal connections and opinions. This helped the student make sense of the

novel. I learned that students approach literature differently and taking a personal approach may

be helpful for some. I was proud that I was able to help this student work towards such a great

grade and understanding. The last sample from Student A is the test from Pearl Harbor is

Burning, which solidified for me that he truly had made progress.

Student B was an excellent student throughout my practicum time. I always expected his

work to be well done. However, his first sample shows that even an excellent student sometimes

loses focus and motivation. His answers are not written in complete sentences, which all students

knew was the expectation, and he made a very weak connection in question one. This page was

part of the packet that the students completed while reading Pearl Harbor is Burning. The next

sample is another page from the packet where the student demonstrates his usual complete

sentences and focused answers. The student’s growth with these two samples is mainly a

function of his own self motivation. I made it clear to the students that I would be grading the

packet at the end of the novel and I expected that all answers be well thought out and written

completely. This student was able to self correct by knowing expectations. The next samples are

a 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. It

was effective to ask the students to first do a web. Even though this student is very capable, I

know the paragraph would not have turned out as organized without the use of the web. Using

graphic organizers and webs is something that I will continue to do in my teaching. The last

sample 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 higher

level. However, I think it is important to acknowledge that students will not always be at one

hundred percent at all times, as Student B demonstrated in the first sample. It is also important to

challenge students who are already at a higher level. There is always room for growth. As I

reflect 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 that

using novels to teach reading is an excellent way to differentiate because there are various points

of entry for students. For the students such as Student B, I could have challenged them with

questions that asked for deeper connections and interpretations of the novels. For students such

as Student A, I could have used more of the personal connection questions to then build up to

text comprehension questions. Following these two students showed me the importance of

effective instruction being tailored to student needs.