ED' 088 712

.

DOCUMENT RESUME

\ SE 017 495

AUTHOR Walzl, F. NeilTITLE Using a Potential Method of Maintaining the Basic

Skills of Arithmetic Through the Summer Mcnths toReduce the Review. Time in the Fall.

INSTITUTION Ncola Univ., Fort Lauderdale, Fla.,PUB DATE Nov 73NOTE 28p.; sPracticum repint fot .Ed., Nova University,

Ft. Lauderdale, Fl.; National Ed.D. Program forEducational Leaders

EDRS PRICEDESCRIPTORS

ABSTRACT

MF-$0.75 HC-A1.85'Achievement; *Basic Skills; *Elementary SchoolMathematics; Independent Study; Instruction;*Mathematics Education; *Research; *Retention;Worksheets-

Fourth- and fifth -grade studefits were given 'a seriesof five lessons.for individual stud/ over the summer vacation. Thelessons, which sought to help maintain .basic skills, were to becompleted and mailed back to the schools. Over half of tbeparticipating studehts.dompleted all the lessrOns. Retults of the STEP

.

,Computation Test administered it Septedher shoved that these, students,maintained their levels of hasic'skillt while ones that did not

. complete the lessons, as well as' students in .a control group, badlower scores. As A result of the summet lessons, some teachers wereable to reduce substantially the amount of time devoted to review atthe 'beginning of the following school'year. (Author/LS)

I

,14

U Nil V E Ft 81 Tlf4 COLLEGE AVENUE, TORT LAUDERDALE, FLORIDA 33314 3011/5117.6640

NATIONAL ED.D. PROGRAM FOR EDUCATIONAL LEADERS

U S DEPARTMENT OF HEALTH,EDUCATION A WELFARE.

NATIONAL INSTITUTE OFEDUCATION

THIS OOCUMENJ HAS BEEN REPRODUCED EXACTLY AS RECEIVED FROMTHE PERSON OR ORGANIZATION ORIGIN%TING IT POINTf OF VIEW OR OPINIONSSTATED DO NOT NECESSARILY REPRESENT OFFICIAL NATIONAL INSTITUTE OFEDUCATION POSITION OH POLICY

USING A POTENTIAL METHOD OF MAINTAINING THEAASIC SKILLS/

OF ARITHMETIC THROUGH.THE SUMMER MONTHS TO,REDUCE THE REVIEW

TIME IN THE FALL

T,

by

F. Neil WalzlSupervisor, of Mathe7ctics

'Newark School District; Newark, DelaWare

Practicum report, submitted in partial fulfillment of the require,,ments for the degree of Doctor of Educaticn, Nova Untversity

I 4

NoVember 1973A'

t

TABU; OF CONTENTS

ABSJRACT

INTRODUCTION

THEPROPOSED SOLUTION - PART I . . .

PAGE,:

.

..1

Population' Description -1

cleneral Plan 2

Student Materia18 .3'4,

Experimental vsControl Group Assignment 5

Data Analysis 7

THE PROPOSED. SOLUTION - PART II . 15

CONCUSION 1.8

APPENDIX A!. Sample Student Lesson 20

BIBLIOGRAPHY 22'

)

4

.4

44.

4

ABSTRACT

/ The purpose of this practicum.was-to attempt to .

maintain the bAsiCarithmetic skills of- group of

gradefourth and fifth .students during t summer,

.vacation in order that the amount of review time in

th-e' fall could he redud<I'd.. Lessons were developed

for the students to use during-their vacation. At

the end of the-summer, the results indicated the skills

of the students who completed the lesso.ns remained at

a high :Level than the control,grOup.. Supsegnent139,

the teachers pf these students' were Alowle..tuA

reduce the

amount Of review time necessary for the st dents to .

-

successfully.approach the n0

material f grade

level.

'l

I

%

z

INTRODUCTION

t- 1

'Teachers at all levelsan0 in all -subject areas

'frequently'complain that their, students don't remember

'important facts, skills, or information which are nec-e

, epsary for the students to continue with their course

1cOmplaint is especially pr v4alent inof study. \his

the .fall of the year and'is frequently directed toward

the basic skills-of mathem tics. With this. complaint

in mind, teachers then proceedto.spend as much as nine

to twelve weeks in the fall of the year in review of

"basic skills."

This complaint is not entirely unfounded.. Evidence

was presented by Kurtz (1973) that there' was a- signi-

ficant loss of ability of beginning fifth grade students

to: work division problems.wAn compared to their ability

to work similar problems at the end of fourth grade. . He

also reportod that students in the upper quartile regis-

tered considerably more loss than the' students in the

lowest.quartije,,Suggesting that"-this-was probably due

to the fact that.t4ey.have more to forget.

On the other hdnd, Mousley (1073)-presented data

which indicated there was, no losslin -the reading. ability

\

a

4 r

of thi:rd-grades, and in fact reported a slight gai,p, /

,

between. May and Septembpr. lieproposed

that the chAdren's, normal maturation and their tendelicy

1 4"

to pyacbice/readind for pleasure might account fO the. "O.

.

.

maintenanc of theirbreading skill is while. they do not,

practice ather basic Skills such as arithmetic

The lass 'Men .is probably not as bald .as teachers'

r

tend to oela.eve, but probably does.exist to some extent..Or

This ,sit ation logically leads/to two basic questions

for whi. hianswers should he smight. .They are:. . .

.

.1.. Can some simple scheme be develeped.by which,the basic arithmetic skills can be maintainedover the surroll.e mciiths?

If such a scheme'is developed and proves ':successful, how can the results be:used toreduce the amount of time spent:by teachers'

_ or4\--"basic skills"? .-

1.

A search of the literature,revealed many Studi_ds

similar to the one done by Kurtz in which the legvling

loss was established.' However, few solutions were

attempted, with Most utilizi4g a regular summer schoOl

app.voach;and nearly allwere directed toward the under1

achiever.. For instance, Sinatra (1973) conducted ,a. .

summer reading program, utilizing a point reinforcer

I.

system. In this system, a Child earns points contingent'

-

upon task eamplet?on which *con he traded forftangible

ewar4. 1l1 ; majorgoal however, was instruction rather

than maintenante and was designed for.underachieVers

and low achievers.

Acknowledging. the fact that the best solution would

beto extend the school year, it must be recognized that

it is financially impossible to do this at the present

time. hence, the reason for the following alternative

proposal which -utilizes self study. lessons to maintain

theskills and uses the results of a statistical analysis

to persuade teachers to reduce. the review time.

Xi:NT) ...,

."'

r

THE 1?ROPOSE6 SOLUTION - PART I

1,1

- .

In order to keep the investivation of the prpposed A

solution 'manageable, it was necessary to limit this

'study to only include students who compieted the fourth'

or fifth'grades in June,, 1973. These students currently

-attend one of four elementary schools in three districts.

The purpose of using student, from these school districts

was,to ensure a. range of backgroundS, ability, and varied

'qeathing strategies.

One of the districts chosTA1.is primarily -rural,-one,/

,Trimarily middle class suburban and urban,, and one pri-,

)

marily-upper middle class suburban. In addition the

teaching strategies used in the four schools range from/

se1fcAntained classrooms to open - nongraded teams.

After eStablishing the population limAs for manage-.

ability,, c, ttib problem.of'cooperation was considered. kf\

,

the scrlool personnel are, note and/or do not.

..

,..

i

approve of the proposed solution,- it is useless toS.

attempt it. Therefore, school personnel input and

approval .were sought at each step .of.the.proposedt.

a

solution.

General Plan.

r

.1

The general scheme th4t was decided upon to attempt'

to mainta) the basic aritilmeticaskills-over.the summer

consisted 'of a series of lessons (five) which were'sentA

.home with thefstudentS at-thernd of the year, The

series of lessons was. to be completed at the rate of'

approximately one every other week during:the summer

months4 Along with the lessons, direction's and answer ,

Xeys'wer'e sent for, the parents' -use.: When the-c4ild

completed each lesson it was either self corrected,,or

th4 parent corrected it for him. The attempted or cm-.

pleted-lessen was then returned in a stamped pre,.1

-4

addressed enve'lOpe proVided.for its return.

The reasons for setting up a return scheme m;pre'fdr

record keeping pertaining to the number of lessons com-

'pleted by each student and to act as a link betwPen,the

home and the school. It was felt that' the link tretween"

home and school needed to be maintained even thpugh a

study conducted by Sabers (1972) indicated that post

cards and letters of encouragement' not reduce the, .

attrition its corrcspmndencn study courses. 'Ho-0- wever, his'),..

. . ,....

.,

.

study Aid indicqte a-positive-difference based 4n, .

stndenttide inr the'program, and it. could be ,construed

that this proposed solution is a quasi- correspondence

- course with students who are continuing 0-keir studies.;

int() the glimmer program. Honce, they, are'/

"enrolled" in t4 course./

I.

ApStudenaterials

Looking at the lessonS more closely, each one eon-

sists of two parts (See Appendix A). The first .partisa series of computational problems. utilizing one ,of 'the' .,

.

. .. .1....- . -

p. ...

. ' 4..

'

basic skins and resenlbles- a' traditional Worktheet. 111e. /.

,,

_N-\

, . 1 ,.second part is a puzzle utilizing, the basic bperations' -

.

Cross number puzzles and Spacedust(R pictures are:used\ 9

-1 . , \ .

I.

'for.thiS p rp. .4 (Spacedust pictures are publishedN,

.. .

.. 3 ' ( ,k 'Spacedust, Iric., Ashtabula, Ohio, gar are a part .of4 .

.,.

their. rithmetic-,FunbOoks series..) The purpose of using,.

the'two part approach was to inailitain.the stuotentsI

.-I..

,)- iklterest-when attempting th lesson,. Furt,OT?, thePuZzle

ljage could po.stibly/act as A review wh)ch could slow thei

.

lear.ning loss.

Overall, the lessons were-not designed to present

new concepts. Rather, they werextes.igned'aS a'review

3 a

14.

A

intrument This. wits done for several reasons.O

. *'

first was to keep the parents frem finding themsc

The

lees

in the embarassiAg f:nd/or.time consuming on of

playing teacher% The second was that, according tali --

psychologist's, review at gradually increasingJn ervals__..-! ...

enables materal to be retained for some time. Finally,

each time .a topic is relearned) the time for,madtery is

Turning to the directions .and ariSwer k6yS, the need

for their inclusion was very evident. Withoue*directions,

nearly, all lessonS.-faiJA, dine to the lack of a definitive'.

directiOn. Answer keys were neAed to act as reinforce-

ment; and reinforcement. to be most effective in learning

must follow closely after the desired behavion and be

clearlyaSsqciated with that behavior in the mind of the

learner: Also behavior whi6h is neivi-ded is more likely.

to

.

reoFcnr.: Finally, practice, i8 not enough. Ander-son

(1967) concluded. that a knowledge of.resUlts facilitates

learning. which implies that the learner cannot improve.by repeated efforts unless he ,is informed about holewell

(or poorly) he has-done.

'Keeping. in mind:the-psychological principles about

learning, forgetting, reward, and r6i'nforcement, the

1.

e

C

5

,

lessons were developed in May, 1973. The-teachers and

administrators in tne. schools involved were asked to

critique the overall plan as wall as the materials which.

would be sent hoMe .-After the staff approval was gained,4,)

the, lessons were further cridqued by Mrs. Verona Sharker,.

Elementary Mathematics Spetialist, Newark School.DistrictG

-and Dr. Ailliam B. Moody,, Professor of Elementary.Mathe-'

maticS Education, UniVersity of Delaware for the purpose

of determining their applicability and grade level4place-.

men

Experimental vs. Control Group.Assignment

Concurrently, with the development of the student. .

materials, the pupils were assigned'to oneof three

ability aevels; high, average, or-low. This assignment4 --

was muciron the pa'sis ot-their ability test results on

"the'Delaware EdliCational Assessment Program (DEAP).'

ThiIreting prograM is administered each year'by the

State of Delaware to all.first,fourth, and eighth grade..

students and was designed by Educational. Testing Service.,~

Princeton, New Jersey.' The students-Jere there pre tested

'Using Form 4A-of the Sequential Test& of Educational

Progress,(STEP)" rithmetiC Computation Test,. copyVight.,

(

-'

A

6

.e"

1969. 'On the basis of this test, the students were

aSisignPd to the ,experimentalior control group. This

assignment was done by first ranking the students within

the ability levels on the basis of their test scores

and then by using a random number table making the

'assignments of each pair of studentsto either the

.control or experimental grovp,'

Fina4ly-t the parents of, the students assigned to

the experimental group were Rptified and given the

option.pf not participflting, Five parents refused to1

il

'permit their hildren to participate. Four indicated

they were moing to another area, and the fifth gave no

reason. After -the parents-l-pormist,sion was obtained,

the materials were then distributed to---..the student on

the last day of.the 1972173 School year.

. During* September, the first week of .the 1973-74

School yea, the students were given the same STEP

Computation Test as a post test. This,bompleted the

first phase of the study. At this point then the data

was, analyzed in order that it could be used as a tool to

attack the next part of the'problem. Namely', if the

results were'positiver could the teachers be persuaded

..

to reduce the amount of time spent en review?

Data Analysis

Recognizing the fact that there would be'students

who would notcomPlte the lessons.,' the decision was

made to consider three categories of students: those, who

satisfactorily completed the summer lessons, those whe

partially completed the summer lessons, and those who

did not attempt the summer lessons. The' satisfactory

completion category consisted of students who completed

two or three lessons, while the did not attempt category

consisted of the students who completed zero or one

lesson.

A 3 X 2 X 2 factorial-design based on three ability

levels, two grades, and experimehtal or centre]. (treatpd

as repeated measures) was conducted on the data of the

students who satisfactorily completedthe summer lessons:

The data for the-Students who did not complete the

lessons were analyzed for indicatiohs or trends InrintAg

to\particular types of students who might not have com -,1

pleted the work, and were further. analyzed using a 2)(

2 X2 factorial design based on two-gradestwo leverg*.. %

completed qere or one, two or three), and.,experimental.''

My

vs. control (treated as a repeated meashre).

Overall, 322 students were originally included in

the study of which 1784ere fourth graders and 144 were

fifth graders. Table 1, Table 2, Table 3A, and TEible 3B

which follow give a complete breakdown of the students

by number and percent in each category.

TABLE 1

Grade Four Students Categorized by Numbdr ofLessons Cotpleted

.1issons Completed

0 -]) (2 -3 4 -5) .Other Total

Boys , 10 6 21 3

.

40

% 11.2% 6.7% 23.6% 3.4% 44.9%

Girls 13 . 9 24 3 ' 49

% , 14.6% 10.3% 27.0% 3.4% 55.1%

Total 23 15 .45 6 89

cwro 25.870_4616.9% 50.6% 6.7% 100%,

c

4

TABLE 2

Grade Five Students Categorized by Number ofLessons Completed

Lessons Completed

(0-1) (2-3) (4-5) Other Total

Boys 4 7 18 8 37

% '5.6% 9.7% 25.0% 11.1% 51.4%

Girls 6 2 21 6 35

% 8.30 2.8% 29.2% -8.3% 48.6%

Total . 10 9 39 14 72

of/0 13.9% 12.5% 54.2% 19.4% 100%

°TABLE 3A-

Distribution of Grade Four Students. Who DidNot Complete Lessons by Ability Level

Lessons Completed Totals

High AbilityGrade 4

Percent

(0-1) (2-3)

8 5 13

21% 13% 34%

Aver, Ability.Grade 4

Percent.

,8 5 13

21% 13% 34%

Low AbilityGrade 4-

Percent

7 5 12

c18% 13% 32%

Total Grade'4

Total Percent

23 '15.. '38-

61%

>

30% 100%

TABLE 3B

Lessons Completed Totals

High Ability .

Grade 5

-Percent

(0-1)

1

(2-3)

2

5% 5% 11%

Aver. AbilityGrade 5 5 3 8

26% 16% 42%(Percent

Low AbilityGrade 5 4 5. 9

.Perceht .21% 26% 47%

Total Grade 5 10, .9 -19

Total 'Percent 53% 47%. , , 100%

4

10

Of the 57 students .whb did 0.1 comPilete the lessons,

30 (53%) were girls and 27 (46%) ,were boys, 'which implies

that sex is not. an import factor in 'whethe'r or not

the student completed the. lessons. Ther.p was. also little

Aidifference when considering the school or district they

attended.

. .

When investigating ab lity levels, little difference

was noted among the fourth graders who failed to complete/

the lessons, with 13 (34i) fallihg into the high ability

.11

Ity

1 /

range, .13 (34% falling into the average ability. range,

and 12 (,340 falling into the low ability range." For

the fifth graders, however, only 2 (10%) fell into the

high ability 'range, while 8 (42%) and.9 (47%) fell into

the average and low ranges respectively.

Although a small sample, the fifth grade pattern

seems to indicate ability level might be a predictor of

failiireto complete the lessons. Indeed, a similar

pattern might have possibly been found in the fourth 11*

grade, ex'cept for the fact that a school boundary shift

was made in one of the districts during the summer

vacation. Fourteen students indicated they did not

complete the lessons for this reason. Nine bf these

students were in the high ability range, four were in

the averaxe.ability range, while one was in the low

ability range.

Table #4 which follows summarizes, the results of ,

the analysistof variance performed on the data obtained

from the'students who did not complete the lessons,

while Table #5 lists theemeans for the various groups.

As stated before, this analysis was based on two grades,

two levels of lessons completed, and experimental vs.

n

ti

12

control (treated as a repeated. measure).

TABLE #4

Analysis of Variance Results for Students WhoDid Not Complete the Lessons

Source . SS . df . MS

Between Subjects ,

A (grade level)B (lessens cQmpleted)AXB ..

9275.74504.03

1.7817.75

561

1.

1

504.31.78 .

17.75

3.0541.00<1.00

'Error 8752.18 .53 '165,13

Within Subjects 2005.00 57 .

C (exp.-control) 16.98 1 16.98 <1.00AXC al5.27 1' .15.27 41.00BXC 11073 1 110.73 3.54.AXBXC 205.79 1 205.79 6.58Error 1656.23 53 31.24

' TABLE #5

Means for .Student Groups Who Did Not CompleteLessons - I

No. of Lessons Completed Exp. Control

(0-1)(2-3)

36.338.6

37.235.5

It is interesting -Co note that grade level, is not

significant, but this is to be expecteWdue to the dis- 4

tribution by ability, with many more 4th graders in the

I

13

' I

high ability raiwe than 5th graders. While not Sit-

nificant at the .051evel,.the interaction of lessons

completed and experimental-contvl'indicates a tendency

toward a higher mean for the students who completedI

more lessons. This trend might lead one to ispect

that completing lesSOns did help to maintain the basic

4' 'skills!

'Turning to the analysis of the data for the' students'.

-----,4.who completed the lesson's, the dedign was a: 3X2X2

'factorial design with 3 ability'levelS, 2 grades, and

experimental - control groups. (treated as repeated

measures). Table #6 summarizes the analysis of variance

performed, while Table #7 lists -the means for the

various groups.

TABLE #6

Analysis of Variance Results for Students Who4. Completed the Lessons'Satisfactorily J

SOurce . SS . df . MS

Between .Subjects. 19175.50 83A (grade) 1975.85, 1 1975.85 49.34*B (ability) 1:1916.01 2 6958.00 173.64*AXB 158.01 2 79.00 1.97Error 3125.63 78 40.07

4

WOW

0

TOle #6 continued

Sou'rce

Pa

14

iWithin Subjects'CAXCBXCAX[3XCError

/34. .001

SS . df . MS F.

2741-5013881.77

4 14.44.'92.753,22

1242.25

/

TABLE #7

8411

2.278

1388.77 87.23*14.44 <1.0046.37 2.721.61 41.0015.92.

Group Means for Students Who Corppleted the

I

Lessens by Grade

Iii

Exp.(Post) Control (Post)

46.7a

50.5

Grade Aver. 39.5 34.5

Low 28.1 21.3

Total Grade 4 39.4. 34.2

50.7

Grade 5 Aver. 49.0.

42.4

Low 36.7 28.3

Total Grade 5 46.8 40.5

1 TotalGr. 4 .& 5 42.8 37/

3

7

0"^"..'

-e

ZJ

As is to be expected, the differences between

grades and between abilify.levels are 'highly stgilificant.

Of interest however, is the signifitant difference

between the'experimental and control groups. At each

of the ability levels, the students inthe experimental

group maintained the;;Tsceres, while qe studehts in the-,

control group dropp d' an average of 4 to 8 points.

Overall,. the mean diffe/ence was better' than. 5 pointsift

favor, of the experimental. group: The ,conclusion obvi-

ously, seems to 'be that :the summer lesson's did help:-to

maintain the basic,skills.

THE PROPOSED SOLUTION - PART. IIA

Even though the result's of the data analysiS were

highly significant in -favor of the experimeqal.group,

-the project would be little more than an academic

endeavor "(and indeed could be considered a. waste of ,time)

if the teachers,invol-ved do note accept the results and

modify their behavior accordingly. Therefore, an

- attempt was made to Use the results of this stucly:as the

basis for persuading teachers to change their outlook

toward the need for review in the fall of the yeai.

,

/

160

With he preceeding in mind, the results of the

data analy:As were shared with the teachers and admin-

istratorsistrators of the students involved in the study. 'The

nuMber of teaAers initially involved consisted of six.

fourth grade teachers and five fifth grade teachers. In

addition, the students in fifth grade in May,..entered-

tnree different middle Schools and were, assigned to seven

different middle school teachers. Thus, students of

18 teachers were involved in the study.

Each of the 18 teachers received the results of

'the study shortly-before a meeting was held with them

in order that they could have time to look over.the

results.

, The purpose for holding the meeting was three fold.

The first was to determine the amount of'time the.

teachers ,expected to Tpend on review. This was

gathered, and the results are summariztld in Table #8.%

TABLE #8

Teacher Estimate of RevietvTime Needed by Their Students(Second Week of School)

Number of Weeks 7 -8 9-10 11-12-Grade. 4 Teachers. : 1 3. 2G?ade 5 Teachers 2 2 1

Grade 6 Teachers 3 3 1

CO

O

17

V

As can be seen by inspecting Table 8, the average

amount of time to be spent on review 'is about 9, weeks,

or about 25% Of 'the c..hool year, while 'four' teachers, ,

were.Oanning to spend nearly-33% ofthe'school year'

reviewing basic skills!

The second purpose of, tli6d4neeting was to ,clarify

any questions lhe teachert might have had concerning the.-4

restlts of the summer study, while the third was to use

the data results ks. the basis of an appeal to the

teachers to reduce the review time.

The teachers were not discouraged from using 'periodic

review, in fact, this use of review was highly encouraged..

After .a period of six weeks4(eight-weeks After the6

start of the 1973-L74 school'year) A follow-up survey was

conducted, and personal observations in each classroom

were made. Through the survey and the obAervationg' it

was determined that two teachers reduced their review ,

time to three weeks three had teduced their review time

to four weeks, while only. one

still utilizing twelve weeks..

40

results of the followup visitations and tsurveys.

ind4.cated a need for , A

VTable #9 summarizes the

I "

A

4

TABLE #9

\'Teacher- Use of Review TiMe fin- Their Students

(Eighth Wee4 of Septe.mber)

.

Number 'gfWeeks 3 4 5

.., \./.

:Grade 4 Teachers l' ,2

Grado5 TeacherS, I 1 1

A

Grade 6 leachers 1 2 1

18

6 7 8 9 -10 11 -12

- 1 - ' 1

1 - - 1,

2 -.

- 1 -

It can readily be seen that the average time spent

on review time as about six, weeks. This was a decreasek

of 33%'from the original egtimap of nine weeks, Obvi-

ogsly,,this represents a considerable number of student'

4days which .car beF

used for.other pursuits.4

CONCLUSION

In light of the fact that the basic skills were

maintained during the summer vacation, and the teachers

subsequently reduced the- amount of time spent on review,

this method seems to have considprabfle merit and attempti-will be male.to expand ts:use in the Newark District.

However, if, one were considering the adoption of

such a scheme, it must be'rffembercd that there was

no attempt to teach ew mate ial and ori'ly basic skills

,/,

4

were 'presented. .Further, it is imperative' to involve

the teachers and administrators at each step of the

proce: , for this ihvestigator' feels that this con-.

tributed to.ihe,success of tie, project as much 'V's the.

convincing statistical rekults.

bs

19

1111111.

4

APPENDIX'A

Name School

Example:

20

LESSON #1,A

ADDITION AND SUBTRACTION

%i A. Add the ones.4325 5 + 8 + 4 = 17 one's6078 B. Rename 17 as 1 ten' and 7 ones

+ 5294. C. Add tens1Y07 .1 + 2 + 7-+ 9 = 19 tens

D. Rename as 1 hundred and 9 tensE. Follow .a similar pattern for the

hundreds and thousands

1. 342+ 325

5. 4317

+ 13

2. 725+ 146

6. 43516

+ 127

3. 425+ 1723

74 41131590

+ 2671

4. 3156+ 1327

8. 234357214

+ 526

Example:

n

120 , A. SubtraCt the ones. 3 - 2 = 1

-582 B. to subtract tens, rename 1000 +200 +.50 as 1Q00 + 100.+ 150.Subtract tens. 150 - 80.= 70

C. To 'subtract hundreds rename 1000 +100 as 1100. Subtract hundreds.1100 500 = 600.

9. 625 10. 634 11. 908 12., 1765.401 -307 -436 -934

13. 2576-882

FNW:mjh6/7/73

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