Salem EE3 Candidate A

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Erica Sigley Salem College Student Teaching Candidate Fall 2011

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Division Unit Overview

Logistics

Unit designer: Erica Sigley (Student Teacher)

Grade/Subject: 4th Grade Mathematics

Title: Concepts and Skills in Division

Length: 4 week unit (this overview includes the first 8 lessons)

Time: Each lesson is 90 minutes long

Statement of Purpose and Rationale

Division is an essential skill for academic and authentic success. Students will continually bulid

upon their skills in division for factoring, fractions, percents, ratios and probability, polynomials,etc. Strong skills in division are essential for students to be successful with these concepts. In

addition, we use division regularly when we create budgets, determine resources for various

events, manage our time, cook, and more. Division, whether we realize it or not, is a major part

of our daily lives. Therefore, it is important that students develop strong conceptual

understanding of and skills in division. This unit will help students to develop both of these as

well as teach them to use division to problem solve.

NCSCOS goals and objectives:

Week 1: students will review third grade division skills and concepts. (the pacing guide refers to

3rd Grade objectives for this week, so in trying to be consistent with the pacing guide, I will use

3rd grade objectives from the NCSCOS as well.)

3rd

Grade Mathematics Competency Goal 1: The learner will model, identify, and compute

with whole numbers through 9,999.

1.03 Develop fluency with multiplication from 1x1 to 12x12 and division up to two-

digit by one-digit numbers using:

a. Strategies for multiplying and dividing numbers.b. Estimation of products and quotients in appropriate situations.c. Relationships between operations.

Week 2: Students will extend their division skills to work a wider range of numbers at the fourth

grade level.

4th Grade Mathematics Competency Goal 1: The learner will read, write, model, and

compute with non-negative rational numbers.


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1.02 Develop fluency with multiplication and division:c. Strategies for multiplying and dividing numbers.d. Estimation of products and quotients in appropriate situations.e. Relationships between operations.

Essential Questions:

1. What strategies can you use to divide numbers?2. What are some strategies you can use to estimate quotients, and when would you use

these strategies?

3. How are multiplication and division related?

Unit Overview

Scaled Drawings

Nutrition and

caloric intake

per serving

Division

Language

Science

Art

Map Scales

Mathematics

Social

Studies

Weight on

the Moon Supply and

Demand

Connect to

Multiplication

Writing

to Explain

Book

about

division


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Objectives Addressed in Integration

4th

Grade Science Objective Competency Goal 4: The learner will conduct investigations and

use appropriate technology to build an understanding of how food provides energy and materials

for growth and repair of the body.

4.02 Show how calories can be used to compare the chemical energy of different foods.

4th Grade Science Objective: Earth in our universe (this is new to 4th

grade this year, so there

are no NCSCOS objectives listed)

4th Grade Social Studies Objective: Competency Goal 6 The learner will evaluate how North

Carolinians apply basic economic principles within the community, state, and nation.

6.01 Explain the relationship between unlimited wants and limited resources.

4

th

Grade Social Studies Competency Goal 1: The learner will apply the five themes ofgeography to North Carolina and its people.

1.01 Locate, in absolute and relative terms, major landforms, bodies of water andnatural resources in North Carolina.

4th

Grade Visual Arts Competency Goal 1: The learner will develop critical and creative

thinking skills and perceptual awareness necessary for understanding and producing art.

1.02 Apply knowledge and concepts gained across the curriculum as a source of ideas for

art.

1.06 Refine images of self, pets, family, friends, and environment.

4th

Grade Language Arts Competency Goal 2: The learner will apply strategies and skills tocomprehend text that is read, heard, and viewed.

2.02 Interact with the text before, during, and after reading, listening, and viewing by:

setting a purpose using prior knowledge and text information. making predictions. formulating questions locating relevant information. making connections with previous experiences, information, and ideas.

4th Grade Language Arts Competency Goal 4: The learner will apply strategies and skills to

create oral, written, and visual texts.

4.02 Use oral and written language to:

present information and ideas in a clear, concise manner.discuss.


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interview.

solve problems.

make decisions.

Prerequisite Teacher Knowledge:

Concepts

Multiplication and division are inverse operations. In other words, they undo each other. The basis for division is separating objects or groups into equal groups. Some strategies for division include repeated subtraction and sharing. Properties of division: any number divided by itself is 1; and number divided by 1 is

itself, and numbers cannot be divided by 0.

Vocabulary

Dividendthe number that is to be divided Divisorthe number by which the dividend is divided Quotientthe result or answer Fact Familya group of mathematical facts using the same numbers

27 9 = 3 27 3 = 9 3 9 = 27 9 3 = 27

Remainder- the remaining number once division is completed Prime numbera whole number larger than 1 that is only divisible by 1 and itself. In

other words, it only has 2 factors. Composite numbera whole number that is larger than 1 that has more than 2 factors.

Big Ideas

Addition, subtraction, multiplication, and division are all related. There are properties and rules that are always true that control mathematics Doing math involves problem solving and reasoning and can be represented many

different ways.

Mathematical patterns are predictable and can be generalized and represented.

Estimation and approximation are important skills in mathematics and can be used in anumber of real world situations

Algorithms are tools for solving mathematical problems once conceptual understandinghas been established.

Considerations about the Learners

Prior Knowledge

27 9 = 3

Dividend Divisor Quotient


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Pre-assessment: I will be referring to my students performance during the multiplicationunit to determine their level of understanding prior to beginning the division unit. I will

also complete a quick check on the first day.

Students must have a thorough understanding of multiplication, addition, and subtractionprior to this unit. An understanding of multiplication is important because division is so

closely related to multiplication. Addition is also important for this reason. Subtraction isimportant so that students will be able to use repeated subtraction to divide. Finally,

students must understand how to judge of groups are equal in order to work with fairsharing.

Students will need to connect their knowledge of division to multiplication by breakingapart arrays. It will also be helpful if students can perform simple sharing problems suchas sharing cookies or candy among friends and tablemates.

A thorough understanding of how multiplication is repeated addition will help students tothink of division as repeated subtraction.

Fair sharing and equity is an important cultural concept for students to understand to helpthem with division.

Unique Learner Consideration

I will need to refer to the mathematics PEP notes for several of my students. I have a number of LEP students in my classroom and will need to differentiate for them

by integrating images, hands on experiences, and language development goals into my

instruction.

I will use a variety of techniques such as guided practice, independent practice, modeling,hands-on work, visual demonstrations, manipulatives, real-world application, etc. in order

to suit a number of learning styles.

Considerations about the Learning Environment

Physical Space

The classroom is a medium-sized room with tables organized into clusters. Student attention isoften directed towards the ActivBoard in the front of the classroom; however, there is space for

the teacher to move around. We also have a window, and we are in a classroom near the exit.

Directly outside of our room is a small field and the parking lot.

Temporal Resources

The math block is 90 minutes long; however, this time is divided into two sessions. We have 60minutes during the first part, and then we break for lunch and recess. We return to math one

hour and fifteen minutes later, and finish off the last 30 minutes. Generally, we use the first 60minutes for instruction and guided practice and use the last 30 minutes for spiraling review and

independent practice. This if course changes depending on the lessons.

Learning Materials


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I have the activboard, the computer, several professional and content specific books, games,

manipulatives, and a media center as resources. Many of my lessons use the ActivBoard and

manipulatives. We have adopted the EnVision math program, and I will be using resources fromthat program throughout my lesson as well. I like that this program is very well suited for

adaptation and integration of other activities and subjects.

Personnel Resources

There will be two teachers in the room, myself and my cooperating teacher. I would like to have

my CT help with small group and individual instruction as needed.

Technological Resources

In terms of technology, we have three computers in the room, two for student use and the other ishooked up to the activboard for teacher use. We also have speakers, the ability to play videos

and use activvoters, and manipulatives in the room.

Timeline for Unit

Day 1: What does division mean?

Objective: 3rd Grade Mathematics Competency Goal 1: The learner will model, identify, and

compute with whole numbers through 9,999.

1.03 Develop fluency with multiplication from 1x1 to 12x12 and division up to two-digit by one-digit numbers using:

a) Strategies for multiplying anddividing numbers.b)

Estimation of products and quotients in appropriate situations.c) Relationships between operations.

Strategies:

Hands-on work with grouping counters real-world connections (sharing situationspossibly integrate supply and demand during

this lesson)

Guided practice and modeling. (activboard)Assessment: I will ask students to record their groupings on graph paper and write a division

sentence for each one. I will be using this activity to determine their ability to create equalgroupings and connect them to the division algorithm. I will also provide my students with a

preassessment quiz to determine their level of background knowledge. Since the multiplicationunit directly precedes this unit, I will have already gathered some important preassessment

information. During the lesson, I will be observing my students abilities to solve and model

division problems using manipulatives.


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Day 2: How are multiplication and division related? How can you use your knowledge of

multiplication to solve division problems?

Objective: 3rd

Grade Mathematics Competency Goal 1: The learner will model, identify, and





Strategies

Hands-on work with manipulatives Group WorkUsing two factors, students will practice constructing and grouping in

arrays.

Guided Practice and modeling (activboard)Assessment: I will assess my students abilities to connect multiplication and division by writingfact families for a given array and drawing an array for given fact families. I will also be

assessing whether or not my students are able to connect division sentences to these arrays.

Day 3: What are some special properties of division?

Objectives: 3rd





a. Strategies for multiplying anddividing numbers.b. Estimation of products and quotients in appropriate situations.c. Relationships between operations.

Strategies

Group Work (students will practice sharing things in their groups) Writing to explain: Students will write stories where people must share things using the

properties of division. Students will work with the properties of dividing by 1 and

dividing a number by itself. Their peers will identify the dividend, the divisor, and the

quotient in each story.

Guided Practice and Modeling Game


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Assessment:I will be observing my students ability to determine how to find quotients during

the game. I will also assess my students ability to write a story using a division property as well

as their ability to identify the dividend, divisor, and quotient and the property illustrated by the

story.

Day 4: How do we use division to problem solve?

Objectives: 3rd






Strategies:

Representing problems with pictures Guided practice and modeling Problem solving graphic organizer

Assessment: I will be using the problem solving graphic organizer to assess my students ability

to identify important information, identify the problem they need to solve, draw a picture to

solve the problem, and check their work for reasonableness. I will be looking for all steps of the

problem solving process.

Day 5: Assessment- Summative assessment for this weeks skills (formative for next weeks

skills). I will be using a traditional multiple choice test with EOG style problems.

Day 6: How can you apply your knowledge of division facts to perform mental division?

Objectives: 4th

Grade Mathematics Competency Goal 1: The learner will read, write, model,

and compute with non-negative rational numbers.

1.04 Develop fluency with multiplication and division:c. Strategies for multiplying anddividing numbers.d. Estimation of products andquotients in appropriate situations.e. Relationships between operations.

Strategies


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Modeling of mental division math using fake money. Students will connect what theyknow about money and place value to dividing larger numbers.

Guided Practice and modelingAssessment: I will provide all of my students with patterns of division problems such as 355;

3505, and 3,5005 and ask them to describe the pattern. I will ask them to predict the next 2events in the pattern and then write their own pattern. Students will then switch with a partner

and solve each others division problems.

Day 7: How can you use estimation to create simpler division problems?

Objectives: 4th

Grade Mathematics Competency Goal 1: The learner will read, write, model,

and compute with non-negative rational numbers.

1.05 Develop fluency with multiplication and division:c. Strategies for multiplying anddividing numbers.d. Estimation of products andquotients in appropriate situations.e. Relationships between operations.

Strategies

Group work Real-world connections using food levels to determine caloric intake per serving Guided Practice and Modeling

Assessment: Students will demonstrate their ability to estimate and divide by 2, 5 and 10 todetermine the healthier servings of various food items using nutrition labels.

Day 8: How do you divide numbers that result in remainders, and what do these remainders

mean?

Objectives: 4th

Grade Mathematics Competency Goal 1: The learner will read, write, model,and compute with non-negative rational numbers.

1.06 Develop fluency with multiplication and division:c. Strategies for multiplying anddividing numbers.d. Estimation of products and quotients in appropriate situations.

e. Relationships between operations.Strategies

Work with manipulatives to divide counters into equal groups and identify leftovers. Group discussion about the meaning of remainders


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Independent practice Game

Assessment: Students will be presented with a number of story problems that result in

remainders. They will be asked to judge what should happen for each remainder. I will assess

their ability to perform the operation as well as use judgment making decisions with theremainders. For example, I will pose a problem such as: Ethan is throwing a party. He is

inviting 25 people and needs to buy cups for everyone. There are 10 cups per package. How

many packages does Ethan need to buy? How did you figure this out?

Day 9: How can you connect your knowledge of division to the long division algorithm?

Objectives: 4th

Grade Mathematics Competency Goal 1: The learner will read, write, model,and compute with non-negative rational numbers.

1.07 Develop fluency with multiplication and division:c. Strategies for multiplying anddividing numbers.d. Estimation of products and quotients in appropriate situations.e. Relationships between operations.

Strategies

Students will work with base ten blocks and money to connect their knowledge of thebase ten system to the traditional division algorithm.

Guided practice and modelingAssessment: I will be assessing my students ability to model a division problem with

manipulatives, transfer it to graph paper, and show and solve it in algorithm form.

Day 10: Assessment- Summative assessment for this weeks skills (formative for next weeks

skills). I will be using a traditional multiple choice test with EOG style problems.

**Note** This unit overview was used primarily as a planning and brainstorming tool. The

actual lessons planned and used turned out to be quite different. Therefore, the days, objectives,

and activities actually completed do not completely match up with this overview.


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Erica Sigley SALEM COLLEGE STUDENT TEACHER CANDIDATE FALL 2011

Division

Division as Equal Sharing

GRADE/CLASS: 4th Grade SUBJECT AREA: Mathematics

UNIT TOPIC: Division DAY: 1 (one day)

Desired learning outcome(s): Students will learn how to divide by sharing objects into

equal groups. They will demonstrate their knowledge by solving a story problem,

drawing a picture showing the equal shares, and writing an appropriate division sentence.

Essential question(s) from learning objective: How can you use sharing to solve

division problems?

NCSCOS goal and objective(s) assessed: (note: the 4th grade NC pacing guide lists 3rd

grade objectives for the first week of division; therefore, I am listing 3rd grade objectives

for this lesson to maintain consistency)

3rd





NCSCOS goal and objective(s) addressed:

4th

Grade Language Arts Competency Goal 2: The learner will apply strategies and skills

to comprehend text that is read, heard, and viewed.



Learner prior knowledge/ learner background experiences: Since the lessons duringthis first week are a review of third grade standards, students should already be familiar

with the concept of sharing to achieve division. However, I will still review this

thoroughly for students who need extra help. Therefore, the main background thatstudents need for this lesson is the ability to create equal size groups.

Materials and resources needed:The Doorbell Rangby Pat Hutchins


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Paper Plates

Cookies

Document CameraActiv Board

Manipulatives

Think Together Center Activity from EnVisions Math (lesson 4-1)Division/Equal Shares homework fromwww.superteacherworksheets.comVirtual Cookies Powerpoint

Teaching strategies

anticipatory strategies (background knowledge)I will begin anticipatory strategies by getting a general idea of my students view of

division. I will begin by asking questions such as what is division? How can you divide?

What situations will require division? How do you know when to divide? What are some

strategies you can use? Etc. These questions will help students begin thinking about

division, and they will also help me judge their comfort level with the topic.Next, I will introduce the topic for the day which is dividing by sharing by reading

aloud the bookThe Doorbell Rang to my class and using the document viewer to show

my students the pictures. I will read the book all the way through once, and then we willdiscuss some observations from the book. I will ask questions such as how many cookies

did each person get at the beginning of the story? What happened as more and more

people showed up at the house? Why did the number of cookies each person got get

smaller as more people showed up? As I ask these questions, I will informally pre-assessmy students ability to link division concepts to the story.

developmental strategiesI will begin developmental strategies by rereading The Doorbell Rang and having groups

of students model the story activities with their cookies and paper plates. I will divide the

students into groups of four or five based on their clusters. I will give each the

appropriate number of plates and cookies according to the story. Students will divide thecookies evenly between the plates and write a division sentence based on this model. I

will model and explain to students how to do this with the first couple of scenarios using

a powerpoint with images of cookies and plates. As more people arrive, I will give mystudents more paper plates, and they will be required to share out the cookies evenly

between those plates and then draw a picture and write the appropriate division sentences

on a piece of paper. While the transition from hands-on manipulatives, to pictures, to

division sentences is useful for all students, my ESL students will benefit from this visualbridge to the more abstract concept (process differentiation for ESL students). Once

we are finished with the story, students will work in pairs to discuss the patterns and

trends they see on their paper. Students may also share the cookies evenly with theirclusters and have a snack while working. I will give students about 5 -10 minutes to

discuss this and then we will meet back together as a whole group to discuss our

observations. During this time, I will introduce some of the vocabulary we will be using

throughout the unit: dividend, divisor, and quotient. I will ask students questions abouttheir observations while also modeling how to use the appropriate vocabulary. I will ask
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questions such as what happened to the quotient as the divisor got larger? Were some

problems easier to divide than others? Why? Etc.

Once we have finished the above activity, I will give students about 15 minutes for

guided/independent practice. I will project several story problems on the board that

require sharing to solve. I will also provide each student with manipulative counters.Students will use these counters to solve the problems and will then record a drawing andan appropriate division sentence on paper for each problem. I will be checking each

problem to assess my students understanding of the concept. I will also have my

students record a problem on a notecard that I will assess to group my students forintervention or practice during concluding strategies.

concluding strategiesDuring concluding strategies, students will either be playing Think Together (seeattachment) or meeting with me for intervention and reteaching. Students who play

Think Together will be completing letters A, C, and E to divide counters and determine

the number of counters in each group. Students will record their work on a sheet of paperso that I may assess their participation. Groups or students who finish this activity

quickly will then write story problems to go along with each sharing scenario (Product

differentiation for advance learners).While students play this game together, I will meet with my students who need

reteaching and intervention and model for them how to divide a group of counters into

groups. During my modeling, I will think aloud as I work so that my students can hear

my thought process. I will also draw a picture and write a division sentence for eachaction. I will first have students watch me. Next, they will use their own manipulatives

to follow along. Next they will follow verbal instructions, and finally, they will complete

the activity independently (process/product differentiation for struggling learners).For homework, students will complete aDivision/Equal Groups worksheet from

superteacherworksheets.com. This sheet is excellent for all learning types because it

requires students to solve word problems by first drawing pictures and then writing the

division sentences.

AssessmentAnticipatory strategies: During anticipatory strategies, I will be informally assessing mystudents responses to my questioning as well as their ability to relate the story to

mathematical processes. I will be using my observations to guide further questioning and

review.

Developmental strategies: During developmental strategies, I will be assessing a numberof things. First of all, I will be assessing my students process in determining how to

share out the cookies and write appropriate division sentences. I will be circling the room

and providing assistance as needed during this part. I will also be informally assessingmy students responses and observations about the trends in the patterns of cookies being

shared out. Finally I will be using my students work during independent practice to

assess their ability to use sharing to solve a word problem and write an appropriate

division sentence. I will be using this quickcheck as a formative assessment to determinewho will need extra instruction and who understands the activity well. I will place my


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students into three groups: Got It, Almost There, and Needs Help. I will be using a

checklist to keep track of these groups.

Concluding strategies:During concluding strategies, I will be assessing my studentsability to work with many different grouping situations as well as their ability to relate

them to story problems. I will also be assessing my struggling learners as they follow my

modeling examples and learn how to work with the problems more and moreindependently.

Wrap-up: Finally, during wrap-up, I will be assessing my students ability to apply what

they have learned by creating and solving their own problems.

EC accommodations/modifications to strategies or assessments

(refer to IEPs or 504 plans)

The accommodations and modifications for my students with IEPs and 504 plans consist

of preferential seating, extended time, and read-alouds on tests and assignments.

Wrap-up and reflection by the students

For wrap-up, students will be asked to write and solve their own division problem usingsharing on index cards. We will use these cards towards the end of the unit to review for

our assessment. Struggling learners will write a simple division sentence and its answer.

Average learners will write a simple word problem that involves sharing to divide.Advanced learners will write two related word problems that require the solver to solve

each and make a judgment about the outcome.

Resources

Pearson Education Inc. (2010). enVision Math North Carolina: 4th

Grade Interactice

Textbook: Teachers Edition. Retrieved fromwww.kz.com

Equal Groups/Division (2011).Basic division worksheets. Retrieved from

www.superteacherworksheets.com
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There are 12 cookies and 12

plates. I was able to use the

activboard pen to move the

plates and cookies to model

the sharing problems.


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Sample Sharing Word Problems

1.Beth is making cupcakes for her friends birthday party. She makes 18 cupcakes. If 9people attend the party, how many cupcakes will each person get if Beth gives each

person the same number of cupcakes?

2.Justin is playing a card game. Each player gets the same number of cards. If there are 35cards, and Justin is playing with four of his friends, how many cards will each player get?

3. Six friends went out to dinner together. Their dinner cost $54. If each friend paid thesame amount for dinner, how much did each one pay?

4.Brittany wants to make money walking dogs to buy a new game she wants. If the gamecosts $28 dollars, and 4 of her neighbors have dogs, how much should she charge to walk

each dog in order to make enough money to buy the game?

Sample basic facts problems to be modeled for struggling learners

1. 35 7 =2. 56 8 =3.27 3 =

4.


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Skill/Objective __________________________________________

Date__________________

Student Name Got It! Almost There Needs Help

Comments

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3. _____ ____________ _________

4. _____ ____________ _________

5. _____ ____________ _________

6. _____ ____________ _________

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10. _____ ____________ _________11. _____ ____________ _________12. _____ ____________ _________13. _____ ____________ _________14. _____ ____________ _________15. _____ ____________ _________16. _____ ____________ _________17. _____ ____________ _________18. _____ ____________ _________19. _____ ____________ _________20. _____ ____________ _________21. _____ ____________ _________22. _____ ____________ _________23. _____ ____________ _________24. _____ ____________ _________25. _____ ____________ _________


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Work Samples and Assessment

Quickcheck Checklist

Ms Work SamplesMath Journal Sample


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Quick Check Card

Think Together Work


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Homework

Notes and Assessment


M did quite well during all parts of the lesson. She worked well with her group and

recorded her drawings and division sentences on her classwork to illustrate how the

cookies were being divided onto the plates. This showed me that she understood how to

move from the concrete to the abstract. M also answered several questions during mypreassessment. She was placed in the Got It! Category for my quickcheck because she

completed the division problems correctly. Her work, however, showed more of a

repeated subtraction strategy than an equal sharing strategy. I decided, however, that herwork during the The Doorbell Rang, activity demonstrated her ability to think of division

as sharing. It was my fault for not specifying to use pictures showing equal groups to

divide. During the Think Together activity, M only wrote the answers to the questions

although I had asked students to also write the corresponding division sentence. Heranswers are correct, however. Based off of Ms homework assignment, I was able to see

that she had mastered the concept because she got 5 of the 6 problems completely right.

She did however, make one minor mistake and list that there was a remainder for number2 on the equal groups worksheet. I have noticed in the past that M has the tendency to

make careless mistakes, and based on how well she did on the rest of the problems, it is

likely that this is one of those mistakes. I often have to encourage M to review her work

and check over it. I will continue to encourage her to be more careful.


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Cs Work SamplesMath Journal

Quick Check Card


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Think Together Work

Homework


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Homework Close-up


C has the tendency to be inconsistent with his work. He will have days when he does

very well during one part of a lesson, and then struggle with the next. This was one ofthose days. Although he participates with his group, he rarely raises his hand to share

answers in class. Therefore, I have a difficult time assessing his understanding until I get

a chance to observe him individually or in his small group. He also did not draw picturesfor our book activity, so I was unsure of his ability to connect the story with math. I

placed C in the Almost There group after reviewing his quickcheck because he solved the

problem correctly but did not complete the drawing. Although I could see that he wasable to solve and write the division problem, although he did not use pictures. The

sentence he wrote for his answer did show me that he is able to think of division as

sharing. I chose to place him the Almost There group based on his past performance.Although it seems that he understands quite well, I know that in the past his performance

is inconsistent, so I wanted to make sure to give him plenty of practice as well as remind

myself to keep my eye on him. C did very well during the Think Together activity. He

was able to answer several of the questions, and he also wrote a word problem for one ofthe problems he solved. The activity was intended to be an extension activity if studentsfinished early. No one finished completely, but I was glad to see that C attempted the

word problem anyway. His written problem shows that he understands equal shares. C

continued to struggle with drawing pictures to represent equal sharing on his homework.I will continue to have him work with manipulatives and then draw what he models on

paper to reinforce his ability to connect graphic representations with math.


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Bs Work SamplesMath Journal


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Quick Check Card

Think Together Work


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Homework


B has been doing exceptionally well. I would like to see her participate more in our

discussions so that she can practice her language skills; however, her math computation isvery good. Although she has some trouble with the language of word problems, she is

able to write and solve the appropriate division sentences with a little guidance. Her

quickcheck showed that she understood equal shares quite well. She solved threeseparate problems on her index cards, and they were all correct. Her pictures also

demonstrate her ability to think of division as equal sharing. The main reason I included

her in my reteach group was to provide her with more direct language practice. Modelingand small group work builds her confidence to speak. Having the problems read aloud is

also very beneficial for her. She is also very helpful with my other Karenni students, and

assisting them is also great practice for her. She showed her understanding during the

Think Together activity when it only took one time for me to model for her to be able to

solve a problem on her own. Finally, she scored a 100% on her homework,demonstrating mastery.

Reflection by the teacher

Overall, I feel like todays lesson went quite well. I conducted a short preassessment

during anticipatory strategies before beginning my lesson, by asking my students to tellme what they knew about division. I heard ideas such as it can be written two ways, it is


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multiplication backwards, it breaks one bigger group into more smaller groups, it undoes

multiplication, and there might be left overs sometimes. It was clear to me that my

students have a good background in procedural and conceptual knowledge of division.One thing I did notice that we need to work on is using appropriate mathematical

vocabulary such as dividend, divisor, and quotient as well as the ability to discuss

mathematics clearly. Therefore, I have decided that since my students will not require asmuch review as I anticipated, we will spend much of the time in our lessons this weekpracticing how to talk about division and processes. We will still use the same lessons

and activities; however, added emphasis will be on the students ability to communicate

about what they are doing.Before doing my lesson, I was concerned that reading the story The Doorbell

Rang once through before beginning the activity would take too much time; however, I

am glad that I did because the students were able to predict what would happen as more

people rang the doorbell. I heard several students mention that the characters were goingto have to keep sharing their cookies as more people showed up and that each of them

wasnt going to get very many. I was glad to see that they made this observation and

they were able to anticipate what we would be doing in the activity. I am also glad that Iread the story ahead of time because it made the activity go a lot smoother. Knowing the

story ahead of time helped them realize that they would be adding plates and sharing out

the cookies each time the doorbell rang.During the activity, students were engaged and worked well together. I heard

many of them talking about strategy as they solved each problem. Some students put all

of the cookies back into a pile and started fresh with each sharing activity. Others

figured out how many they would need to take from each plate to accommodate the newplates. Finally, others simply solved the division problem and put the appropriate

number of cookies on the plates. Although, my intention was for student to using their

experience modeling a sharing activity to write a division sentence, I was happy to seethat many of my students knew how to translate the story into a division sentence right

off the bat. This shows me that they are able to solve story problems. The biggest

difficulty I had during this part of the lesson was having students record their work on a

separate sheet of paper. I had to remind students many times to write the correspondingdivision sentences in their notebooks. I explained that I wanted them to make the

connection between the story and the math. I think they may have been unsure of what to

do at first, so I modeled the story scenarios with them after each time the doorbell rangusing a powerpoint I made that allowed me to move pictures of cookies onto pictures of

plates. After each scenario, we worked as a class to model the problem and write a

division sentence. If any of the groups had incorrectly shared out the cookies or written a

division sentence incorrectly, they were given time to fix it after we worked through eachas a class. By the end of the activity, even students who had trouble in the beginning

understood well.

I was unfortunately running low on time and was not able to provide as muchguided and independent practice as I would have liked. I still wanted to perform the

quickcheck so I had students choose one of the sample word problems to solve on an

index card. I realized that I had made a mistake by not asking them to draw a picture to

solve the problem. Since many of them are already comfortable with basic division, theywere able to come up with the division sentence right away and solve it. This is not


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necessarilybad, but it doesnt show me their ability to think of division as making equal

groups. If I were to do this again, I would specifically state that I want them to draw a

picture and write a division sentence. Luckily, the homework that I assigned includes aplace for students to draw their pictures, and I did emphasize that to them. Overall, the

quickchecks were mostly correct. I had a few students forget to put their name on their

card (this is something I struggle with daily, though it has gotten better). Fortunately, Iknew enough from observing my students who would need extra help.The last thirty minutes of class were eventful, and I felt pressed for time. After

the hour long break away from math for lunch and recess, we started working on the

Think Together activity. Rather than use a separate source for problems, I used the ThinkTogether activity to work with my ESL and struggling students as well. However,

instead of having them work with partners, I worked with them in a small group. The

modeling worked very well. By the third problem, my students were able to able to

complete the problem and write a division sentence for it on their own. Unfortunatelythis is all we had time for because I had two students vomit in class within half an hour of

each other. There is bug going around my school right now, and students are getting sick

often. When these kids got sick, I had to walk them to the nurses office and call for acustodian to clean up. It took a while to refocus the class. I will be looking forward to

seeing their homework performance so that I can assess their understanding. I was also

unable to get to the wrap-up assignment where students would have been asked to writeand solve their own sharing problems.

If I were to redo this lesson, I would make sure to be much clearer when I explain

directions to my students so that they are all on the same page. When students ask if I

want them to show their work, I will need to be much more specific about what kind ofwork I would like to see. For this lesson, I would ask my students to show me a drawing

depicting sharing. This would help me assess not only if my students can solve division

problems, but also if they can do it by creating equal groups. I would also make some ofthe problems that I give my students more difficult, assuming I would be working with

the same students. I know now that I will need to use more difficult problems during the

review week. Although we are still reviewing third grade skills, we will review them at a

higher level of complexity throughout the remainder of the unit. I also have the tendencyto overplan for lessons. In other words, I plan too much for what I have time for. I know

that it is good to have backup activities in case students finish quickly, but I will need to

make sure that these activities are not really vital to the lesson.


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Division

Division as Repeated Subtraction

GRADE/CLASS: 4th

grade SUBJECT AREA(S): Mathematics


Desired learning outcome(s): Students will relate division with repeated subtraction.

They will demonstrate their understanding by using counters, drawings, and number lines

to solve problems requiring repeated subtraction.

Essential question(s) from learning objective: How can you use subtraction to solve

division problems?

NCSCOS goal and objective(s): (note: the 4th

grade NC pacing guide lists 3rd

grade

objectives for the first week of division; therefore, I am listing 3rd

grade objectives for

this lesson to maintain consistency)

3rd



1.03 Develop fluency with multiplication from 1x1 to 12x12 and division up to

two-digit by one-digit numbers using:


Learner prior knowledge/ learner background experiences: Students should know the

vocabulary for quotient, dividend, and divisor. They should also know how to subtractand show their subtraction using counters and number lines.

Materials and resources needed:

ActivBoard Counters Student notebooks Notecards for quickcheck Computer with internet access EnVision 4th grade topic 4-1 Think Together center activity Video fromhttp://www.eduplace.com/math/mw/models/tm_3.html.Teaching strategies

anticipatory strategies (background knowledge)During anticipatory strategies, I will review with students how multiplication is repeated
http://www.eduplace.com/math/mw/models/tm_3.htmlhttp://www.eduplace.com/math/mw/models/tm_3.htmlhttp://www.eduplace.com/math/mw/models/tm_3.htmlhttp://www.eduplace.com/math/mw/models/tm_3.html


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addition. We will solve a problem for multiplication using repeated addition. For

example,Mary is baking cookies. She can make 6 cookies per batch, and she makes 7batches. How many cookies does Mary make? We will work together to model on theActivBoard and with counters how to solve this multiplication problem using repeated

addition. I will then write an accompanying division problem using repeated subtraction.

For example,Mary has finished making her cookies. She wants to give the cookies awayas presents. If she gives 6 cookies to each friend, how many friends can she give cookies

to? Students will solve the problem using their counters and discuss with their group

how they solved the problem. We will then work together to solve the problem. I will

ask my students questions such asHow did you solve this problem? What operation did

you use to solve this problem? Walk me through this problem, explaining each step

clearly. Did you use subtraction to solve this problem? We will then discuss briefly how

we can use subtraction to solve division problems. I will explain that this strategy is

called repeated subtraction and that we will be learning how to use it during the lesson. developmental strategiesDuring developmental strategies, I will provide my students with a number of problemsthat they can solve by using repeated subtraction with their counters. I will model a

number of these for my students and then provide them the opportunity to practice in

small groups and then on their own. Students will write the repeated subtraction sentenceand related division sentences for each problem. I will go over each problem with

students as well.

Next I will show my students a short video demonstrating repeated subtraction on a

number line fromhttp://www.eduplace.com/math/mw/models/tm_3.html. This videoprovides a nice visual and guiding questions to help students understand repeated

subtraction using this method. I will ask my students follow-up questions such as how do

you use a number line to show the division? How do you determine how many groups

are created? What kinds of questions will this be helpful with?

To provide a direct visual for my ESL and struggling students, I will model a

problem on the activboard using a frog, a pond, and lily pads. The pond will have a

number line written across it. I will state a problem such as A frog is trying to cross a

pond. The frog can hop across a distance of 4 spaces onto a lily pad. How many times

will the frog need to hop to reach the other side of the pond? We will solve several

problems like this to create a visual model for the students (process differentiation for

struggling and ESL students).

I will now provide my students with a number of word problems that they will

solve using the number line method for repeated subtraction. I will model a couple of the

problems for my students as they follow along in their notebooks. For each problem,students will also be writing the appropriate division sentence. Students will then work

in small groups or pairs to solve additional problems. Finally, students will work

independently to solve a problem, so I can see what they are able to do. I will ask mystudents to complete a quickcheck card to see how well they understand the concept. For

this card, students will solve a problem on an index card. One side will show the

students work. They can choose to use either the counter or the number line approach.

On the other side of the card, the students will write the related division sentence. I willbe using these cards to determine my grouping during concluding strategies.
http://www.eduplace.com/math/mw/models/tm_3.htmlhttp://www.eduplace.com/math/mw/models/tm_3.htmlhttp://www.eduplace.com/math/mw/models/tm_3.htmlhttp://www.eduplace.com/math/mw/models/tm_3.html


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my students comprehension of this days lesson and strategy as well as their retention of

information from the previous day.Wrap-up and Reflection: Finally, during wrap-up, I will assess my students overallunderstanding of the concept by assessing and grading their word problem or lily pad

activity.


(refer to IEPs or 504 plans)

The accommodations and modifications for my students with IEPs and 504 plans consist



To wrap-up the lesson and provide me with an assessment of their understanding.Students will be completing several short activities. My advanced students will write and

solve a problem using repeated subtraction. My average students will solve a pre-written

pre-written problem about a frog trying to cross a pond using repeated subtraction. Theywill draw the picture and write how many lily pads will be needed to cross the pond. All

students will be required to show their work and write the accompanying division

sentence. (Product differentiation for all learning levels).

Resources

Houghton Mifflin Company (n.d). Teaching model 10.2: model division as repeated

subtraction [video file]. Retrieved fromhttp://www.eduplace.com/math/mw/models/tm_3.html.

Pearson Education Inc. (2010). enVision math north carolina: 4th grade interactice

textbook: teachers edition.Retrieved fromwww.kz.com
http://www.eduplace.com/math/mw/models/tm_3.htmlhttp://www.eduplace.com/math/mw/models/tm_3.htmlhttp://www.kz.com/http://www.kz.com/http://www.kz.com/http://www.eduplace.com/math/mw/models/tm_3.html


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Work Samples and Assessment

Ms Work SamplesQuick Check

Word Problem


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Homework


M has been participating in class more often lately. Her confidence seems to be highwhen she knows that she understands the material. She has also been doing wellclarifying answers that other students provide. According to my observations of her as Iask questions and conduct guided practice, she seems to understand the information verywell. This is confirmed by her performance on the quickcheck. She was able tocomplete two of the problems I assigned before lunch, although I only required one. Shegot the first problem correct by using the number line approach. Her number linestrategy for the second problem was correct; however, she forgot to subtract the last 25cents when she ran out of room on the index card. This resulted in her answering 19 for

$5 divided by $.25. If she were to check her work more carefully, she would haverealized this mistake. I will continue to encourage her to be more careful with her workand check over her solutions when she is finished. Ms performance on the quickcheckplaces her in the Almost There group simply because she will need to learn to be morediligent. M also demonstrated how good she is in math with her word problem I assignedas the concluding activity. Without prompting from me, M wrote a two-part wordproblemJack had 58 apples. Sam had 28 apples. They combined them and put them in 6groups. How many apples were in each group? This problem shows that she is able to


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think through multi-step problems. The main criticism I have of her problem is that it

shows a problem of equal shares rather than repeated subtraction. Despite this, it still

shows understanding of situations that call for division. Finally, Ms homeworkdemonstrates that she has a decent grasp on the information. She got all problems correct

except for one, and the one that she answered incorrectly was solved using a correct

method; however, she over counted the number of times she subtracted 4 from 12. 12divided by 4 is a problem she should already be able to solve mentally, so I willencourage her to stop and think more carefully about whether or not her answers make

sense to her. Since Ms mistakes seem to be inconsistent, it is likely that they are more of

careless origin rather than not knowing how to solve the problem.

Cs Work Samples

Quick Check


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Word Problem

Homework


I am still having trouble encouraging C to participate in class discussions. When I call on

him, he seems to be lost. Based on past performance, I would have expected him to be


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performing on the average learner level; however, he seems to be having a difficult time

with the division unit so far. Cs quickcheck shows that he is having difficulty translating

word problems into division sentences. He also tried to solve both problems, but theywere both incorrect. Im not quite sure how C arrived at 5 9 = 9 for the problem there

are 45 kids in the 4th

grade. How many teams of 5 kids can be made? The other problem

showed a similar pattern 5 4 = 4. I had planned on working individually with C duringthe after lunch reteach session; however, with my time cut short, I was unable to. Hisword problem demonstrates that he understands appropriate situations for division;

however, similar to M, his scenario involves sharing rather than repeated subtraction.

Finally, some of Cs earlier problems seemed to resolve on his homework. For most ofthe problems, he was able to correctly translate word problems into division sentences

and solve these with pictures. He did make a few mistakes; however, he is much

improved from where he was earlier in the quickcheck. I will continue to work with C on

basic facts and on translating word problems into math sentences.

Bs Work SamplesMath Journal

These are Bs notes about the relationship of the divisor and quotient when the dividend

remains the same.


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Quick Check


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Word Problem

Homework


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B is still tentative about sharing her answers; however, she does volunteer to share from

time to time. I make sure to call on her when I see her hand up so that I can build her

confidence. Bs quickcheck showed that she is able to use pictures to help her solvedivision sentences. B made a mistake on her horizontal division sentence and wrote 4 5

= 9 but wrote the vertical format correctly. It is possible that she simply for to write the 5

in 45. She also solved the problem correctly. It appears that B attempted to use the

number line strategy to solve the quickcheck but that she erased it before finishing. Shestarted the strategy correctly. It does seem that she started to run out of room, so maybe

that is why she erased it. I had still planned to include B in my reteach group to provide

more direct help with the language of math; however, this reteach time was cut short.

Instead of asking B to write her own word problem, I gave her a division problem tosolve. She solved this by both drawing a picture and using a number line. Both

strategies were used and executed correctly resulting in the correct answer. Her work

demonstrated mastery of the lessons concept. Finally, B showed that she understoodhow to translate word problems into division sentences on her homework which is an

important accomplishment considering her limited English. She did not use pictures to

show her work; however, to differentiate for language ability, we are not as strict withour ESL students regarding following written instructions since they may not be fully

understood. Overall, B is well on her way to performing very well throughout the

division unit.


Todays lesson did not go quite as planned, and I was forced to simplify it a bit.Fortunately, I had some help with my ESL differentiation, and my students also seemed

to catch on quite quickly. As I mentioned in my reflection from day 1, I would like to

spend some additional time working with my students on their ability to communicate

about mathematics. Therefore, I began my lesson today with a short mini-lesson aboutthe relationship between divisors and quotients when dividends remain the same. We did

this by discussing how the number of cookies on each plate from the previous lesson

changed as more people showed up. I emphasized that the total number of cookiesremained the same. The students remarked that the number of cookies each person got

was smaller the more people there were to share them. To illustrate this concept using

math, I wrote 36 9 on the board and had my children solve it. I then asked them to

predict what would happen to the quotient if I decreased the divisor to 6, for example.My students predicted that the quotient would increase. I then did the same thing with

increasing the divisor and again had my students make a prediction. Finally, I asked my

students to do a quickwrite in their math journals to communicate the concept theyobserved. Many of my students were able to communicate that when a dividend stays the

same, the quotient will decrease when the divisor increases because the dividend is being

divided out to into more groups. Many of my students also had difficulty communicatingtheir idea; however, I will be incorporating quickwrites into my lessons more often to

provide my students with more practice. In addition, I like to have work for my students


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to begin as they come into my classroom in the morning. For the next several mornings,

I have decided to include math quickwrites as morning work. Although they will be done

the following day, I will include them in the current lessons assessments since they haveto do with the content of that lesson. These are not included in the lesson plans because I

decided to do them after I had finished writing the lesson plans.

As can be expected, this mini-lesson took from the time that I had planned for my

repeated subtraction lesson, but overall, I feel like I was able to cover a substantial

amount of information. As planned, I began with a review of repeated addition using a

question about batches of cookies. As I was reading the problem aloud, I realized that Iwould need to explain batch to my ESL students. It took a while to get students to use

repeated addition to solve the problem because they just wanted to use traditional

multiplication. I generally do not have a problem with this; however, I wanted to include

repeated addition so that we could relate it to repeated subtraction in division. We werethen finally able to move on to the division problem. Students seemed to have trouble

figuring out what to do with the manipuatives at first since the strategy today was

different from yesterday. When I noticed that groups were having trouble, I visited eachone and modeled how to begin the problem. They caught on quickly and were able to

complete it on their own. There were still some students who did not quite understand

what I meant by repeated subtraction, so I thought it would be good to show the videoand the number line strategy earlier than planned. This worked quite well because the

students who had trouble with the manipulatives understood the number line method with

ease. I was excited to see that each of my students found a strategy that worked for them.I did not end up using the frog illustration for my struggling and ESL learners because

my ESL learners were getting one-on-one attention from a school assistant who has

experience working with ESL students. She was providing modeling and assistance

throughout the instructional part of the lesson, so I did not use my ESL differentiation forpart of the lesson. The rest of my students seemed to understand the other methods quite

well. The quickcheck showed that most of my students were able to use at least one of

the strategies to successfully solve a problem. I am still noticing that my students are

mixing up the dividend and divisor in the division sentences, and I will draw attention tothat during tomorrows lesson. They are still getting the correct intended answers;

however, they are not reading or writing the division sentences correctly.

When I originally planned this lesson, I neglected to include Math Superstars Q & A inmy plans. We do this session every Wednesday, and I should have remembered it.

Because of the time I spent providing assistance to my students for these questions, I only

had about 10 minutes left to the math block to complete my concluding strategies. I

decided against doing the Think Together activity again and simply asked my students towrite a division sentence that can be solved using repeated subtraction. They were asked

to complete these as part of their homework if they did not finish. Instead of asking my

ESL learner to write her own problem, I wrote a division sentence for her to solveshowing her work for repeated division.

If I were to do this lesson again, I would be more careful of the language I use in myword problems. While exposure to words such as batch is valuable for my ESL students,

explaining the meaning of the word did detract a bit from the math instruction.


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Vocabulary is, however, a meaningful integration so I will just need to consider time

limits when choosing whether or not to include uncommon vocabulary. I would also

model how to solve a repeated subtraction problem using the manipulatives before tryingto see if my students could solve it on their own, especially since the strategy differed

from that of the day before. I, as usual, also need to simplify my lessons and plan for a

shorter amount of time. I have the tendency to plan for more than what I have time for.


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Meaning of Division: Choosing a Strategy

GRADE/CLASS: 4th

Grade SUBJECT AREA(S): Mathematics


Desired learning outcome(s): During this lesson, students will learn how to determine

the appropriate strategy (sharing or repeated subtraction) for word problems. Students

will demonstrate their understanding by solving and writing several word problems and

discussing which strategies they used.

Essential question(s) from learning objective: How do you use story problems to help

you choose appropriate division strategies?

NCSCOS goal and objective assessed: (note: the 4th grade NC pacing guide lists 3rd

grade objectives for the first week of division; therefore, I am listing 3rd grade objectives

for this lesson to maintain consistency)

3rd





Learner prior knowledge/ learner background experiences: Since this lesson is based

on 3rd

grade standards, much of the information will be review for students; however, tounderstand the relationship between division, subtraction, and grouping, students willneed to understand subtraction and be able to identify when groups are equal. They

should also be proficient with multiplication since division is the inverse of

multiplication. Although this inverse relationship is not addressed in this lesson,

knowing their multiplication facts will still help them to divide more efficiently. Finally,this lesson assesses student abilities to apply the various division strategies they have

learned over the past couple days.

In addition to this lesson, students will have about 5 minutes of basic division factspractice.


EnVision Math books/workbooks and companion website Counters Division Dilemmas Graphic Organizer EnVision leveled homework (reteach, practice, and enrichment 4-1)


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Teaching strategies

anticipatory strategies (background knowledge)During anticipatory strategies, my students will compare and contrast the two strategies,

sharing and repeated subtraction that they have learned. I will remind my students about

the problems they have solved so far using each one, and we will work together tocomplete a venn diagram comparing and contrasting the strategies and problem types on

the ActivBoard. To help my students, I will ask questions such as, what did you do to

determine how many cookies each person received? How is this different from how you

figured out how many groups of three you could make with 24 people? How did you

determine how many people could play a card game if each person needed 12 cards?

When is repeated subtraction most useful? When is sharing most useful? Etc.

Eventually, I will sum up the conversation by discussing how we use repeated subtraction

when we know how many objects are in an unknown number of groups and sharing whenwe know how many groups have an unknown number of objects.

developmental strategiesDuring developmental strategies, my students will be using manipulatives to model a

number of division word problems. I will model how to choose a strategy and solve a

problem using several different examples of problems and a graphic organizer (seeattachment 1) to assist in the decision. Once students are comfortable using the

manipulatives to solve the problems with my guidance, I will pair them up and present

them with a number of story problems that they will solve with manipulatives. They willthen complete the graphic organizer by listing the total number of objects, the number of

groups, the number of objects in each group, the strategy chosen, a drawing, and a

division sentence for each problem. During this time, I will be circling the room

providing assistance to my students as needed.Finally, I will provide my students with several repeated subtraction problems

and a sharing problems from EnVision 4-1 problem solving to work on independently.

My students will draw a picture and solve the problems to demonstrate their

understanding. They will also write a division sentence to describe the problem andexplain in words how they solved the problem. To help my ESL students, I will provide a

prewritten sentence for each explanation with blanks for them to fill in the numbers and

groups for the specific problem. For example, There are _________ objects separatedinto ___________ groups of __________. I used the ___________ strategy, and the

division sentence is ____________.(product differentiation for ESL students). I will

be assessing these papers to determine my intervention groups for the concluding

strategies of this lesson.

concluding strategiesDuring concluding strategies, my students will be writing their own word problems foreach a repeated subtraction problem and a sharing problem. They may use their graphic

organizers to help them. When they are finished, the will switch problems with a peer

and solve each others problems and explain how they got the answers. Students whohad trouble with my quick-check in developmental strategies will work with me to

review how to model division problems with manipulatives. Rather than start with a


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story problem during this reteach/intervention, I will be working with division sentences

only to help my students. I will provide my students with a division sentence such as 12

4, and ask them to model the problem and find the answer using counters. As studentsbecome more comfortable, I will ask them to start drawing pictures instead of using

manipulatives. I will also have students begin practicing independently as I observe them

becoming more comfortable (process differentiation for struggling learners). As mystudents become more comfortable, I will ask them to tell me a math story to represent

the division sentence. I will then write this sentence down, and the students I am working

with will try to solve it.

Finally, I will assign my students homework that I will use to assess studentunderstanding. I will assign tiered homework depending on student understanding and

ability. My students who are having difficulty with the concept will complete reteach 4-1

since it reviews the information from the day (product differentiation for ESL and

struggling learners). My average students will complete practice 4-1, which asks themto solve a number of word problems. Finally, my advanced learners will complete

enrichment 4-1 since it presents a real-life situation that requires students to use division

to analyze several situations and make a judgment based on the information (productdifferentiation for advanced learners

AssessmentAnticipatory strategies: during anticipatory strategies, I will informally assess my

students responses to questions to determine their ability understand story problems and

choose appropriate strategies to solve the problems. I will use student answers to guidemy questioning.

Developmental strategies: during developmental strategies, I will informally assess my

students ability to follow along with my modeling. I will use this assessment to

determine how much more explicit modeling I should do as well as determine who willmost benefit from guided practice during the activity in pairs. Finally, I will collect and

assess the quickcheck index cards to determine the groupings for Think Together and

decide who needs extra help and reteaching. I will also assess my students completed

graphic organizers to determine how helpful the tool is.Concluding strategies: Finally, I will be assessing my students homework performance to

assess how much we should review, who I need to work with to provide further

reteaching, and how difficult successive lessons should be.Wrap-up: I will assess my students ability to write an appropriate division problem.


(refer to IEPs or 504 plans)The accommodations and modifications for my students with IEPs and 504 plans consist



To wrap-up the lesson, I will be asking students to write and submit a division problem

on an index card that I will use to compile a study guide for the end of unit assessment.


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Resources

Pearson Education Inc. (2010). enVision Math North Carolina: 4th

Grade Interactice

Textbook: Teachers Edition. Retrieved fromwww.kz.com

Public Schools of North Carolina. (n.d). Grade 3 black line masters: black line masterspp 1-32. Retrieved fromhttp://mathlearnnc.sharpschool.com/cms/One.aspx?portalId=4507283&pageId=50512

38
http://www.kz.com/http://www.kz.com/http://www.kz.com/


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I did not use this lesson because I felt that trying to differentiate between the two

strategies would confuse my students rather than help them. Instead, I moved connecting

multiplication and division to day 3, and wrote a basic facts practice lesson for the 4

th

day.


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Division

Connecting Multiplication and Division

GRADE/CLASS: 4th Grade SUBJECT AREA(S): Mathematics

UNIT TOPIC: Division DAY: 4 (one day) (this was actually taught on day 3)

Desired learning outcome(s): During this lesson, students will learn how to solve

division problems by using arrays to create several different combinations. This activity

will help to begin developing students association of division with multiplication.Students will demonstrate their understanding by creating different arrays and writing the

multiplication and division fact families for each one.

Essential question(s) from learning objective: How can you use arrays to illustratedivision problems in which objects are separated into equal rows and columns? How do

these arrays relate multiplication and division?

NCSCOS goal and objective(s):

(note: the 4th grade NC pacing guide lists 3rd grade objectives for the first week of

division; therefore, I am listing 3rd

grade objectives for this lesson to maintainconsistency)

3rd

Grade Mathematics Competency Goal 1: The learner will model, identify, andcompute with whole numbers through 9,999.



NCSCOS goal and objective(s) addressed:

4th

Grade Language Arts Competency Goal 2: The learner will apply strategies and skillsto comprehend text that is read, heard, and viewed.



Learner prior knowledge/ learner background experiences: Previous knowledgeabout arrays and multiplication will be a tremendous help during this lesson. In addition,

students should know how to create arrays and divide objects into same size groups.


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Finally, students should be aware of fact families for addition and subtraction, for these

will serve as an example for how to create multiplication and division fact families. All

of these skills will have been addressed in previous lessons.


100 Hungry Ants by Elinor J. Pincez.

Raisins Counters Index Cards Paper ActivBoard Document CameraTeaching strategies

anticipatory strategies (background knowledge)During the anticipatory strategies, I will be activating my students backgroundknowledge by reading them a story about a situation where division can be used to solvea problem. I will read 100 Hungry Antsby Elinor J. Pincez. This book discusses how an

army of ants divides their group of 100 into many different formations to reach a food

supply faster. Since this lesson is about using arrays to connect division andmultiplication and solve division problems, a story is the perfect way for students to

visualize a scenario in which division is useful. Once we have finished reading the story,

I will ask my students questions such as what was the problem the ants were having?How did they try to solve their problem? What strategies did they use? Can you show

their strategies using numbers? What strategy do you think was best? Worst? How

could the ants have been more successful? What mathematical operation were the ants

using? Etc

developmental strategiesDuring developmental strategies, I will be rereading the story, and my students will be

working in small groups of three or four to model the arrays formed by the ants usingraisins. As they do this, they will be drawing the array on paper. I will model how to do

this the first time for my students. I will pause after each section of the story and circle

the room as my students work to create the appropriate array and write a divisionsentence for it. Once we are finished with the story, I will ask my students to observe

their arrays and their division sentences and note any patterns or trends they observe. I

will also ask them to write a multiplication sentence for each array and note any trends

they observe. As a class, we will talk about the arrays and their division andmultiplication sentences. I will ask questions such as how did the arrays change

throughout the story? How did you decide on the division sentence for the arrays that

you created? How did you decide on the multiplication sentences? What do you notice

about the division and multiplication sentences? What do you think would be an

appropriate division sentence to be paired with 6x5=30? What does this remind you of?

What is the fact family for 6x5=30?

Once we have finished with the above portion of the lesson, we will have guided


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practice as a class. We will be using EnVision lesson 4-2 to continue to develop the

relationship between multiplication and division. I will be using the guided practice

portion of the lesson to work interactively with students and provide immediate feedbackfor each question. When we are finished with the guided practice, students will have

time to work independently on the independent practice section. Finally, I would like to

distribute a quickcheck to each of my students to help me assess and decide who needsreteaching and intervention. For my quick check, I will ask my students to draw an arrayand write a fact family for one of the problems in independent practice. I will be using

their responses to create my groups for concluding strategies. The mix of concrete,

visual, and abstract representations will provide differentiated modes of instruction for alltypes of learners as well as learners at various levels of understanding. In addition, the

tactile and visual representations will be beneficial to the ESL students (Process

differentiation for ESL learners).

concluding strategiesDuring concluding strategies, my students will be designing a parade. Each student will

choose a type of performer and a number that can be represented by an array. On a largesheet of paper, each student will draw their parade formation in the form of an array and

write a fact family. Students who demonstrated difficulty during the quickcheck will

work with me to create their parade formations. I will first model an example for them asI think aloud. I will then have them follow along with manipulatives. Finally, they will

use their manipulatives to create a representation of their parade formation and then copy

it onto a piece of paper(product/process differentiation for struggling learners).

Students who finish quickly will create a second formation for their performers using thesame number of people. They will relate this second formation to the fi

Salem EE3 Candidate A

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Transcript of Salem EE3 Candidate A