Teacher Work Sample - Church Street School

Teacher Work Sample

Fihayya Plair

Grade: 1

Mathematics

Church Street School

Hamden School District

Principal Stacie D'Antonio

October 19th - December 11th 2015

Date Submitted: December 8th 2015

2015 Student Teaching Work Sample Plair 2

Table of Contents

Contents Section 1: Contextual Factors: ................................................................................................................... 3

School and Community .......................................................................................................................... 3

Classroom ................................................................................................................................................ 4

Section 2: Learning Goals and Objectives: ............................................................................................... 5

Section 3: Assessment Plan: ....................................................................................................................... 7

Section 4: Design for Instruction: ............................................................................................................ 15

Section 5: Analysis of Student Learning ................................................................................................. 35

Section 6: Reflection and Self-Evaluation ............................................................................................... 43


Section 1: Contextual Factors:

School and Community

Church Street School is a pre-kindergarten – 6 grade elementary school serving 371 students

with a faculty base of 30 teachers. Of all the students in the school, 80.3% of these students are

eligible for free/reduced price meals, 14.6% of the students are not fluent in English, and 6.8%

have disabilities.

Church Street Elementary School has a diverse student population drawing from several

neighborhoods in close proximity to the school. Approximately 50% of our students are Black,

20% are White, 25% are Hispanic and 5% are Asian. Languages spoken at home include

English, Spanish, Italian, Greek, Albanian, Arabic, Bengali, Chinese, French, Hindi, Malay,

Turkish, Urdu, Vietnamese, Uzbek and Cantonese.

The school is set in an urban and very diverse socioeconomic community. Church Street School

is set in Hamden which consists of families of low, middle, and high socioeconomic statuses.

However, according to the eligibility of free and reduced price meals, a large majority of the

school’s families are of low socioeconomic status. Approximately 73% of Hamden’s population

are White, 13% are Black, 0.26% are American Indian, 16.5% are Hispanic, 3.8% are Asian, and

2.9% are multi-racial.

The improvement of literacy is an ongoing initiative in this school. This year, Church Street

School increased its literacy support by hiring an additional literacy specialist and two additional

Title One tutors. The school implemented consistent instructional strategies in Literacy using

shared, guided and independent reading and provided interventions for students below

benchmark in reading. Using the data team process, teachers meet weekly to develop data cycles

in literacy in collaboration with the external data facilitator. In order to improve instruction for


all students, three resource teachers worked closely with classroom teachers, media specialist,

literacy specialists, ELL tutors and support staff to develop individualized programs based on

current and on-going assessments. Lexia and Head sprouts, a bilingual aide, peer tutors,

Experience Corps volunteers and university students were part of intervention plans using the

SRBI model. CMT scores indicated a continued need for improvement in reading. Summer

programs to support literacy included free school-based initiatives with a focus on vocabulary

development for 15 students scheduled to enter kindergarten, 40 students entering grades 3 and 4

and ECO Science Camp for 46 students entering grades 3-6.

Classroom

Room 12 is one of 3 first grade classrooms at Church Street with a total of 15 students: 6 boys

and 9 girls. 3 of the students have IEPs for speech impairment and one has both a speech

impairment and a seizure disorder, for which she has a full-time one-on-one aid by her side. Two

students are ELLs, both of whom had Spanish as their native language. Concerning ethnicity, 2

of the students are White/Caucasian American, 3 are Hispanic, 1 is Asian from the Middle East,

and the remaining 9 are Black/African American. For the ELL students, intervention specialists

pull them out for some one-on-one language training. For the students with IEP’s, it is required

by the school that they get a certain amount of hours on the educational apps on the school iPads.

According to their DRA scores, the majority of these students are considered on grade level

when it comes to reading.

The teacher uses responsive classroom techniques to manage her classroom. She follows a strict

behavioral/reward system used by the entire school called bucket fillers. This really keeps the

students motivated in monitoring their own behaviors. As for instruction, the teacher uses lots of

games and active hands-on types of materials that keep the students engaged in their lessons. She


uses songs and rhymes as well to help the students memorize key concepts and ideas. Also, the

teacher always askes intriguing questions to tap their prior knowledge and get them thinking.

Structural wise, students are grouped in small groups all the time, unless they are on the carpet

for morning meetings or group lessons. After group mini lessons and instructions, students work

in groups in work stations for both math and reading for the remainder of the academic block.

Section 2: Learning Goals and Objectives:

The content area of this unit is first grade mathematics. There will be three-four lessons,

including a pre and post assessment. The overall goal of this unit will be using addition and

subtraction to solve story problems. The three lessons of this unit that I will teach will have one

overarching goal in the whole number operations math strand:

Learning Goal #1: Students will make sense of and develop strategies to solve addition and

subtraction problems with small numbers.

Objective 1: Students will be able to visualize and demonstrate, using an equation the action in

subtraction situations involving removal

Objective 2: Students will be able to subtract one number from another, with initial totals of up

to 12

Objective 3: Students will be able to develop and use various strategies for solving subtraction

(removal) problems

Objective 4: Students will be able to model the action of a subtraction (removal) problem with

counters or drawings.



Additional standards for mathematical practice aligned

with the objectives of this unit include the following:

MP2: reason abstractly & quantitatively

MP4: model with mathematic

MP5: use appropriate tools strategically

MP7: look for & make use of structure

Section 3: Assessment Plan:

Pre-assessment – The pre-assessment will be a worksheet

that I create myself that reflects the objectives that I want

students to be able to do by the end of this unit. The

intention is to help me determine the knowledge gaps and

misconceptions that students have from the previous year

of instruction. It is crucial that these gaps and

misconceptions are identified and addressed throughout

instruction of this unit. Failure to do so will result in

frustration for both students and myself, as math is a

supremely cumulative subject.


The pre-assessment will be graded out of 10. The first question will be worth 2 points. 1 point for

if they can show that this is a subtraction problem, and 1 point for giving the correct answer. For

the second problem, students can receive 2 points, 1 for each strategy. The third problem is

divided up into 4 smaller problems and is thus worth a total of 4 point. The last question will be

worth two points. If students modeled the subtraction properly with a drawing, they receive one

point. If they just answer the question without any picture, they receive one point. If they draw

an accurate model of the subtraction situation and answer the question correctly, they receive

two points. If a problem is left blank, the student will not receive any credit.

Results of this pre-assessment may also lead to identifying the specific needs of my lower level

students with disabilities, as well as my English language learners. The pre-assessment also

contains material that will be covered in this unit. If a student has already mastered some or all of

the material that is contained within this unit, accommodations will be made for the advanced

student as well, allowing them to progress to more challenging material. Differentiation is not

easy, but we all know that students become bored, either because they are behind or because they

are waiting for more challenging material. In this case, differentiation is very manageable –the

advanced student will be offered double-digit numbers to subtract, starting with problems where

there is no borrowing and then including borrowing if they can handle it.

Formative assessments – These will be concise assessments, intended to measure the learning

targets for this unit in small intervals and inform lesson planning for subsequent sessions. These

assessments will be on going and varied. We will have worksheets from time to time as well as

games or quick assignments. Homework may also be used as a formative assessment for me to

see what needs to be taught, skipped, re-taught, or enforced and with what students. Verbal and

informal assessment will often be used at the end of a lesson during discussion or at the


beginning of a lesson to see what they already know or what they remember from the previous

lesson.

Post- assessment – By the end of this unit, students are expected to demonstrate a mastery of the

basic material presented on this assessment. Student performance on the final assessment should

continue to inform the teacher regarding the gaps and misconceptions that students may still

possess relative to this material.

The post-assessment will be summative. It will be a worksheet very similar to the pre-assessment

to see how much the students actually learned as a whole class. Individual student growth will

also be monitored to determine how effective my teaching instruction and strategies were.

The four learning objectives that the students will be assessed on are:

Can students demonstrate with an equation the action in a subtraction story problem?

Can students subtract one number from another with initial totals up to 12?

Can students use and record strategies for solving subtraction problems?

Can students model the action of subtraction using counters and/or drawings?

Similarly, the post-assessment will be graded out of 10. The first question will be worth 2 points.

1 point for if they can show that this is a subtraction problem, and 1 point for giving the correct

answer. For the second problem, students can receive 2 points, 1 for each strategy. The third

problem is divided up into 4 smaller problems and is thus worth a total of 4 point. The last

question will be worth two points. If students modeled the subtraction properly with a drawing,

they receive one point. If they just answer the question without any picture, they receive one

point. If they draw an accurate model of the subtraction situation and answer the question

correctly, they receive two points. If a problem is left blank, the student will not receive any

credit.


Objectives Pre-Assessment Formative Assessment

Post-Assessment Rubric/ Grading Criteria

Objective 1: Students will be able to visualize and demonstrate, using an equation the action in subtraction situations involving removal.

Q#1: There are 12 fish swimming together. 8 fish swim away. How many are left? Write this problem as an equation. Make sure you use an equal sign.

Student Activity Book, p. 20: “15 Is the Number” Informal observation of students during game “Five in a Row: Subtraction”

Q#1: There are 15 birds flying together. 7 birds flew away. How many are left? Write this problem as an equation. Make sure you use an equal sign.

Q#1: 2pts Proficient= 2 Basic= 1 Below Basic= 0

Objective 2: Students will be able to subtract one number from another, with initial totals of up to 12.

Q#3: Fill in the missing numbers: 9 – 0 = 3 – 2 = 10 – 5 = 7 – 4 =

Student Activity Book, p. 21-22: “How many Squirrels?” Informal observation of students during Game: “Roll and Record: Subtraction”

Q#3: Fill in the missing numbers: 8 – 1 = 5 – 3 = 10 – 8 = 6 – 2 =


Objective 3: Students will be able to develop and use various strategies for solving subtraction (removal) problems.

Q#2: What is the difference between 7 and 5? Name 2 strategies you could use to solve this problem?

Student Activity Book, p. 23: “Finding the Total” Student Activity Book, p. 26: “Fill in the Dots”

Q#2: What is the difference between 6 and 2? Name 2 strategies you could use to solve this problem?

Q#3: 4pts Proficient= 3-4 Basic= 2 Below Basic= 0-1

Objective 4: Students will be able to model the action of a subtraction (removal) problem with counters or drawings.

Q#4: Story Problem Draw a picture or use counters to model the following action. Tim had 8 blocks. He gave away 3 blocks. How many blocks does Tim have left?

Student Activity Book, p. 24: How Many Apples?

Q#4: Story Problem Draw a picture or use counters to model the following action. Kim had 9 blocks. He gave away 4 blocks. How many blocks does Kim have left?



Name: Date:

Teacher: Ms. Plair First Grade Math

Pre-Assessment

Subtracting Single-Digit Numbers

1. There are 12 fish swimming together.

8 fish swim away.

How many are left?

Write this problem as an equation. Make sure you use an equal sign.

2. What is the difference between 7 and 5?

Name 2 strategies you could use to solve this problem?

3. Fill in the missing numbers:

9 – 0 = 3 – 2 =

10 – 5 = 7 – 4 =


4. Story Problem

Draw a picture or use counters to model the following action.

Tim had 8 blocks. He gave away 3 blocks. How many blocks does Tim have

left?


Name: Date:

Teacher: Ms. Plair First Grade Math

Post-Assessment

Subtracting Single-Digit Numbers

1. There are 15 birds flying together.

7 birds flew away.

How many are left?

Write this problem as an equation. Make sure you use an equal sign.

2. What is the difference between 6 and 2?

Name 2 strategies you could use to solve this problem?

3. Fill in the missing numbers:

8 – 1 = 5 – 3 =

10 – 8 = 6 – 2 =


4. Story Problem

Draw a picture or use counters to model the following action.

Kim had 9 blocks. He gave away 4 blocks. How many blocks does Kim have

left?


Section 4: Design for Instruction:

My pre-assessment was given the week before my unit was planned to be taught. Students are

still deeply embedded in addition problems and have not yet seen the connection between

addition and subtraction. Students were briefed before taking the pre-assessment to let them

know that they were not expected to know how to solve subtraction problems. They were told to

simply try their very best and that I only wanted to see what they already knew about subtraction.

After the assessment, students were then debriefed to ensure that they understood that it was OK

that they did not know how to do the pre-assessment. Next week they would learn all of the skills

they needed to ace this test.

During the pre-assessment, I equipped all the students with their own worksheets and

administered the test verbally to the students. Students were asked to read along with me as I

explained their job for each question. After every question I gave the students some time to

complete the problem before moving on to the next.

In order for a student to be considered proficient at the objective the students must score a 3 or 4

(on problem #3 only) and a 2 on all other problems on the pretest or posttest. Students who are

proficient have shown that they have mastered the respective content objectives. Students who

are basic score a 2 (on problem #3 only) and a 1 on all other problems on the pre or post

assessment. Students who score a 0 on the pre or post assessment are considered below basic. A

score of below basic means that the student does not indicate any understanding of the concepts

presented in the content objectives.

The pre-assessments were graded according to the criteria rubric explained on page 9.

The data displayed below shows the student performance relative to the entire pre-assessment as

a whole and then student performance relative to each of the learning objectives.


Figure 1:

Student

performance on

the entire pre-

assessment.

Figure 2: Student performance on

Objective #1:

Objective # 1: Students will be able

to visualize and demonstrate, using an

equation the action in subtraction

situations involving removal.

5

3

2

5

0

0-20% 30-40% 50-60% 70-80% 90-100%

0

1

2

3

4

5

6

Pre-Assessment

Students

Proficient13%

Basic47%

Below Basic40%

Objective #1

Proficient Basic Below Basic


Figure 3: Student performance on

Objective #2:

Objective 2: Students will be able

to subtract one number from

another, with initial totals of up to

12.

Figure 4: Student performance

on Objective #3:

Objective 3: Students will be

able to develop and use various

strategies for solving

subtraction (removal) problems.

Proficient 0% Basic

13%

Below Basic87%

Objective #2


Proficient 40%

Basic20%

Below Basic40%

Objective #3



Figure 5: Student Performance on

Objective #4:

Objective 4: Students will be able to

model the action of a subtraction

(removal) problem with counters or

drawings.

Analysis of Pre-Assessment

Student performance on objectives 1, 2, and 3 were as expected. On the other hand, more than

half of the students were proficient at objective 4. Because of this I will focus less on picture

modelling of a subtraction situation and introduce things like using a number line or

decomposition to help students model/solve story problems. This means that for the students who

were not proficient at objective 4, they will learn the process of drawing circles or some sort of

figure and crossing out a given amount to find out what is left. However, for the students that

were proficient, I will encourage them to use some of the other strategies such as drawing a

number line, using addition facts, and decomposition.

As far as differentiation, there are about 5 students that I know need to be further challenged and

about 5 that need explicit support. I have modified all my lessons with a plan to help all of my

Proficient 54%

Basic7%

Below Basic39%

Objective #4



advanced and struggling students. Everyone will learn something new during this mini-unit, and

my goal is that everyone will come out of this unit proficient in all of the objectives. The week

that I will be teaching this unit is thoroughly planned out in the timeline chart below.

Monday B Tuesday C Wednesday D Thursday E Friday A

Arrival/MM 8:00-

8:45

Arrival/MM 8:00-

8:45

Arrival/MM 8:00-

8:45

Arrival 8:00-8:25 Arrival/MM 8:00-

8:45

Writers Workshop

8:45-9:30

Literacy 8:45-

10:15

Content 8:45-9:30 Art 8:30-9:30 Literacy 8:45-

10:15

Music & P.E:

9:35-10:35

Writer’s

Workshop 10:15-

11:15

P.E. & Music:

9:35-10:35

MM 9:35-9:45

Literacy 9:45-

11:15

Writer’s

Workshop 10:15-

11:00

Literacy 10:40-

12:00

Media Center

11:15-12:00

Literacy 10:40-

12:00

Content 11:15-

11:30

2nd Step 11:30-

12:00

Content

11:00-12:00

Lunch & Recess

12:05-12:50

Lunch & Recess

12:05-12:50

Lunch & Recess

12:05-12:50

Lunch & Recess

12:05-12:50

Lunch & Recess

12:05-12:50

SRBI 1:00-1:30 SRBI 1:00-1:30 SRBI 1:00-1:30 SRBI 1:00-1:30 SRBI 1:00-1:30

Math Workshop

1:30-2:45

Introducing

Subtraction

Lesson 1:

Math Workshop

1:30-2:45

Solving

Subtraction Story

Problems

Lesson 2:

Math Workshop

1:30-2:45

Subtraction

Strategies

Lesson 3:

Math Workshop

1:30-2:45

Review and Post-

Assessment

Math Workshop

1:30-2:45

Equal Sums

Lesson

Dismissal

2:45-3:05

Dismissal

2:45-3:05

Dismissal

2:45-3:05

Dismissal

2:45-3:05

Dismissal

2:45-3:05


Introducing Subtraction Lesson Plan #1

1. Introductory information at the top:

Your name Fihayya Plair

Date of Lesson 11/16/15 Name of

school

Church Street Elementary School

Grade level First grade Subject

area(s)

Math

Topic of lesson Subtraction

CT/district

standards

1.0A.1: Use addition and subtraction within 20 to solve word problems involving situations of

adding to, taking from, putting together, taking apart, and comparing, with unknowns in all

positions, e.g., by using objects, drawings, and equations with a symbol for the unknown

number to represent the problem.

1.0A.5: Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).

1.0A.6: Add and subtract within 20, demonstrating fluency for addition and subtraction

within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 =

14); decomposing a number leading to a ten; using the relationship between addition and

subtraction; and creating equivalent but easier or known sums.

1.0A.7: Understand the meaning of the equal sign, and determine if equations involving

addition and subtraction are true or false.

1. NBT.1: Count to 120, starting at any number less than 120. In this range, read and write

numerals and represent a number of objects with a written numeral.




Instructional

Group

Whole Classroom and work stations

References Hamden School Math Investigation

2. Rationale

The objective focuses on two of the four CCSS critical areas for Grade 1: Operations and Algebraic

Thinking as well as Number and Operations in Base Ten. The CCSS outline the mathematics concepts

that should be the focus of instruction in Grade 1 and while each area is important for laying the

foundation for future study of mathematics, these two are considered to be most predictive of future

mathematics learning. Students who leave first grade with a proficient grasp of these two concepts and

skills will largely be prepared to begin second grade mathematics.


Students retell and solve a story problem in which one amount is removed from another. They think

about how the problem is similar to and different from stories about combining two amounts. Students

learn and play subtraction variations of Roll and Record and Five-in-a-Row.

3. Materials

Connecting cubes,

chart paper/ white board,

Dot cube; number cube with numbers 7-12; connecting cubes

Student Activity Book p.19 and p.20

Student Math Handbook pp. 38

Subtraction Recording sheet

Five in a Row: Subtraction Game board

Assessment chart Number line

Enrichment Worksheet

4. Objectives

Students will be able to

visualize and retell the action in subtraction situations involving removal

Subtract one number from another, with initial totals up to 12

Use numbers and standard notation (+,-,=)

5. Procedure

Initiation

10-15 minutes

Tell students a subtraction story.

Do not alert students to the fact that this will be a different type of story: instead,

encourage them to follow the same routine of visualizing the action of the story.

The teacher will discuss how this kind of story is different from those that students

have been solving after students have heard, retold, and solved the problem.

Story problem: Max had 9 toys. His friend Rosa came over to play with him. Max

gave 3 of the cars to Rosa to play with. How many cars did Max have then?

Encourage students to visualize the action in the story.

Ask students to retell the story after they have heard it. (Students may alternatively

turn and retell the story to a partner). After students have had a chance to retell the


story, ask students whether Max will have more or fewer cars at the end of the

story.

Possible student responses: Max has more cars at the end of the story; Max has less

cars at the end of the story.

Finally, ask student to solve the problem. Give each student a tower of 9 cubes to

use as needed.

Ask several students to share strategies for solving the problem. These might

include

Breaking 3 cubes off the tower of 9 and counting how many are left

Counting backward (on a number line, mentally, or on their fingers)

Counting up from 3 to 9

Thinking about addition (“I know that 6 and 3 together make 9”)

As you discuss strategies, focus on developing language that helps students acquire

an image and understanding of the action of subtraction: take away, went away,

give away, separate, remove, less, fewer, and so on. However, do not use the words

subtraction or minus yet. Those words will be introduced in the next lesson.

Instead, use the above vocabulary.

Ask students to think about how this problem is different from the problems they

have been solving.

Students might say:

“Max ends up with less. In the other problems, the person usually ends up with

more.”

“Usually we put two numbers together and find out how many. This story is

different because you have to take some away. “

Lesson

Development

20 minutes

Introduce subtraction games for Math Stations.

Remind students that when they play Roll and Record and Five in a Row, they

always roll two cubes, and have so far combined the rolls to figure out what

number to write or what number to cover. Today, instead of adding, they are

going to be subtracting.

Show students the number cubes they will be using to play. The 1-6 dote cube

will be familiar to them. Take a minute to look at and establish what numbers

on the new number cube (7-12).

Explain to students that they will roll both cubes. The number cube tells them

how many cubes they start with. The dot cube tells them how many cubes to

subtract, or take away, from that.


Play a few sample rounds to demonstrate. Give each student 12 connecting

cubes to use as needed, and then roll the number cube and the dot cube.

Say: Let’s say that I rolled a 9 on the number cube and a 2 on the dot cube. I’m

going to start with the bigger number (9) and take away the smaller number (2).

The answer to 9 take away 2 will tell us what number to write on our recording

sheet.

Ask a few students to share how they would solve this problem. Possibilities

include:

Using the cubes

Counting back mentally on their fingers or on a number line

Using an addition combination they know

Counting up from 2 to 9

Students might say:

“I made a tower with 9 cubes, and I took away 2 of the cubes.”

Continue with other examples until students understand how to play and record

for Roll and Record: Subtraction.

Quickly review the rules for the second game: Five in a Row: Subtraction.

Students will again be very familiar with this game. Be sure to point out that

we be using a number cube and a dot cube. We will subtract the smaller

number (on the dot cube) from the larger number (on the number cube). They

will then use a counter to cover the result on their game board. The goal is to

completely cover one row horizontally, vertically, or diagonally.

Students will be grouped based on academic ability. Based on the pre-

assessment that I gave the week before, I had a pretty good idea of who

understood the basics of subtraction and who did not. Thus, I decided to place

students who were competent with students I thought would struggle. That way

they could help them out and really get the most out of the games.

Closure

10 minutes

Pose another story problem or two for students to retell and solve as a

whole group. Remember to ask students whether the end result will be more than or less

than the initial amount.

1. Toshi had 8 pennies. He went to the store and bought an apple for 5

pennies. How many pennies did he have left?

Students might say:

“First, I put up 8 fingers for the 8 pennies. I had to take away 5 fingers –that’s

one whole hand of fingers. Look, I have 3 fingers still up.”


2. Libby had 10 crackers for a snack. She shared them with her friend Neil.

She gave Neil 4 crackers. How many crackers did Libby still have?

Students might say:

“I built a tower of 10 cubes for the 10 crackers. Then I took off 4 cubes. Six are

left -1, 2, 3, 4, 5, and 6.”

6. Assessment

Ongoing assessment: Observing students at work

The games provide the students practice with subtracting small numbers and with writing

numbers.

How do students determine the problem that a given roll represents? For example, if they

roll 3 and 7, how easily do they know or figure out that the problem to solve is 7-3?

How do students solve the problem? Do they use counters? Their fingers? A number

line? Do they work mentally? Do they count all, remove some, and count again? Count

back from the total number? Count up to the total number? Use an addition fact they

know?

Are student able to accurately and legibly record the results?

The teacher will use the on-going assessment chart and go around to every student during

our workshop games.

Homework: Student Activity Book pg. 20

7. Reflection

The lesson as a whole went well. Based on the pre-assessment, I understood that the students would need

sometime before subtraction would come more naturally to them. The majority of the students did not

understand the action taking place in the first story problem. I had to model the action of taking away and

removal to find what is left quite a few times before I felt that students could do it themselves. All

students were very engaged and very interested in understanding what subtraction was, which was great.

The lesson was exciting for them and they were eager to learn and play. The games are a very great way

to keep the students engaged at the end of the day. I will definitely try and incorporate a game into every

workshop of this mini-unit. The students need and love them.

If I could teach this lesson again, I would definitely not group students based on academic ability. First of

all, the pre-assessment wasn’t that good of a pre-judge into the academic abilities of the students. Student

that I thought would struggle did ok and some student that I thought would do fine, needed some extra

help. Instead I would let students pick their partners so that they are grouped with people that they know


8. Modifications/Differentiation

Student A This student will need some extra support

determining the problem to solve after

rolling the cubes.

The teacher will ask the student to tell her

which cube shows the larger number.

Remind the student that you start with the

larger number and take away the smaller

number. The final answer will be what is

left.

Student B This student will need some extra support

determining the problem to solve after

rolling the cubes.

The teacher will ask the student to tell her

which cube shows the larger number.

Remind the student that you start with the

larger number and take away the smaller

number. The final answer will be what is

left.

Student C This student will be given a behavior

modification.

The teacher will incorporate instant bucket

slips for appropriate behavior. This includes

student working cooperatively with his

partner, taking turns, being respectful,

sharing items, and following the teacher’s

instructions without argument.

Extension for Student X (if necessary)

If they quickly gets the hang of subtraction, encourage him to use different strategies to figure out the

solution. For example, if he is used to using his fingers or doing the math mentally in his head, encourage

him to try counting down, or counting up, or even using his addition facts to solve the problems.

they work well with and would be comfortable diving into new information with. Because I did not do

this, some students were frustrated with their partners because they did not work well together on top of

the frustration that they were feeling from not quiet understanding the concept of subtraction.

Also, as far as management goes, I would introduce the idea of jobs to students, such as forming our ten

rods, after fully giving my instructions for the lesson. Students were more interested in these jobs than in

understanding what they were supposed to do once they started their workshops.

Finally, during clean up, instead of just telling students to clean up their stations and return their supplies,

I could have done much more to make this transaction much more orderly. I could have called certain

tables up one at a time and placed the bins that they would return their number cubes and counters in

some place that was easily accessible. As soon as students were done returning their supplies they could

hand their papers into to me and take a seat on the carpet.


Solving Subtraction Story Problems Lesson Plan #2




school



area(s)

Math


CT/district

standards

1.0A.1: Use addition and subtraction within 20 to solve word problems involving situations of

adding to, taking from, putting together, taking apart, and comparing, with unknowns in all

positions, e.g., by using objects, drawings, and equations with a symbol for the unknown

number to represent the problem.


1.0A.6: Add and subtract within 20, demonstrating fluency for addition and subtraction

within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 =

14); decomposing a number leading to a ten; using the relationship between addition and

subtraction; and creating equivalent but easier or known sums.

1.0A.7: Understand the meaning of the equal sign, and determine if equations involving

addition and subtraction are true or false.

1. NBT.1: Count to 120, starting at any number less than 120. In this range, read and write

numerals and represent a number of objects with a written numeral.




Instructional

Group



10. Rationale








Students solve subtraction story problems in which they find how many are left when one quantity is

removed from another. They record their solution strategies individually and then share their strategies

with the class.

11. Materials

Connecting cubes, or counters

chart paper/ white board,

Student Activity Book p.21-23

Student Math Handbook p. 38

Subtraction Bowling recording sheet

12. Objectives



develop strategies for solving subtraction (removal) problems

Model the action of subtraction (removal) problems with counters or drawings

Develop methods for recording subtraction (removal) strategies

13. Procedure

Initiation

10-15 minutes


Pose one or two subtraction stories for students to retell and solve.

Story problems:

1. Felipe found 7 seashells on his trip to the beach. When he came home,

he gave 1 of them to his sister, Martha. How many shells did he still

have?

2. Seth was playing at the part with 6 of his friends. Two of them had to

leave to go home for dinner. How many were still at the park?

These problem provide a good opportunity to talk about what happens when you

take away only one or two things from a group. Focus some discussion on counting

backward (in their heads, on their fingers, and/or on the class number line) as one

strategy for solving this kind of problem because this can be a powerful strategy for

students to consider.

Ongoing assessment:

Can students retell the story to a partner accurately?

Can students figure out the action taking place (subtraction or addition)?

Can students come up with a strategy for solving this kind of problem?


Have students come up to the board and share their ideas:

Verbally have students retell the story.

The teacher will then write it down.

Beneath the retell, have students volunteers come up to the board and write an

equation that demonstrates the action that must be taking to solve the problem, but

do not solve the problem.

Then have students brainstorm some possible strategies that they could use to solve

this problem. Write them underneath the equation.

(Strategies may include

Breaking cubes off the tower and counting how many are left

Counting backward (on a number line, mentally, or on their fingers)

Counting up )

Finally, ask student to pick one of the strategies and solve the problem. Have a

volunteer come up to the board and circle the strategy that they used, demonstrate

the strategy, and write the answer.

Lesson

Development

30 minutes

Read aloud the problem on student activity book page 21 and 22, and ask two

or three students to put the story in their own words. Keep the emphasis on

retelling the story and not solving it.

1. There were 12 squirrels on the ground. Then 4 of them ran up a

tree. How many stayed on the ground?

2. I saw 15 squirrels in the park. Then 8 ran away. How many

squirrels were left?

These two story problems will be our first station.

The next station will be subtraction bowling. Review with the students how we

play bowling and model one round. Go over the bowling recording sheet.

Directions: Students will be using 10 cups and a ball. They will roll the ball in

the array of cups and record how many get knocked down. They must then

subtract how many were knocked down from how many they originally had to

answer the question of how many are left. They must simply count the

remaining cups, and record that number after the equal sign.


Then have the students break off into their stations. Each station will be 15

minutes. There will be two stations.

Station 1: Story problems page 21 and 22

Station 2: Subtraction Bowling

For the story problem, students must show their work.

They need to give me an equation and name a strategy before solving the

problem.

Possibilities include:

Using the cubes

Counting back


Counting up

Closure

15 minutes

Bring everyone back to the carpet for discussion and sharing.

Have students share their answers for the two story problems: equations,

strategies and final answers.

Have students share some of their bowling results.

Wrap up with having students review the strategies for subtraction.

14. Assessment


The problems provide the students practice with subtracting small numbers and with writing

numbers.

How do students determine the problem that the story presents? For example, if they see

a 3 and 7 in a problem, how easily do they know or figure out that the problem to solve is

7-3?




know?

Are student able to accurately and legibly record their results?



15. Reflection


Advanced

students

These students can solve the given

problems easily and can record their

strategies well.

The teacher will ask these students to show

a second way to find the answer or solve a

related problem with larger numbers.

Struggling

students

These students need more support solving

the problems and modeling the situations.

The teacher will re-read the problem with

students who are having difficulty getting

started and encourage them to tell the story

in their own words. Some may need help

directly modeling what is happening in the

situation by using counters.

Today’s lesson went a little better than yesterday. I changed up my groups and that seemed to help. The

students seem to be getting the hang of subtraction. We went through the process of answering story

problems with retelling the action with an equation, picking a strategy, and then using the strategy to

solve the problem. Some students still need some extra help with this but most students seemed to

understand it.

Roll and record seems to be a struggle for some of my students, even though they have played this game

many times with addition. The concept of subtraction is something that they need more time to be

immersed in before it will start coming naturally to them.

According to yesterday’s homework, students understand the missing addend problems quite well. My

formal and informal formative assessments are showing me that the students just need more exposure. So

at the beginning of every lesson I will be holding quick subtraction drills using the number line, mental

math, and counting on/counting backwards strategies.

I feel the need to give the strategies that students already know of and do a name, so that they can identify

them and talk about their problem solving processes.


Subtraction Strategies Lesson Plan #3




school



area(s)

Math


CT/district

standards

1.0A.1: Use addition and subtraction within 20 to solve word problems involving

situations of adding to, taking from, putting together, taking apart, and comparing,

with unknowns in all positions, e.g., by using objects, drawings, and equations with a

symbol for the unknown number to represent the problem.

1.0A.3: Apply properties of operations as strategies to add and subtract.2 Examples:

If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of

addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2

+ 6 + 4 = 2 + 10 = 12. (Associative property of addition.)

1.0A.4: Understand subtraction as an unknown-addend problem. For example,

subtract 10 - 8 by finding the number that makes 10 when added to 8.


1.0A.6: Add and subtract within 20, demonstrating fluency for addition and

subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8

+ 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten; using the

relationship between addition and subtraction; and creating equivalent but easier or

known sums.

1.0A.7: Understand the meaning of the equal sign, and determine if equations

involving addition and subtraction are true or false.

1. NBT.1: Count to 120, starting at any number less than 120. In this range, read and

write numerals and represent a number of objects with a written numeral.

MP2: reason abstractly & quantitatively



Instructional

Group



18. Rationale








Students solve another subtraction story problem in which they find how many are left when one quantity

is removed from another. Math Workshop follows. Class discussion focuses on strategies for subtraction.

19. Materials

Connecting cubes, or counters

Chart paper/ white board,

Roll and Record: Subtraction board game

Five in a row: Subtraction board game

Student Activity Book pg. 24

20. Objectives



develop strategies for solving subtraction (removal) problems

Model the action of subtraction (removal) problems with counters or drawings

Develop methods for recording subtraction (removal) strategies

21. Procedure

Initiation

10-15 minutes


Present the problem on SAB (student activity book) pg 24.

Story problems: 1. Max picked 12 apples. He gave 6 of them to Rosa. How many apples did

Max have then?

These problem provide a good opportunity to talk about what happens when you

take away only one or two things from a group. Focus some discussion on counting

backward (in their heads, on their fingers, and/or on the class number line) as one

strategy for solving this kind of problem because this can be a powerful strategy for

students to consider.

Ask student to retell the story to a partner. Then ask two or three students to retell

the story to the class.

After retelling the story, ask whether Max will have more or fewer than 12 apples.


Lesson

Development

30 minutes

Explain to students that everyone will begin Math Workshop by solving this

problem.

Math workshop will consist of math games, math story problems, and math

conferencing with the teacher.

Conferencing will be introducing a new strategy: number lines.

We will be working on the How many apples (problem).

Games will consist of roll and record and five in a row. All games students should

be very familiar with, but teacher should review the rules before sending the

students off.

The last station will be independent math, where students will work by themselves

to solve another how many apples word problem.

For the story problem, students must show their work.

They need to give me an equation and name a strategy before solving the

problem.

Possibilities include:

Using the cubes

Counting back


Counting up

Number line

Closure

15 minutes

Bring everyone back to the carpet for discussion and sharing.

Have students share their answers for the two story problems: equations,

strategies and final answers.

Review the number line strategy and have students come up to the board to

demonstrate some of their answers.

Wrap up with having students review the strategies for subtraction.

22. Assessment


The problems provide the students practice with subtracting small numbers and with writing

numbers.

How do students determine the problem that the story presents? For example, if they see

a 3 and 7 in a problem, how easily do they know or figure out that the problem to solve is

7-3?





know?

Are student able to accurately and legibly record their results?


23. Reflection


Advanced

students

These students can solve the given

problems easily and can record their

strategies well.

The teacher will ask these students to show

a second way to find the answer or solve a

related problem with larger numbers.

Struggling

students

These students need more support solving

the problems and modeling the situations.

The teacher will re-read the problem with

students who are having difficulty getting

started and encourage them to tell the story

in their own words. Some may need help

directly modeling what is happening in the

situation by using counters.

Today’s lesson showed me that my students all know how to subtract. The problem comes when they are

required to figure out whether they are supposed to subtract or add. Figuring out this difference is hard

for them. However the actual process of solving a subtraction story problem, modeling it with an

equation, choosing and using a strategy, and solving the problem is not hard for them. At this point I have

been trying to get it through to the students that they don’t have to figure out whether this is a subtraction

or addition problem. All of the problems for this week are subtraction problems.

Tomorrow, we will review everything we learned in the last 3 days, in preparation of the post assessment

I will give on Friday.


Section 5: Analysis of Student Learning

After reviewing the post-assessments, I have concluded that my students have learned a

phenomenal amount of knowledge when it comes to the concept of subtraction in just these last

four days. If students received a total of 70%-80%, they were considered proficient. If they

received a total of 90%- 100%, they were considered goal or exceeding expectations. All of my

students fell within these two ranges. With the mass majority falling in the 90%-100% range. I

was very impressed.

To further analysis the results of this unit design and I have analyzed the results of my pre-and

post-assessments in several different ways. The first will be an analysis of the pre and post

assessments of the entire class in respects to every students on every learning objective. The

purpose of this analysis will be to see the individual and average progress of my students from

pre- to post-assessment.

Table 1: Whole Class Student Achievement Data based on Learning Objectives

Students

#

Pre-

assessment 1st Learning Objective Q#1:

Post-

assessment 1st Learning Objective Q#1:

Pre-

assessment 2nd Learning Objective Q#3:

Post-

assessment 2nd Learning Objective Q#3:

Pre-

assessment 3rd Learning Objective Q#2:

Post-

assessment 3rd Learning Objective Q#2:

Pre-

assessment 4th Learning Objective Q#4:

Post-

assessment 4th Learning Objective Q#4:

Student1 50% 50% 25% 75% 50% 100% 0% 100%

Student2 50% 100% 50% 100% 0% 100% 0% 100%

Student3 50% 100% 0% 100% 0% 0% 0% 100%

Student4 0% 100% 50% 75% 0% 50% 100% 100%

Student5 0% 50% 100% 100% 50% 50% 0% 100%

Student6 0% 0% 25% 100% 0% 50% 0% 100%

Student7 50% 100% 100% 100% 0% 0% 100% 100%

Student8 0% 50% 25% 100% 0% 50% 50% 100%

Student9 50% 50% 100% 100% 0% 100% 100% 100%

Student10 0% 100% 25% 100% 0% 100% 0% 100%


Student11 100% 100% 100% 100% 0% 100% 100% 100%

Student12 100% 100% 100% 100% 0% 100% 100% 100%

Student13 0% 100% 0% 100% 0% 50% 100% 100%

Student14 50% 100% 50% 75% 0% 100% 100% 100%

Student15 50% 100% 100% 100% 0% 100% 100% 100%

I am proud to say that all of my students improved over the course of this unit. No one remained

stagnant. Everyone received a better grade on their post assessment than they originally had on

their pre-assessment.

Figure 6: Average student progression from pre to post assessments.

As a whole, the progress of my students’ knowledge and skills, when it comes to the learning

objectives designated for this unit, is very apparent in the graph above. The average achievement

grade on the overall test was 43% for the pre-assessment; the average achievement grade for the

post-assessment was 88%. For LO1, average student achievement rose from 37% to 80%. For

LO2, the average student achievement increased from 57% to 95%. For LO3, average student

achievement rose from 7% to 70%. Finally, for LO4, the average student achievement increased

from 57% to 100%.

4337

57

7

57

8880

95

70

100

0

10

20

30

40

50

60

70

80

90

100

OverallAchievement

Objective #1 Objective #2 Objective #3 Objective #4

Gra

des

Objectives

Whole Class Achievement

Pre-Assessment Post-Assessment


The next form of analysis will be an analysis of the pre and post assessments of the class in terms

of subgroups based on a specific characteristic. The achievement of these subgroups will be

compared in respects to only one learning objective. The purpose of this analysis will be to see

the achievement and average progress of my students from pre- to post-assessment, when

organized into different groups. I chose performance levels to be the characteristic that I based

my subgroups on. I came to this conclusion based on student performances on the pre-

assessment. There were three distinct levels of performance: proficient, basic, and below basic.

Subgroup 1 were proficient meaning they scored a 70-80 on their pre-assessment. Subgroup 2

were basic, meaning they scored a 30-50 on their pre-assessment, and subgroup 3 were below

basic, meaning they scored a 0-20 on their pre-assessment. Surprisingly, having a class of 15

students, 5 landed nicely in each of the three subgroups. The learning objective I chose to

analyze these subgroups in was LO3. This is the objective that students showed the most

interesting growth in, seeing how they all had no prior knowledge of the concept. Learning

objective #3 stated that students would be able to identify strategies that they could utilize to

solve subtraction problems. The average student achievement in this objective was 70%. But

how did each subgroup compare when dealing with this objective? The graph below shows the

comparison between the three subgroups in reference to the third learning objective.


Figure 7: Performance level subgroups comparing results of post assessment.

The student progress on this objective is simply amazing. Subgroup 2 is the only subgroup that

had any points for this objective, because two student out of this group were able to determine

that the question was asking them to subtract. Because of that, I awarded them a point. However,

not one of the students in any of the groups understood how to identify any strategies for solving

subtraction problems. Because of this, students made the largest growth in this objective, even

though the average student achievement across the objectives was lowest in objective 3. Even so,

when you compare the subgroups another story is told. Subgroup 1 completely mastered this

objective, scoring a total average of 100% on their post assessment. Subgroup 2 scored a total

average of 80% on this objective, proving them proficient. Subgroup 3 received a total average

score of 50%, proving them basic. This group is the factor that slightly skewed the data for this

objective. However, these results are understandable considering the academic abilities of each

0

10

0

100

80

50

0 20 40 60 80 100 120

Subgroup 1

Subgroup 2

Subgroup 3

Subgroup Perfomance on Learning Objective #3

Post-assessment Pre-assessment


subgroup. Subgroup 1 consisted of my brightest students. Subgroup 2 were my average students,

and subgroup 3 happened to consist of my more struggling students.

The last form of analysis will be an analysis of the pre and post assessments of the class

in terms of individuals. I will select two students that demonstrated different levels of

performance, picking one student from my high performance group and another student from my

low performance group. The two students I will be analyzing will be student #6 and student #15.

It is very important to understand the learning of these two students seeing how they were very

different when it came to learning abilities, learning styles, and performance levels. Student #6

was one of my students who did not make any progress in LO1, which was a very important

objective that showed that students can demonstrate they understand the action being asked of

them in a subtraction problem. Student#15 did not show any progress either. However, their

reasons as to why they didn’t make any progress are very different. On the one hand, Student #6

came into the pre-assessment with zero knowledge of this objective. This student definitely came

out of this unit with lots of knowledge in this area, however, his post-assessment failed to show

this. He ended up scoring a zero for this section again. On the other hand, Student#15 came into

the pre-assessment with complete knowledge of this objective. This student came out of this unit

with a new assurance and deeper understanding of this objective, while his post-assessment

simply showed that he scored 100% on this section. For each student’s overall achievement, they

both showed progress in their level of understanding of subtraction in general. However, both

received differentiation. Student #15 often received alternative worksheet to work on and dealt

with higher two digit numbers when it came to subtraction. Student #6 received more of the

teacher’s one-on-one time and repeated explanations and demonstrations. Student #6 also was

given extra tools such as the print out number lines to assist him in computations. He also never


had to deal with numbers larger than 12. This student required lots of re-directing and focusing.

With these adjustments and modifications, I am confident that both of these extremely different

students received the materials and support they both needed to learn something new and retain

their knowledge throughout this unit. According to several of the formative assessments during

and after lessons, as well as the post-assessment, I confirmed that these students attained the

learning goals and objectives for this unit. And even though student #6 showed no progress in

the problem designated for LO1, several of the other questions incorporated this objective to

build on other skills and he did really well in these areas. If he did not master this first objective,

he could not have succeeded in the other objectives, which he did.


Student #15 Pre Assessment Homework

Post Assessment

Extra Practice


Student #6 Pre-Assessment Homework

Post Assessment

Extra Practice

Keep trying


Section 6: Reflection and Self-Evaluation

When I stand back and look at the end results of this project I cannot help but to feel

extremely proud. This unit had its ups and downs but overall, I would say that it went really well.

The learning objective that my students were most successful in showing mastery was objective

4: Students will be able to model the action of a subtraction (removal) problem with counters or

drawings. Every single students scored 100% on this section of their post-assessment. One

reason for this success might be that a majority of them came into this unit having experience

modeling their work with drawings and counters. According to the pre-assessment data, 60% of

the students were already proficient in this objective coming into this unit. A reason for this

might be that they carried this skill over from their work in addition into their growing

understanding of subtraction, and it really helped. Another reason for this success might be

simply the effect of good teacher. I constantly modeled the proper procedure for solving

subtraction story problems and story problems in general. I drilled it in mini lessons, formative

assessments, homework, and station work. By the time they took the post-assessment, this type

of problem was very familiar to the students and they were naturals at solving them.

The learning objective that my students were least successful in showing mastery in was

objective 2: Students will be able to develop and use various strategies for solving subtraction

(removal) problems. One reason for this occurrence might be in part due to the fact that none of

the students showed any prior knowledge or familiarity in naming the strategies that they use

when it comes to solving problems. According to the pre-assessment, everyone received 0%

strictly in the area of naming strategies, coming into the unit with no prior knowledge. A reason

for this might be that they did not focus much on the names of strategies when they did their

addition unit. The process of naming the strategies that they would automatically do in their


heads or on their fingers seemed very foreign to them. They seemed to understand the strategies

but not their names, such as counting on, counting backwards, addition facts, or number lines.

Another reason for student’s lack of mastery might be based on the question posed in the pre-and

post-assessments. The task of naming strategies for solving subtraction problems was a part of a

larger question that asked students to find the difference between two numbers. Now we had not

spent as much time on finding the difference as some of the other skills students were expected

to learn. Because of the lack of exposure to this phrase, students of then answered with responses

of comparison, such as 6 is greater than 2 instead of the difference between 6 and 2 is 4;

completely forgetting the second part of the question to list the strategies that they would use.

Basically, many of them did not consider the phrase difference to mean subtraction; thus not

comprehending what strategies they should be listing.

This is basically a technical issue with the test itself. Students reviewed and drilled the concept

of naming strategies and I have confidence that they could all do it. What I would definitely

change as far as instruction is the amount of time and focus that I put into teaching the students

the concept of finding the difference between two numbers. Alternatively, I would simply take

out the phrase and ask students just to name two strategies they could use to help them solve

subtraction problems. This would diminish the amount of confusion that surrounded this problem

and helped students focus on the learning objective.

Two professional learning goals that have emerged for me during my experience with the

teacher work sample are meaningful differentiation and classroom management. Increasing the

chances of all students, no matter their learning abilities, to learn the skills and meet all of the

objectives of any unit is definitely something that I need work on. Sure there will always be

students that perform better than others. But how can I modify or accommodate or even motivate


students to not just work hard, but give me their best when it comes to showing what they know.

Because that is what it all comes down to when you are a real teacher. Can your students

demonstrate their knowledge and skills? They may know how to subtract and know the basic

strategies for solving subtraction problems, but unless they can prove that on a test, their scores

will not reflect it and the school will not recognize it. A step that I can take to improve in this

area is working more closely with the special education teacher. I plan to take some time at the

end of my placement to shadow and interview the special education teacher, the math coach, and

the ELL teacher to try and learn some strategies and techniques for dealing with these types of

students and getting them to perform to the full potential on tests and assessments.

The second area of improvement that I recognize that I need is in classroom management.

Ensuring that management problems, such as students being confused about instruction,

frustrated about working groups and buddy partners, lack of materials or students being

distracted by materials, do not get in the way of student learning and the allotted time of daily

learning. In a classroom such as a first grade classroom, these factors occur too often. Students

are worried about helping you erase the board or gathering materials such as magnets, or

collecting papers that sometimes the teacher’s instructions are ignored or not fully paid attention

to. The teacher than repeats instructions or has to straighten out confusion and this takes time and

effort. Creating systems such as classroom jobs, organized fashions of handing in work,

established station rotations and getting all students to stop look and listen before giving any

form of instruction seems to be the only solutions for this sort of problem.

Documents

Teacher Work Sample - Church Street School