Emily Miller Longwood University Cumberland Partnership ... · Emily Miller Longwood University Cumberland Partnership Fall 2013 Dr. Horne Teacher Work Sample . 2 Introduction This

Emily Miller

Longwood University

Cumberland Partnership

Fall 2013

Dr. Horne

Teacher Work Sample

2

Introduction

This document is a sample of my work as a teacher candidate. My partnership placement was

with Cumberland Elementary School in Cumberland, Virginia and I had the pleasure of being placed in a

third grade classroom. The classrooms in this elementary school are created based on the achievement

level of the students in my class consisted of the higher level learners. My two week unit focuses on

fractions and because my students are higher level learners, my lessons take them through all levels of

blooms. This also allowed me to introduce multiple concepts relating to fractions such as mixed

numbers, improper fractions, and equivalent fractions.

A major theme in this unit is real world applications. The students see and use fractions in their

everyday life from the half of an apple they receive with their lunch to the class being broken up into

three reading groups. It was my goal to open the student’s eyes to the fractions that they see in their

lives to reinforce what they are learning in math class. Through my observation, I have seen the

students ask why they needed to know something and the teachers reply that it will be on the SOL or on

the test at the end of the week. The students become discouraged and disinterested in learning when

the only reason they need to know it is to pass a test. A majority of my instructional decision made

throughout the course of this unit was to show the students that fractions are more important than just

getting a good grade.

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Table of Contents

Developmental Considerations………………………………………………………………………………………..

Assessments………………………………………………………………………………………………………………………

Unit of Instruction…………………………………………………………………………………………………………….

Data Tables………………………………………………………………………………………………………………………

Summation of Data Tables…………………………………………………………………………………………………

Reflection………………………………………………………………………………………………………………………….

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Contextual Factors

Cumberland Elementary School is the only elementary school in Cumberland, Va. In order to

understand more about the students in my classroom, it is important to understand the community that

they come from. In order to do this, I will focus on Cumberland as a whole and progressively narrow my

research until I am looking at the individual characteristics of the students in my room.

According to the 2012 census, Cumberland County is home to 9,849 residents, 64% of which are

white, 33% are black, and 3% are Hispanic, Asian, American Indian, or Pacific Islander. 5.8% of the

people in Cumberland speak a language other than English at home and only 1.3% were born in a

foreign country. Educationally, 77% of the people in Cumberland ages 25 and up have a high school

diploma, but only 14% have a bachelor’s degree. The median income of this community is $45,184 and

15.2% of the residents below poverty level. Although the superintendent of Cumberland County Public

School, Dr. Griffin, told us that the Cumberland school system is the major employer in the county, a

very low percentage of the teachers in those schools actually live in Cumberland. My mentor teacher

told me that the majority of students’ parents are employed by fast food restaurants in the surrounding

counties, especially the Town of Farmville.

Cumberland County Schools is starting a new project based learning initiative. All the teachers

are going through professional development to be trained in this new instructional technique that

allows the students to work together and find the answers to their own questions as opposed to

traditional direct instruction. The school board also works diligently to receive funds from the

government to finance large scale project based learning assignments such as the solar powered energy

project at the high school. Because Cumberland is a community of low socioeconomic status, the

passionate and dedicated professionals in the school board have completely changed the potential for

education in Cumberland.

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According to greatschools.net, Cumberland Elementary has 587 students in pk-4th grade with a

demographic of 50% white, 45%black, and 5% other. Of these students, 62% are on free and reduced

lunch. The climate and culture of the school reflects a safe and student entered environment. There

are new safety measures in place such as the double doors in the main lobby that require a visitor to

enter through the office in order to get inside the school. Every classroom is automatically locked when

the door closes making it easier to protect the students and teachers are trained on what to do in a

variety of emergencies such as weather, fire, and intruder. The school is welcoming and engaging as

demonstrated by the pencil columns lining the hall, and vibrant murals in the pods. This also reflects the

parent involvement because it is a parent group that has so painstakingly painted these murals for their

students.

The Cumberland County Schools mission statement is “student centered, teacher inspired”

which reflects their student centered approach to teaching especially their initiative to start project

based learning. Although this is the mission statement and initiative from the school board, the student

centered approach has not fully trickled down to the teachers in the schools. A lot of the instruction I

have observed has been worksheet and direct instruction based with little scaffolding and support. The

teachers are currently going through professional development so hopefully there will be more evidence

of student based approaches in the classrooms soon.

When you walk into my placement classroom, it looks like a friendly student centered room.

The class rules and behavior management system are clearly displayed on the board, but the daily

schedule is posted on a piece of computer paper behind the teacher’s desk. The student desks are

arranged in two groups of seven and one group of six to accommodate the 20 students. This desk

arrangement will facilitate small group work and collaboration between students. The desks are

arranged around a carpet area in front of the promethean board to allow for whole group instruction.

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There are also areas around the room dedicated to science and language arts work stations. The third

grade is departmentalized and while my teacher teaches language arts and science, her partner teacher

teaches math and social studies. The students move between the classrooms throughout the day. The

school also separated the students based on ability to further differentiate instruction. The higher level

learns are in my teacher’s homeroom, while the lower level learners and special education students are

in her partner teacher’s homeroom.

The students in my class are ages 8-9 and are all the higher level learners between the two

classes. The students, with a few exceptions, are on grade level in reading and from what I have

observed in math they are also on grade level, but seem to be struggling with place value and number

sense. They are doing what the teacher asks them to do and receiving good grades for it, but I believe

the instruction could be stronger to reinforce important math concepts and not the importance of

finishing a worksheet. They are all English speakers and there are no students with disabilities in the

class. There is one student in the class with an IEP that I do not have permission to access, but the

special education teacher told me that it is not learning or behavioral based so his IEP will not be

impacted by my instruction. A few of the students are in a karate class taught by my teacher and they

enjoy playing organized games at recess. They also enjoy video games and when I ask what they are

going to do over the weekend a lot of them talk about the games they are going to play.

Knowing information about the community my students are a part of will definitely impact my

instruction. I know that these students come from low income homes so I must ensure that every

student has the material they would need for the day even if that means buying it myself. The

superintendent talked to us about how important it is to take these kids on field trips because they do

not have very many opportunities to get out of Cumberland County. I also really like how they offer

breakfast everyday which gives students with free or reduced lunch an opportunity to eat in the

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morning. I have noticed that the students are generally really well behaved and I definitely think it has

something to do with the fact that they are all eating breakfast. The classrooms have a lot of technology

for a school in a low income area, but that is where the dedication of the school board comes in and

because of their dedication these students have access to technology in the classroom. When I teach

my unit knowing this background information on my students will help me tailor my instruction to

meeting their needs, interest, and prior knowledge.

References

http://quickfacts.census.gov/qfd/states/51/51049.html

www.greatschools.net

http://quickfacts.census.gov/qfd/states/51/51049.html

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Developmental Considerations

The students in my partnership class are in the 3rd grade ages 8-9. It is common knowledge that

the 3rd grade is a defining year cognitively for children. National Public Radio describes the importance

of the 3rd grade in an episode titled Third Grade a Pivotal Time in Students Lives which aired on May 14,

2012. Host Neal Conan explains “The age of eight or nine, when kids complete third grade, represents a

key turning point. Up until then, children are learning to read. Afterwards, they read to learn” (2012).

Conan continues to discuss the issue throughout the program, but the most profound information

comes from Tim Taylor, president of a Colorado Succeeds, who stated the following:

If you’re unable to read coming out of the third grade, and in fourth grade, we no longer teach

reading in U.S. public schools, the kids can’t read a math problem. They can’t read instructions

on a science experiment, the teachers’ notes on a white board. Their odds of success are so low

at that point. We know that 90% of high school drop outs did not read on the third-grade level,

and it’s one of the strongest predictors of high school graduation success. (2012)

It is especially important for a teacher to understand where her students are developmentally this year

because it is so pivotal.

According to Ryan, Cooper, and Tauer in Teaching for Student Learning (2013), Piaget states that

my students are in the concrete operational stage of their cognitive development. Piaget explains that

children in this stage are becoming logical thinkers. Although these children are becoming more logical

in their thought processes, they still require concrete examples such as physical object. They are less

egocentric and able to see and understand something from another person’s point of view (p.72-73).

This is already apparent with the 3rd graders in my classroom. They are definitely more aware of

their surroundings by becoming involved in class conflicts that do not involve them and telling each

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other what they should be doing. In the reading lessons led by my mentor teacher, the students are

asked to think about the book from the character’s point of view. They are also asked to reason why a

character would feel that way and how we, as readers, can determine what they are feeling based on

description. Knowing that my students are in the concrete operational stage will guide my instruction

by ensuring that my students have access to physical representations of the material and manipulatives.

They are capable of logical thought but they need physical representations, so my manipulatives will

encourage the logical and critical thinking in my lessons as opposed to memorization.

Vygotsky’s Zone of Proximal Development is important to consider with any age group including

the 3rd graders in my class. Vygotsky explains that a child learns best in their instructional level with

support from peers and instructors. The Zone of Proximal Development is synonymous with scaffolding.

This is applicable to all ages in all areas of study because if a child is working within their independent

level they will be more successful than if they are not challenged in their independent level or struggling

in their frustration level (Ryan, Cooper & Tauer, 2013, p.73-74).

These theories need to be used together in order to create a balanced and appropriately

challenging learning environment. The teacher needs to understand where the students are in their

cognitive development in order to create appropriate assignments. Instructional needs to meet each

child on their instructional level within his/her zone of proximal development. It is within the zone that

they learn new material and once they understand it they are able to work independently.

Traditional views on intelligence state that people are born with a certain amount of intelligence

and that is why there are different levels of learners in classrooms. Contemporary views on intelligence

disagree by saying that everyone has the potential for higher levels of intelligence, it is just a matter of

having high expectations for each student. This relates back to my classroom by encouraging

differentiated instruction to meet each student on their instructional level so they are able to learn and

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improve. If a student is struggling, they will only continue to struggle if they are never met on their

level. Some students receive more support at home than others so it is important as the teacher to

ensure that everyone is getting the support that they need to succeed while at school. This is especially

important for my 3rd graders because if they are struggling now they will only continue to struggle as

they get older because they are no longer learning to read, they are reading to learn. Someone with a

traditional view on intelligence would just think that student is not very “smart”, but someone with a

contemporary view would recognize that this student simply needs more support and she will be able to

reach the level of her peers.

Students in the 3rd grade are becoming more aware of themselves and their surroundings. Boys

are girls, who once played together, begin to separate on the playground and recognize that there are

differences between the sexes. They begin to see each other in new ways and may develop “crushes”

on each other. This is especially apparent in my classroom where the students tell me about which

students like the other ones and how pretty my fellow partnership students are. They are also more

aware of their own bodies and may become shyer in class than they were in previous years and less

willing to offer answers to questions.

There is little diversity in this classroom. My students are mainly Black and White, but the

students have reached a socio emotional developmental stage in which they have noticed a difference

in skin color. When asked to sort each other into categories for a science lesson, my students chose to

categorize themselves into “White”, “Black”, and “Mixed”. No one was offended by the categorization,

but they all recognized how they could divide themselves.

Students in the 3rd grade are able and expected to regulate their emotions. When they are

making poor choices they are asked to change their card to promote the self-regulation. Students are

able to control their emotions and express them to peers and adults. This relates to behavior theories

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and best practices of behavior management. Although I agree with expecting students to regulate their

emotions, I do not agree with the behavior management system currently in place in my classroom. The

students are asked to change their color when they are misbehaving, but they are not given any

opportunities to correct their behavior and move their color back up. The purpose of the color reward

system is to encourage students to be aware of their behavior and make good choices, but it is

ineffective when students cannot correct their mistakes.

This behavior management system directly relates to behaviorist theories. The color system is

operant conditioning in which teachers are encouraging students to learn from their behaviors based on

the response they receive. B.F. Skinner explained in his operant conditioning theory that there are both

positive and negative reinforcements in order to modify a behavior (p. 70). In my classroom, the color

system is wholly negative where students are only able to move down and not up. The teachers should

instead focus on positive reinforcement to reinforce the desired behaviors instead of punishing the

undesired behaviors.

Incorporating the cognitive, behavior, and social development of students into the classroom

environment and lessons will make the learning more relatable and effective to the students. After

researching where my students are in their development, I understand where they are developmentally

and I will be able to better tailor my instruction to meet their needs.

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References

Conan, N. (Host) (2012). Third grade a pivotal time in students' lives [Web series episode]. In Talk of the

nation. Washington D.C.: National public radio. Retrieved from

http://www.npr.org/2012/05/14/152683322/third-grade-a-pivotal-time-in-students-lives

Ryan, K., Cooper, J., & Tauer, S. (2013). Teaching for student learning: Becoming a master

teacher. (2nd ed.). Belmont, CA: Wadsworth.

http://www.npr.org/2012/05/14/152683322/third-grade-a-pivotal-time-in-students-lives

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Assessments

Summative Assessment

Pre-Assessment

6 Multiple Choice (5pts each)

4 Matching (5pts)

10 Fill in the Blanks (5 pts each)

Post-Assessment

6 Multiple Choice (5pts each)

4 Matching (5pts)

10 Fill in the Blanks (5 pts each)

1 Model (bonus:5 pts)

*80% or higher will indicate mastery for each learning goal

Narration on Formative Assessments

The first learning goal in the unit is “The students will be able to define fraction, numerator and

denominator.” I will assess this goal formatively through a classroom activity in which students will be

walking around the room and writing what they know, what they want to know, and what they are

confused about fractions on large pieces of poster paper. The students will complete this activity

independently, but they will then work in small groups to discuss fractions and will have the opportunity

to return to the poster paper to write anything new that they learned. This will give me the opportunity

not only to assess what they know through listening to their conversations, I will be able to see what

they are writing on the poster papers. This will guide my instruction not only by showing me what they

already know, but what they want to know and what questions they have.

The second learning goal is “the students will be able to identify ½, 1/3, ¼, 1/8, 1/10, and 1/12

fractions in relation to 1.” While teaching this learning goal I will formally assess the students by walking

around the room and listening to conversations as the students construct a fraction foldable. The

students will then work in pairs to complete an identification activity where I will give the students

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manupulatives of fractions and they will identify the fraction. This will have a corresponding graphic

organizer that I can use to assess the students in addition to listening to their conversations as they

work.

The third learning goal is “the students will be able to illustrate models of fractions.” While

teaching this learning goal, the students will be given a handful of fritloops. The students will work

individually to sort and draw illustrations of fractions to show the different colors. I will be able to use

these posters as a formative assessment. The students will then be asked to create their own

illustration independently that I will use as a formative assessment to ensure that each student is where

I want them to be.

The fourth learning goal “students will be able to compare like and unlike fractions.” After

teaching the unit the students will participate in a whole group activity and individual practice. The

main form of formative assessment will come from an exit card in which the student will answer 2

questions. One will be a content question and the other will ask what they still find confusing. I am

chosing to do this right before addressing my last learning goal because for my last learning goal I am

asking them to go higher in Blooms than is called for in the SOL. Therefore, I want to make sure to

address any holes in understanding of the material mandated by the SOL before I move on.

The fifth learning goal is “the students will be able to arrange fractions in order of size.” For this

learning goal , we will complete a whole group activity in which students will be given a fraction and

they have to work together to order themselves based on size. This activity will serve as practice for an

activity that the students will complete individually. The individual assignment in which students are

asked to order fractions will serve as a final formative assessment before the test so it will cover a little

of everything they have learned so far. This will provide me with one more opportunity to fill any holes

in understanding before the assessment.

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The sixth learning goal is “students will be able to convert improper fractions to mixed

numbers”. For this learning goal the students will work with pattern blocks to manipulate whole, mixed

numbers, and improper fractions. They will also chorally respond with white boards when given a

picture of a fraction on the board. This will allow me to model and formally assess their identification of

mixed numbers and improper fractions. Individually the students will work on an assignment in which

they will label and color different mixed numbers and improper fractions. This will allow me time to walk

around and conference with students who are having difficulty understanding the concept.

The seventh learning goal is “students will be able to identify fractions on a number line.” For

this learning goal the students will use their knowledge of mixed numbers to identify measurements on

a ruler. They will then work in pairs to place measurements on the ruler. Students will work in a small

group with me to indentify measurements on a ruler including ½ and ¼ inches and measuring objects in

the classroom. Working in a small group will allow me to differentiate instruction and offer more one-

on-one support to students.

Assessment Table #2

Learning Goal Assessments Form of Assessments Adaptations

1: The students will be able to define

“fraction”, “numerator” and “denominator”

Pre-assessment

Formative assessments

Post-assessments

3 Multiple Choice (5 pts)

Class work -Discussion

-Group Activity in which they answer question

on poster board


2: The students will be able to identify ½, 1/3, ¼, 1/8, 1/10, and 1/12 fractions in relation to 1

Pre-assessment



4 Matching (5pts)

Class work

16

Post-assessments

-Discussion -construction and

application of a fraction foldable

3 Multiple Choice(5pts) 4 Matching(5pts)

3: The students will be able to illustrate models of fractions

Pre-assessment


Post-assessments

1 Fill in the Blank (5pts)


-Partner Fruit loop illustration activity

-Individual illustration

1 Fill in the Blank(5pts) 1 Model (5pts)

4: Students will be able to compare like and

unlike fractions

Pre-assessment


Post-assessments

3 Fill in the Blank(5pts)

Class work -Discussion - Exit Card


5: The students will be able to arrange

fractions in order of size

Pre-assessment


Post-assessments



-Group Activity in which students are given fractions and

asked to arrange themselves in order -Individual activity

where students order fractions


6. Students will be able to convert improper fractions to mixed

numbers

Pre-assessment


2 fill in the blanks (5 pts)

White boards

Worksheet

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Post-assessments

Pattern blocks 2 fill in the blanks (5

pts)

7. Students will be able to identify fractions on

a number line

Pre-assessment


Post-assessments


-discussion

-group stick note activity

-measurement activity


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What I Already Know About Fractions (Pre-assessment)

Name____________________________________

Multiple Choice Please circle the best answer. Each question is worth 5 points.

1. 1 is called a 2

a. Fraction b. Whole Number c. Numerator 2. This number is called a

1 4 a. Numerator b. Denominator c. Top Number 3. This number is called a

1 4 a. Numerator b. Denominator c. Bottom Number 4. If I have 12 pieces of candy and I eat 3, I will have eaten _____ of my total pieces of candy

a. 1 b. 1 c. 1 2 4

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5. If I have 4 grapes and I lose one, how many of my total number of grapes would I have left?

a. 1/2 b. 3/4 c. 1/8 6. I have 3 dogs. One of my dogs has spots. Out of all my dogs, how many of them have spots?

a. ½ b. 1/3 c. 1/12 Matching Please draw a line to match the picture with the correct fraction. Each is worth 5 points.

7. 8. 9. 10.

1/8

1/10

1/2

1

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Fill in the blank. Please write your answer on the line. Each question is worth 5 points. 11. What fraction of the shapes are moons?

___________________________ 12. Which fraction is larger?

1 1 ___________________ 2 8

13. Which fraction is the same as one half?

4 3 8 4 14. Which fraction is smaller?

1 1 3 12

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15. Please arrange the fraction from smallest to largest.

1 1 1 12 2 3 16. Please arrange the fractions from largest to smallest.

1 1 1 8 4 10

17. How do you write 5 as a mixed number?

3 18. How many slices of pizza are in 3⅓ pizzas? (Use the space below to draw a picture if you want to) ____________________

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19. How long is the pumpkin?

__________________________

20. How long is the piece of candy?

__________________________

http://www.google.com/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&docid=WOVLchWr_wT4OM&tbnid=NtfVRpD92qWoyM:&ved=0CAUQjRw&url=http://swittersb.wordpress.com/2009/12/06/fly-tying-sizing-mm-to-inches-fly-size-and-bead-size/&ei=dBJfUrqtCIPO9QTZg4H4Ag&bvm=bv.54176721,d.eWU&psig=AFQjCNF6cnpZp75KOCZurDtcrWdZu2ECVA&ust=1382048724423550


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What I Know About Fractions (Post-Assessment)

Name____________________________________

*remember to draw any pictures that will help you.

Multiple Choice.

Please circle the best answer. Each question is worth 5 points.

1. A ______ is a part of a whole

a. Fraction b. Whole Number c. Numerator

2. I have 4 shapes. ¼ of my shapes are triangles. Which number is in the

numerator spot?

a. 1 b. 3 c. 4 3. I have 4 shapes. ¼ of my shapes are triangles. Which number is in the denominator spot?

a. 1 b. 3 c. 4 4. If I have 12 pieces of candy and I eat 3 pieces, I will have eaten _____ of my total pieces of candy

a. 1/12 b. 3/12 c. 1/10

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5. For lunch I have a sandwich. I cut my sandwich in 2 pieces and ate 1 piece. How much of my total sandwich did I eat?

a. 1/2 b. 1/4 c. 1/8 6. I have 8 cats. 2 of my cats are boys. What fraction of my cats are boys?

a. 1/2 b. 2/8 c. 1/8

Matching Please draw a line to match the picture with the correct fraction. Each is worth 5 points.

7. 8. 9. 10.

1

1/8

1/3

1/4

Fill in the blank. Please write your answer on the line. Each question is worth 5 points. 11. What fraction of the shapes are suns?

___________________________

http://www.google.com/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&docid=EKoTvePh0gEz9M&tbnid=Rcqm4TVL6ko9KM:&ved=0CAUQjRw&url=http://www.superteachertools.com/jeopardyx/jeopardy-review-game.php?gamefile=1334164573&ei=jCpMUp3qMoT89gT9y4GwCQ&bvm=bv.53371865,d.eWU&psig=AFQjCNGT-GDNOehq5Mt1VZfUqeZvOL52sg&ust=1380809738587451

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12. If you could have 1/2 of a candy bar or 1/8 of a candy bar, which would you want and why?

13. Which fraction is the same as one half? 5 3 _________ 10 4 14. Which fraction is smaller? 1 1 __________ 3 12 15. Please arrange the fractions from smallest to largest. 1 1 1 10 2 3 16. Please arrange the fractions from smallest to largest. 6 2 7 8 8 8

17. What is the mixed number for the shaded shapes above? ____________

http://www.google.com/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&docid=vgD8iRWfHS1LOM&tbnid=Nledyc-6S9ku_M:&ved=0CAUQjRw&url=http://www.conceptuamath.com/help/bi3-conversations.html&ei=qLNxUuSMHK384AOliYDACw&bvm=bv.55819444,d.dmg&psig=AFQjCNHUxszRMbpVqtqRaPZr7bDqAnA5DA&ust=1383269659059497

26

18. What is the improper fraction for the shaded shapes above? ____________ 19. How long is the pumpkin?

__________________________

20. How long is the piece of candy?

__________________________

Extra Credit worth 5 points.

Draw a picture representing 2 in the space below. 6



27

Unit of Instruction

LONGWOOD LESSON PLAN MODEL: Revised, 2007 (D. Locascio)

Date of Instruction: October 21st 2013 (2hrs) Teacher Name: Emily Miller

Subject: Math Grade Level: 3rd

Standard of Learning (write out standard):

SOL #:3.3 The student will

a) name and write fractions (including mixed numbers) represented by a model;

b) model fractions (including mixed numbers) and write the fractions’ names; and

Applicable National Standard(s):

develop understanding of fractions as parts of unit wholes, as parts of a collection, as locations on

number lines, and as divisions of whole numbers

General Objective(s):

Student will be able to… define “fraction”, “numerator” and “denominator”

The students will be able to identify ½, 1/3, ¼, 1/8, 1/10, and 1/12 fractions in relation to 1. The

students will be able to name fractions both as part of a whole and in a set.

28

Rationale:

This lesson provides the base understanding of fractions with which to expand upon in future lessons.

Introduction/ Anticipatory Set:

Bell Ringer: In your math journal, tell me how do you use math in your life?

Big pieces of paper will be set up around the room. We will begin the unit by talking about why it is

important to know math for reasons other than school. The papers will say “home”, “Math your parents

use at work”, “Jobs that use math”, “Activities”, “Life”. The students will each be given a marker and

they will have the opportunity to walk around the room and add anything they can think of to each

category. They can draw lines to make connections and comment on other people’s suggestions. I will

model this for them by adding an idea to each paper. After 10 minutes of quiet circulation, I will break

the students up into 5 groups of 4 and ask them to read over one of the papers and tell the rest of the

class some of the important reasons we should know and understand math for that category.

Specific Learning Objectives Instructional Procedures

The student will be able to…. Discuss with a partner how we would describe a pizza that has some slices missing. Student will be able to… define “fraction”, “numerator” and “denominator” as well as see that fractions can be part of a whole or part of a set

The teacher will…

Challenge students to brainstorm ways to describe a pizza from which some of the slices have already been eaten. Ask how they could describe the pizza now that it is no longer whole. Have students discuss the possibilities with partners or in small groups, and then have a representative from each group share suggestions with the class. I will use direct instruction and a PowerPoint to teach the students about fraction definitions. The PowerPoint will cover the definition of fraction, numerator and denominator as well as show that fractions can be part of a whole or part of a set. At the end of the ppt, the students will watch a brainpop video on fractions and I will pause throughout to ask comprehension questions.

29

Work in a group to develop a list of ways they use or see fraction in their lives. Will create a fraction foldable

http://www.brainpop.com/math/

numbersandoperations/fractions/ Once we review the PowerPoint, I will ask students to talk in their groups and compile a list of ways they use fractions in their lives. Some examples could be cooking, the half an apple they get with their lunch, cutting your sandwich in half etc…anything that they can split and share. The students will share their responses. The students will create a fraction foldable that group fractions into fraction families 1/2, 1/4, 1/8 1/3, 1/6, 1/12 1/5, 1/10 The students will have a greater conceptual understanding of fractions if they group them based on families than if they order them based on ascending or descending order. Each strip will start as a whole piece and we will fold them together to show how to create fractions from a whole. Then the students will glue the whole to their foldable, write the numerical representation, and draw a picture of the fraction in a set on the inside flap. I will have a big strip and fold it to model to the entire class.

Closure: Ask students to look for fractions at home tonight and share it with the class tomorrow. Ask the

students to go home and see how many different ways you can get 1/2

Formative/ summative evaluation:

Formative: Class discussion and creation of the fraction foldable

http://www.brainpop.com/math/

30

Materials/ resources:

Poster paper (4)

Markers

PowerPoint

Premade foldables

Strips

Coloring materials (4 colors each)

Extension/ assignment:

Play a game in which students add up the value of their name to practice addition.

Accommodations/ provisions for individual differences: n/a

31


Date of Instruction: October 22nd 2013 (2 hrs) Teacher Name: Emily Miller

Subject: Math Grade Level: Third


SOL #:

3.3 The student will







The students will be able to identify ½, 1/3, ¼, 1/8, 1/10, and 1/12 fractions in relation to 1. Students

will be able to identify and model improper fractions and mixed numbers.

Rationale:

I am reviewing the fraction foldable made the day previous and having them use it whilel completing

stations working with fractions.

32


Add to our list of fraction in everyday life and sing the fraction song


The student will be able to… identify ½, 1/3, ¼, 1/8, 1/10, and 1/12 fractions in relation to 1 Students will be able to identify and model improper fractions and mixed numbers. Work in cooperative groups to complete station activities

The teacher will… Finish the foldable with the class. I will present a PowerPoint in which students will be engaged in identifying fractions, numerators, and denominators in both whole shapes and sets. The students will respond using the white boards. Station 1: Pattern Blocks Students will use pattern blocks to complete the 1st pattern block activity from NCTM Station 2: Identifying numerators and denominators activity sheet with corresponding manipulatives Station 3: The students will make fractions based on members of their family with accompanying sheet. Station 4: In their math journals, the students will write a letter to second graders about fractions. They will solve a fraction and then explain their thinking in their own words so that a second grader who does not know fractions will understand. This will give me insight to their thinking and address any holes in instruction.

Closure: Ask students to share some fractions that they learned about their family.

33


Completion of station activities and discussion while completing them.


PowerPoint

White Boards

Family Fractions

Math Journals

Pattern Blocks and accompanying sheet

Numerator and Denominator sheet


Fraction Bingo


34


Date of Instruction: October 23rd 2013 (2 hrs) Teacher Name: Emily Miller



SOL #:




c) compare fractions having like and unlike denominators, using words and symbols

(>, <, or =).




use models, benchmarks, and equivalent forms to judge the size of fractions;

recognize and generate equivalent forms of commonly used fractions, decimals, and percents;


The students will be able to illustrate models of fractions

Rationale:

The students will work with the half fraction family (1/2, ¼, 1/8) with both whole numbers and sets

35


Add to list of fraction in everyday life and listen to the fraction definition song.


The student will be able to… Manipulate play dough into different fractions within the half fraction family Work in cooperative groups to find ½ and ¼ of different sets

The teacher will… The teacher will use whole group instruction to work with dividing a whole object into fractions using play dough. The students will create a ball with their play dough and as a class we will cut it into halves, fourths, and eights and put it back together to show that it is still one whole. The students will then be given time to model fractions to show me in any way they would like. To model what the students will be doing, I will use the class as manipulatives. There are 20 students in the class and we will work together to break them up into two groups and 4 groups showing what ½ of the class is and what ¼ of the class is. I will write this in the graphic organizer I wish for them to use as they work. Students will be broken up into 3 groups. Each group of students will be given a different set to work with. One group will have an egg carton (12), another will have a pack of markers (8), and the third will have a pack of gift bows (4). They will each have a blank piece of paper that they will fold into fourths. The first rectangle will have their name, the first will be a drawing and fraction representing their whole set, the third will be a fraction and drawing representing what half of their set it, and the fourth will be a drawing and fraction representing what one fourth of their set is. Once the students are finished they will share their set with the class. Once completed, I will have a set of 16 star

36

bursts and have the students tell me how to find 1/2 and ¼ of my set. When finished the students may eat 2 starbursts.

Closure:

Ask students to look at their foldable and ask them all the ways they could simplify 6/8


Listening to group discussion and completion of graphic organizer while finding ½ and ¼ of set


Play Dough

White boards

Rulers

Paper

Egg carton

Christmas ornaments

8 pack of markers

4 pack of bows

Star bursts

Fraction circles


Use fraction circles to show me how many different ways they can make ½


37


Date of Instruction: October 24th 2013 (1 hr) Teacher Name: Emily Miller



SOL #:





(>, <, or =).






General Objective(s): Students will be able to compare like and unlike fractions

Rationale: The students will work with the thirds fraction family (1/3, 1/6, 1/12)


Review fraction song

38


The student will be able to… Create fraction strips to be used in a game from Marilyn Burns Work in groups to determine what 1/3 of different sets are.

The teacher will… Review how to make the thirds fraction family on the board similar to how we made the foldables. Distribute materials to make fraction strips for the activity. Walk around as students make the strips. Once the strips are made, compare the sizes and see how they are related. Once the thirds are made, make the other fraction strips (1/2, ¼, 1/8, 1/16) so they will have it for the activity tomorrow. Compare1/2, 1/3, ¼. Do you see how as the denominator increases the size gets smaller? Breaking it into more pieces makes the pieces smaller. Students will be broken up into 3 groups similar to the day previous. The groups will have a turn with each set where they will draw a picture and write a fraction representing 1/3 of the set. 3 pack of bows 6 pack of bows 9 pack of bows They will fold a paper into fourths and write and draw in each box for the different sets. Review as class when everyone is finished.

Closure:

Go over 12 egg carton as a whole


Group discussion


39

Fraction strips

Coloring materials

Bows

Egg carton

Extension/ assignment: If the students finish early, they can play the card addition and subtraction

game


Activity left with teacher for Friday

Marilyn Burns Cover Up fraction game. Students work in groups of 3 to play. Each team is given a dice

with ½, ¼, 1/8, 1/8, 1/16,1/16 written on the sides. The students will then roll the dice and use the

fraction strips to try and cover the whole

40


Date of Instruction: October 28th 2013 (2 hrs) Teacher Name: Emily Miller



SOL #:





(>, <, or =).







Students will be able to arrange fractions by size

Rationale:

This lesson will not only ask students to write fractions, but to also arrange them based on size

41


Review Fraction Definition Song

Introductory ppt on arranging fractions


The student will be able to… The students will arrange fractions based on size write fractions with like denominators and arrange them based on size

The teacher will…

The students will be split into 2 groups. The first group will be given fractions with like denominators and asked arrange themselves in order of size 1/10, 2/10, 3/10, 4/10, 5/10, 6/10,

7/10, 8/10, 9/10, 10/10

The second group will be given cards with fractions with unlike denominators and they will be asked to arrange themselves in order based on size

½, 1/3, ¼, 1/5, 1/6, 1/7, 1/8, 1/9, 1/10,

1/11

After the students have arranged themselves, we will have a discussion about the patterns that we see. (When the denominator is the same, the fraction gets bigger as the numerator increases. When the denominator is different, as the denominator increases the fraction gets smaller)

The students will switch cards and try again. The teacher will then distribute a handful of fruit loops to the students and they will be asked to count the total number of fruit loops, sort the cereal into the different colors, and write fractions based on the colors. They will then order the fruit loops and write the

42

Work with pattern blocks Create their own fraction problem on a fraction flower

fractions on a piece of paper with an accompanying picture to represent the fraction. The students will then work with pattern blocks to complete an NCTM activity in which they find the fractions represented by the pattern blocks Students will design their own fraction flower and write and accompanying fraction problem to be solved by peers.

Closure:

Exit card in which students create a model for the fraction 4/5th


Fruit loop activity and station activities


Fraction cards

Fruit loops and accompanying paper

Pattern blocks and accompanying paper

Fraction circle

Coloring materials

Fraction flower materials


Play the Cover Up game that they learned last Friday


43


Date of Instruction: October 29th 2013 (2 hrs) Teacher Name: Emily Miller



SOL #:





(>, <, or =).







Students will be able to convert mixed and improper fractions

Rationale:

This lesson will work with and convert mixed numbers and improper fractions

44


Add to the fractions in everyday life list and review the fraction definition song.

Finish/ edit fraction flowers


The student will be able to… Identify mixed and improper fractions Students will work independently on a worksheet to practice mixed and improper fractions

The teacher will… To introduce mixed numbers and improper fractions, we will watch a brainpop jr video http://www.brainpopjr.com/math/fractions/mixednumbers/preview.weml The teacher will then work with students in a whole group setting using the pattern blocks to manuplate mixed and improper fractions. Ex: if I have 3 red trapezoids, what would my fraction be? I can take 2 of those trapezoids and make one whole yellow hexagon and how many trapezoids are left? 1! So I have 1 whole and 1 half. The teacher will then show and model how to find mixed and improper fractions with a power point. The students will then be given white boards and asked to name the mixed number and improper fractions represented on the board. The teacher will formally assess students as they complete the worksheet and address any individual needs that the students have.

Closure:

Review worksheet as a class


Observation of the students creation of mixed numbers with pattern blocks, white boards, and

worksheet.


http://www.brainpopjr.com/math/fractions/mixednumbers/preview.weml

http://www.brainpopjr.com/math/fractions/mixednumbers/preview.weml

45

Pattern Blocks

White boards

Worksheet


More work with pattern blocks


46


Date of Instruction: October 30th 2013 (2hrs) Teacher Name: Emily Miller



SOL #:





(>, <, or =).







Students will be able to convert improper fractions to mixed numbers

Students will use fractions to determine measurement

Rationale:

Through this lesson, students will not only practice converting improper fractions to mixed numbers, but

they will do so on a number line through measurement.

47


Allow students time to complete mixed number worksheet. Those that are finished will go into the hall

and answer the fraction flower problems written by their peers. When everyone is finished, we will go

over the mixed numbers and improper fractions as a class.


The student will be able to… Put fractions on a number line Create a fraction review sheet with the teacher Practice fractions in fraction centers with their cooperative groups

The teacher will… I will introduce fraction on a number line by reading Inchworm and a Half . Students will interact with text by using the strategy of prediction to engage their knowledge on fraction families. Review how to place numbers on a number line and show how to find ½ and ¼ of an inch. Create a number line on the wall and each student will be given a mixed number and asked to find their spot on the number line. The teacher will create a fraction review sheet with the students. I will have very little input and will wait until they tell me what to fill in the blanks with. I will fill in any holes in instruction at this time. The students will be broken up into 4 groups to allow for extra practice and one small group instruction as review before the test tomorrow. Centers 1. Pattern Blocks with Mrs. Gilbert Students will work with Mrs. Gilbert in a small group setting while working with finding fractions using pattern blocks 2. Measuring/ Fraction on a number line with Ms. Miller Students will work with me to complete a measuring activity from NCTM in which they identify fractions on a ruler and measure objects around the room.

48

3. Bingo Students will review identifying fractions by playing fraction pizza bingo 4. Computer Students will practice identifying fractions by playing fraction games on abcya.com

Closure: Review how we can use fractions on a number line to help with rounding.

“Find the place

And look next door

Five or higher, add one more

Four or less, let it rest”

Review that this poem works because if it is 5 or higher it is over the half mark and is closer to the next

whole number.

The students will use their fraction strips to help them round using their knowledge on fractions.


Activity sheet on rounding and class discussion


Inchworm and a Half

Inchworm manipulatives

Rulers

Paper clips

Scissors

Notebook Paper

49

Desktop

Glue Stick

Math book

Crayon

Unsharpened Pencil

Tissue Box

Classroom Window

Teacher’s Shoe


Students will Practice rounding using their fraction strips. They will measure items in the room and

round it to the nearest whole inch.


50

Pre Assessment Data

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Score

A c c 4/7 3/5 1 1 70%

B c c 1/3 1/3,1/12,1/2 1/10,1/8,1/4 5/3 9 1/4 58%

C c c 1/8 ½,1/3,1/12 1/10,1/8,1/4 Pic 3 1 55%

D c c 1/8 1/3 ½,1/3,1/12 1/10,1/8,1/4 3/5 4/3 1 ½ 55%

E b c c 4/2 1/8 1/3 ½,1/3,1/12 1/10,1/8,1/4 5/1 ⅓/2 2 ½ 45%

F c c 1/8 1/3 ½,1/3,1/12 1/10,1/8,1/4 3/5 3 1 2/3

1 2/3

45%

G c c c 1/8 1/3 ½,1/3,1/12 1/10,1/8,1/4 5/3 pic 01/1 1 1/2

45%

H c c a 1/8 1/3 ½,1/3,1/12 1/10,1/8,1/4 5/3 2 1 1 45%

I c c 2/4 1/8 3/4 1/3 ½,1/3,1/12 4/3 3 ⅓ 1 5 45%

J c c c 2 1/8 1/3 ½,1/3,1/12 1/10,1/8,1/4 3/5 9 4 10 40%

K C C A 1/8 ¾ 1/3 ½,1/3,1/12 1/10,1/8,1/4 3/5 3 ⅓ 0 5 40%

L b a 2/4 1/8 ¾ 1/3 ½,1/3,1/12 1/10,1/8,1/4 3/5 4 1 5 40%

M b a 2/4 1/8 3/4 1/3 ½,1/3,1/12 1/10,1/8,1/4 3/5 5 1 5 1/6

40%

N c c c 1/8 ½ 1/3 ½,1/3,1/12 1/10,1/8,1/4 3/5 4 1 ½ 1 ½ 40%

O c c a 2/1 1/8 ¾ 1/3 ½,1/3,1/12 1/10,1/8,1/4 n/a n/a 9 21 35%

P c c n/a A ½ 1/8 ¾ 1/3 ½,1/3,1/12 1/10,1/8,1/4 3/5 3 0 1/2 30%

Q c c c c 1/8 1/3 ½,1/3,1/12 1/10,1/8,1/4 3/5 4 5 1 ½ 30%

R c c a a 1/2 1/8 3/4 1/3 ½,1/3,1/12 1/10,1/8,1/4 3/5 34 5 5 30%

S c c a c x x x x 1/8 1/3 ½,1/3,1/12 1/10,1/8,1/4 3/5 3 1/4 28%

T c c x x x 2/1 1/8 ¾ 1/3 ½,1/3,1/12 1/10,1/8,1/4 4/5 3 ⅓ 1 5 25%

% Missed 15 100 100 25 25 10 5 10 10 10 50 90 45 90 95 95 100 100 70 100

51

Post Assessment Data

student 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 X

19 20 X

bonus Original Score

w/o

A yes 105%

B 7/8,6/8,2/8 yes 100%

C B c 7/8,6/8,2/8 2/3 ¼ 78% 83%

D C A 2/6 1/3 7/8,6/8,2/8 7/9 7/9 ¼ Yes 71% 75%

E 1/8 1/3 ½,1/3,1/10 1/1 Yes 85% 90%

F 7/8,6/8,2/8 1/3 90% 95%

G ½ Yes 100%

H 1 2/4

yes 100% 105%

I 7/8,6/8,2/8 2 2/7

¼ Yes 93% 105%

J B A X X X X 1/8 more pieces

7/8,6/8,2/8 2 2/7

6/1 2/4 45%

K B ¾ 1/3 ½,1/3,1/10 7/2 1/9 1 1/5

Yes 76% 78%

L C A ½ because it is less

¾ 1/12 6/8,7/8,2/8 2/3 2 ½

Yes 65% 72%

M C B 4/2 2/1 1½ 2 ⅓

73% 80%

N 7/8,6/8,2/8 yes 100%

O B A 4/3 1/3 ½,1/3,1/10 1/3 5 8 60% 67%

P B B 2/1 1 2/1

¼ 78% 8%

Q B Yes 100%

R 3/6 ¾ 1/3 4/3 8 20 Yes 75% 83%

S 7/8,6/8,2/8 12 7/9 1 1/2

yes 88% 95%

T B B A B 6/4 1/8 bigger

¾ 1/3 ½,1/3,1/10 7/12 8/12 __ __ 40 42%

% Missed 25 30 35 5 5 0 5 5 5 5 20 20 25 35 20 45 25 65 25 65

52

Percent Improvement

Student Percent Improvement

A 35%

B 42%

C 28%

D 20%

E 45%

F 50%

G 55%

H 60%

I 60%

J 5%

K 38%

L 32%

M 40%

N 60%

O 32%

P 53%

Q 70%

R 53%

S 67%

T 17%

After the test, as an opportunity to improve the grade to be recorded, I

worked with the students in small groups and then gave them the

opportunity to try the questions they missed for 3 points. This is the final

recorded score.

Student Final score

Percent improvement from post assessment

A 105% n/a

B 100% n/a

C 86% 3%

D 90% 15%

E 99% 9%

F 98% 3%

G 100% n/a

H 105% n/a

I 105% n/a

J 71% 26c%

K 84% 6%

L 85% 13%

M 88% 8%

N 100% n/a

O 76% 9%

P 92% 9%

Q 100% n/a

R 89% 6%

S 101% 6%

T 60% 18%

53

Here is a graph of the pre and post assessments for each of the 20 students in the class.

Class average of learning goals on assessment

0

20

40

60

80

100

120

A B C D E F G H I J K L M N O P Q R S T

Pre-Assessment

Post-Assessment

0

20

40

60

80

100

120

Learning Goal 1

Learning Goal 2

Learning Goal 3

Learning Goal 4

Learning Goal 5

Learning Goal 6

Learning Goal 7

Pre-Assessment

Post-Assessment

54

Summation of Data Tables

The data tables were incredibly informative in not only telling me what the students

learned, but where there is confusion and caused me to rethink my instruction. Questions

eighteen and twenty were missed by 65% of the class so they were removed from the

assessment and the students were scored out of eighteen total questions instead of twenty.

Question eighteen was from learning goal six and question twenty was from learning goal

seven. I was ambitious in teaching seven total learning goals and I was not confident that I

would be able to get to them all, so it is not surprising that those questions needed to be

removed. The material was taught during the last two days of instruction and the students did

not have enough time to work with it before they were assessed on the material.

After looking at the data tables and graph of the pre and post assessments, it is clear to

see that there was student growth after this two week unit. I was very pleased with the 70%

improvement of student Q and the 60% improvement of students H, I, and N, but I was

incredibly perplexed by the post assessment of student J. She went from a 40% on her pre-

assessment to only a 45% on her post-assessment. I saw this student working throughout the

two weeks and I know she should have had more than a 5% improvement with the material.

On her post-assessment in the matching section, instead of drawing lines from the picture of a

fraction to the number form of a fraction, she drew lines from one picture to another picture.

This was especially confusing because she did not do this on the pre-assessment so I know that

she is familiar with matching.

55

I wanted to give the students an opportunity to learn from their mistakes and improve

their score to be recorded in the grade book. It is important that tests are used as a learning

tool as well as an assessment and I am a firm believer that students should have the ability to

improve if they are willing to work harder. I pulled the students in small groups based on what

they needed extra instruction on, and then I allowed them to try the questions that they missed

for some additional points. Student J did a lot better on the assessment with me sitting next to

her and reading the instructions. When I read the instructions and explained what she was to

do with the matching section, she answered the questions with 100% accuracy. She had a 26%

improvement on her final score just by working in a small group with me and having the

questions read to her. I think this is significant because there may be a learning disability or

reading issue that is inhibiting her math ability. It is more important that I am assessing her

math ability instead of how well she can read a question.

The class average for the pre-assessment was 42% and the class average for the post

assessment was 85%. This indicates that there was an average of 43% increase in student

learning. There was also growth in the class average for each learning goal. The most

improvement can be found with learning goal six where the students went from 0% to 75% on

average. Learning goal two showed the least improvement. The students went from 90% to

96%. Although it is only 6% improvement, it is still beneficial because the students almost

mastered it with 100% accuracy.

56

Reflection

I am proud to say that the students improved for each of the seven learning goals thought

during this unit. There was a 42% improvement for learning goal one, 6% improvement for learning goal

two, 30% improvement for learning goal three, 28% improvement for learning goal four, 63%

improvement for learning goal five, 75% improvement for learning goal six, and 44% improvement for

learning goal seven. Overall the class average rose 43%.

A major challenge when teaching this unit was learning how to differentiate instruction. I have

some students who grasped the concept quickly and asked for more challenging material while others

barely understood the concept of a fraction. It was difficult to make sure everyone’s needs were being

met by my lessons. At one point I was standing in front of the class with pictures of fractions on the

board and I wanted the students to write the appropriate fraction on their whiteboards and hold them

up for me to see. As I stood there, I could see students struggling and students breezing through it and

literally asking me for something harder. It was so difficult to know where to put my attention. If I focus

on the struggling learner then the other students are not being challenged and if I challenge the ones

who need it the struggling learners will only struggle more.

I remedied the situation by asking the students to draw their own picture of the same fraction in

another way and as they worked on that I worked one-on-one with the struggling learners. This allowed

the students who were quickly grasping the material some extra practice and an opportunity to

manipulate it on their own while those who were struggling had an opportunity to work one-on-one

with me. It was also nice to see what the other students came up with and a good reminder that math is

not just something that the teacher knows and the students have to learn exactly how the teacher

knows it. The students came up with some very creative examples and it helped them to apply the

knowledge in their own way.

57

If I could teach the unit again I would teach mixed numbers and improper fractions differently. I

was teaching seven learning goals and honestly I did not think we would get to all seven, but the

students really seemed to be grasping the material and they were ready to move on to mixed numbers

and improper fractions. I was very surprised when the students had a very difficult time grasping the

concept. They understood whole numbers and they understood that a fraction was part of a whole

number, but when we started putting fractions together to make wholes they really got confused. They

got even more confused when I started finding improper fractions. If I could go back and teach this unit

again I would devote an entire week at least to working with mixed numbers and improper fractions.

The two days I allotted for that was not nearly enough as evidenced by my data tables.

I learned that I take teaching very seriously and I am going to need to be careful not to take it

too personally. The students are all very important to me and when they do not show that they are

learning the material (such as student J receiving only 5% higher on the post assessment) I feel like I

have personally failed them. I also learned to take this feeling and apply it constructively by ensuring

that each student has the opportunity to improve and working with them in small groups to cover

material that was not mastered. I learned that I spend a lot of time preparing out of nervousness to

ensure I get the lesson right, but that I should continue to be prepared because it is very difficult to

teach when you are not.

I learned that my students are different every day they come in the classroom. Student J is a

great example. One day she would know which was the numerator and which was the denominator and

she could identify fractions and then the next day it was as if she had never seen it before in her life.

This behavior may also explain why she knew how to complete the matching section on her pre-

assessment and not her post-assessment. Student C was also very interesting. This student struggles

severely in reading, but is quite bright in math. He grasped the concepts easily and manipulated the

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fractions on his own. When it came time to take the test, he made mistakes that I did not expect him to

make and even after working in small group with him he still made the same mistakes. It is as if he

understood one day and didn’t understand the next. Most importantly I learned that concepts must be

taught in a variety of ways and reinforced throughout the day in order for students to grasp and retain

the information.

Documents

Emily Miller Longwood University Cumberland Partnership ... · Emily Miller Longwood University Cumberland Partnership Fall 2013 Dr. Horne Teacher Work Sample . 2 Introduction This