Table Of ContentESSENTIAOLFS
ELEMENTARY
SCHOOL
MATHEMATISC
MaxD .L arsen JameLs.F ejfar
UniversoiftyN ebraska-LincolnU niversoiftyN ebraska-Lincoln
ACADEMIPCR ESS New Yori< San FranciscLoo ndon
A Sub1idoifH1 eryn :oun Brace JovPueblniosvhelerh,s
CoPYRIOHT 0 1974B,Y ACADEMIC'P RESS,I NC.
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LibraorfCy o ngresCsa talogiingnP ublicaDtaitoan
LarseMna,xD
Essentioafle sl ementsacrhyo ol mathematics.
Bibliograpp. hy:
I. Mathematics-aSntdtu edayc h(iEnlge mentary)
2. Mathematics-196I1.- FejfaJra,m ejso,i nt
author. II. Title.
QAl35.5.L28 510 73-9433
ISBN0 -12-438640-7
PlllNTEDIN lBE UNITED STATES OPA MBIUCA
Acknowledgments
Thef iguraepspea rinignC hapte1rs2a nd1 3a rea dapteadn dr eprinftreodm t hef ollo winbgo oks:
MotioGne ometryB ook1 ,Sl idesFlips,, andT urns
TeacherE'dsi tioMno,t ioGne ometryB ook1 .S lidesF,li psa,n dTu rns
MotioGne ometrByo ok2 ,C ongruence
TeachttrE'dsi tioMno,t ioGntt ometryB ook2 ,C ongruence
MotioGntto metryB ook 3,S ymmetry
Teacher'Esd itioMno,t ioGntt ometrByo ok3 ,S ymmtttry
MotionG eomtttryB ook4 ,A rea,S imilaraintdyC ,o nstructions
Teacher's EditioMno,t ioGne ometryB ook4 ,A rea,S imilaraintyd,C onstructions
byJ oM cKeeby PhialnldiR psu sseEl.lZ woyer;
CopyrigC>h t1 969B,o ardo fT rusteUensi,v ersoiftI yl linois;
Publishbeyd H arpe&r R ow,P ublishIenrcs.,
ed
DedlCllt
too uwri ves
LilLlaires aenndT hereFseej far
fort heliorv aen dp atience
and
too ucrh ildren
MichaPealu,al n,dC harLlaires en
and
MaryT,o nya,n dE llFeenj far
in htohpete h atth ey waillfislnod
pleasiuntr hese t uodfym athematics
Preface
A primoabjreyc toiftv hebi oso ikst o g ivset udaeb natcsk gnrdso uufficient
tou ndersatnadan nds waetr aapnp roplreivaetlve a trhiqeou uispt een e
tratqiunegs tions yoausnkgT. h esa tuutdhaeornrcetso s m mitttote hde
notiont etahcahotefe r lse mentary schosohlo ubmleaad tw haermea tics
oft hceo ncetphtacsto nsttihteu tesu Tbhjibesoc otwk.a sw rittetnh e on
assumptthiauotnn d ersttahnmeda itnhge mactoinccaeilpn t sctu hrer imc ulu
oft heel emenstcahrowyoi lpl rlo duatc eea cbheetrt er eaxbpllteah ietn o
subjmeactttt eosr t udeannttdos d eviesffee ctwiavyfeso r helping children
leaarrni thmetic.
Thibso ok prae ssyesnttesm daetviecl opomfte hnmet a themaotfi cs
arimtehtTihce.p rincciopnacle pts ofa rsaetr uidtiihniem sdeo tliafictr isotn
to ceanttteerno tnti hoienn divciodnucaelp ts, and then they are studied in
contteoxe tm phastihzeei r role ino ftt hhee ealreismtcehhnmoteoatlri yc
classrTohoefum n.d ameintdaeplar se seinntietdai rauels letydh roughout
thtee xsto;w hifolrem amla steorfty h ceo ncempatybs e u nnecessary,
awareniescs rsu cAinae la.r ly exptohseunsroeet iwtoionla sll low the
concetpo"t pse rcoalsma otreoe"ft hbeo oikss t udied.
The tiopneia cccshh aphtaevrbe e eanb strafcrtotemhd en iorr msaelt ting
ina rithtmoee tnicco uraac gleoe sxea minoaftt ihoebnia rs piorcp erties.
Fort hpeu rpoofsi el lusttrhaectsoienn cge wpittmshe aninegxfaumlp les
xm
we wilals sumteh atth er eadeisrfa miliwairt thh er udimenotfas r ithmetic
(nom oret haenl ementaalrgye barnad)w e realitzheai ttm ayb en ecessary
occasiontaorl elvyi eiwd eawsh ichha veb eenf orgotten.
Theb ookd oenso ta ttemtpotp rodumcaet hematicbiuatran tsh,e tre achers
aware
oft hem athematiincvso lvientd h ec urricuSloumme.e xampleesx.
ercisaensd.d iscussairoenc so ncernepdr imarwiiltyph e dagogiacsaple cts
ofa rithmeTthirco.u ghotuhteb ookt,h es tudoyf t het heoroyfa rithmetic
isa imeadt d evelopainna gw areneisnts h et eachtehra wti lilm provtee ach
ingT.h ea uthohrasv ea ttemptaetvd a riopulsa ceisnt heb ookt oo ffera
rationfoarl per esenttihnesg pe cifitco piicnst hiboso k.
Theb ooki sd ividiendt foou rp art(sT.h eN otet ot heI nstruecxtpolra ins
ther elationasmhoinpgts h ep artsP.a)rO tn ep resentthsefu ndamentcaoln
ceptuss edt hroughtohuert e sotf t hebo ok.C hapteOrn e.o nt hel anguage
ofm athematdiecasl.ws i teh lementary proifnl coigpiulcpe osnw hicwhe
baseo urs tudTyh.e t heoroyfs etisn C hapteTrw o providmeusc ho ft he
notatiuosne dl ateTrh.e c onceopftb inaroyp eratiisos nt udiienCd h apter
ThreeB.i naroyp eratiaornens e edetdos tudsyy steomfsn umberCsh.a pter
Fourd ealwsi tthh er ecogniatnidoi nd entificoaftp iroonp ertoifve asr ious
relations.
ChapteFrisv e-Eicgohntt aai sny stemadteivce lopmoefnt th en umber
systeomfsa rithmewthiocl:ne u mberisn,t egerrast,i onnuamlb erasn,d r eal
numberAs .c arefcuoln strucotfit ohne sneu mbesry steamnsd a ne xplora
tioonf t heiprr opertiisie nst endteoed x pantdh et eachearp'psr eciaotfi on
theisrt ructUunrdee.r stantdhiesn tgr uctoufrt eh en umbesry stesmhso uld
enhancae t eachearb'isl ittory e laat cee rtatienx tbooakp'psr oatcohi ndi
vidusatlu dennete dst,oe valuattheee ffectiveannedsv sa lidoiftt ye aching
techniquaensd m ateriaalnsdt, o c reatues efmuelt hodfosr aidinega ch
child's underosfta arnidtihnmgec toincc eptChsa.p teSre vend ealwsi th
thes pecipfilca ce-vnaaltuuer oefo urn umbesry stemasn dw itthh ea lgo
rithbmysw hicohn eu setsh en umbesry steImnsc omputation.
Thet hreceh aptewrhsi ccho mpriPsaer Tth reaer ei ntendteopd r ovide
stimulafotrit ohner eadaesrw elals t ob roadheines x posutrome a thematics
outsitdheee lementsacrhyo oclu rriculTuhmec. o ncepitnsv olvaerded i
rectly ltione kleedm entsacrhyoo lm athematicsn.o tab luoltf t hema re
taughtth ere Studyitnhge sceh aptesrhso ulidn creatsheet eacher's
pers e.
understanodfit nhgec onceputsse di nt hec lassrooamn dp roviad seo urce
ofi ntrigiunifnogr mattoie onnr itchhe t eachionftg h es tandacrudr riculum.
Topiccso vereadr en umbetrh eorcyl,o cakr ithmeatnidcc .o untitnegc h
niqueasn dp robability.
Thefi napla rits a studoyf g eometfrryo mt wop oinotfsv iewi-nformal
"motiogne"o metarnyd a nalytgieco metrTyh.e c hieofb jectiisvt eod e
veloap " feelifonrg g"e ometarnyd p repaar bea ckgrouonfid n siguhpto n
whiclha tsetru dioefgs e ometcrayn b eb aseTdh. eu seo fm otiotnoss tudy
geometrwyi lfolr m a multisensaoprpyr oacthot hes ignificraenstu lotfs
Euclidegaeno metrTyh.r ougthh iasp proatceha checrasng aian v aluable
insigihntt Eou clidegaeno metarsyw elals e xperiewnicteah n a pproatcoh
geometwrhyi cihs s uitfoerd usew ithe lementasrtyu denTthse.a nalytic
geometirsya ssociawtietdah studoyf f unctiaonndsr elioensa coordinate
system.
Therea rem anyp eoplteo w hom we arei ndebtfoerd s uggestiaonnds
assistanRceev.i ewbsy RoberBtr ownJ,r .( MontgomeCroyl lege),
0.
JamesE . Schult(zM ichigSatna tUen iversiatnyd)J ,o hnC . Peterson
(EasteIrlnl inUoniisv ersiwteyr)ee speciatlhloyr ouagnhd c ontainmeadn y
thoughtrfeumla rkTsh.e e ditorainadpl r oduction osfAt caaffdse miPcr ess
weree fficienatn dp recisPea.s td iscussiwointshR icharSdh umwayh ave
influencoeudrp resentaitnis oenv erpalla ceSsp.e citahla nkgso est oM ary
Huntfo r assistiinnt gh ep reparatoifto hne m otiogne ometmrayt eriaanld
for writitnhgea nswer sectionP.o rtCsacrhoeelx' cse llent mtaydpeit nhge
preparatoifot nh em anuscriepats ier ittho atnh erwimsieg ht hbaeveen .
Alsow e wisht ot hanoku rc olleagaunedss tudenwthso,h aveb eeni nstru
mentailn t hed evelopmeonfot u ri deaWse. ared eepliyn debtteodt he
NebraskTaT T Projewchti cahl lowuesda sp articiptaosn ptesn tdh ea ca
demicy ear workinwgi thc hildraenndt eacheirnes l ementary
1971-1972
schools.
xv
Notteot hIen structor
Iti si mportatnhtay to uu ndersttahnedr elationasmhoinpgts h ec hapters
andp artSsi.n ceea chc haptaetrt empttops r oviad rea thceorm plettree at
mento fe acht opiictm ayb en ecessatrovy a ryt hea mounotf e mphasis
placeodne acho ned ependionntg h el engotfht hec oursaen di tgso als.
ChapteTrhsr eea ndF ourd epenodn C hapteOrnse a ndT wo,b uta re
independoefen atc oh theCrh.a pteFrisv eS,i x. Eaingdh dte penodn t hefi rst
fourc haptebrust.a ref airilnyd ependoefne ta cho theMru.c ho fC hapter
Sevecna nb es tudiweidt hosuttu dyitnhgeo thecrh apteTrhse.r iesn oi nter
dependenbceet weetnh ec hapteirnPs a rTth reeC.h apteTre nu sesc on
ceptfsr omP arOtn e;C hapteNrisn ea ndE levecna nb es tudiaefdt Cehra p
teTrw o.T hec hapteornsm otiogne omethrayv en op rerequicshiatpet ers.
ChapteFro urteuesne sa smalalm ounotf s ett heorfyr omC hapteTrw o
buto therwiissfr ee eo fc onstraint.
Whenu sintgh en otefsr owmh icthh ibsoo k wasw rittienan o ne-semester,
three-creditc-ohuorusaret t heU niversoiftN ye braskwae, f ollotwh is
schemeC:h apteOnre i sd oneb rieflmya inlfoyr then otatiCohna.p tTewro
getas t horoutgrhe atmeInntC .h apteTrh reaes sociatainvdic toym muta
tiviatryet reatceadr efuwliltyah l igthrte atmfeonrtth eo thetro picCsh.a p
terFso ura ndF ivaer ed onen exatn di nd etaMiols.t o ft hem essdye tails
areo mittiendC haptSeirx b utC haptSeerv eins d onet horougWhel fiyn.i sh
xvii
upw ith ptahreot f C haptEeirg hdte votteodr ationnuamJb ertsh.e dno
Chapter Tecno ntforraa sntdt, r tyo s ays omething tharebe oauJt numbers
ift imiesa vailable.
Certnalityh eraer eo ther scthheamwteo su lddo j usatsw elWle. h avae
separcatoeu rfoser geometarnyd dtoh ep ortioofnt hibso ok moont ion
geometWrey .f eetlh aCth apteTrwse lvaen dT hirteweonu lmda kea ne x
ceJJteenxtfot r a q uartceoru rset woor- credit csoeumreassnetd te hra t one
coultdr ecaotm fortaabnlo yfP art Thirnae teh ree-creditc osuermsees.t er
Ino rdetroi nclubdoet ghe ometarnydt het heoorfya rithmeitnai c s ingle
three-csreemdeisttc eoru rse, onlei mctiohtueg l edo mettroMy o tioGne
ometrayn dc oveorn lpya rtosfC hapters Oneb-ylE iimgihttdi insgc ussion
tom ajorpo ints.
Studenwtisld le rimvoer ep leasaunrde learn frmoomra e c oursues ing
thiboso ki fi t aicst ivreellya tteotd h efiurt utreeca hinHga.v inegl ementary
1
schootle xtbooske riesw en Cuisenariordesa ,t tribbultoec kest,c .
as as
redailayv ailawbilUse i gnificiamnptrloytv hee oiprp ortuntiolt eiarnea sn d
wiJeIn hantchee aiprp reciaoftt ihoemn a thematpircess ented.
1T hen amCeu isen®a ainrdte hceo lsoerq ueonfct ehr eo ddse picitnted h iwosr k
aret rademoafrkC su isenCaoimrpea noyfA meriIcnac,. and utshede iwri th
permission.
xviii Instructor
Note to the
Notteot hSet udent
Thibso oiksd esigtnoae cdq uatienatc -hbeortsphr ospetcetaicvhee rs
and teachers w-iwtihtt hh erexu pdeirmieenntcse of mathematics that
formt hbea soifts h aer ithmegteiocm eattnarduy g htth ceoi nn temporary
elemenstcahroyco ulr rliucmTu.h ea pprowaiclbhle a lontghr leie nes,
treatiynouga sm athemattiecaicahanen,rds , t udeSnotm.ed iscussions
wilblea imeadti ncreyaosuiarnb gi laist imeaas t hemastoi cityahonau t
wilhlav aed eepuenrd erstoaftn hdmeia ntgh emoafta ircist hmOetthiecr.
discuswsiilcolen nsto enr yaosau teaocfah reirt hmetict rtyao n d will
stimuyloauttrhe o ugchotnsc ertnhitene gc hnioqftu eeasc hairnigt hmetic.
Finaalsl ys,at udyeonut wbeia lslk etdop erfocremr tfauinnc tiino ns
mucthh sea mwea yt haatc hiilsad s kebdya t eacihnte hree l ementary
sch.oT oolm akfeul uls oef t hbioso yko um usbtew illtioan cgc ept these
differreonlatett s h aep proptriimaetse.
Mosutn iverasnidt iceoslh laevgee sos fee tlse menstcahroyto elx t
bookasv ailTahbelseme.a yu suablelfo yu ndi na specciuarlr iculum
libriantr hype a rotft hsec hotohlat tr aiannsdre trnasti eachTehres .
amouynotu lweialfrrlon m t htee xtbwoiolbkle i ncrecaosnesdi derably
ify ouw ill thueesl ee menstcahrotyoe lx tbtohorkosu gyhoouusrtt udy,
relatthien gm aptreersieahnlet rweeid t thhm ea teyroiua )m bietg ehcath ing.
With etmhpeh aosnii sn dividuailnmi ozsamtto idoenre nl ementary
xix
schooltsh.en otioofn tae achreers ponsibolnel oynfo erg radlee v(efolr
instanac teh,i rd-gtreaadceh enrol )o ngeexri sAtnsy.t ecahecro ulbde
asketdot eacahr ithmaetta ilcm oasnty l evneolm atttehrea geo f tchhei l
drein nt hec lasCso.n sequenytoluy .s hould avoid tsokpiibpcep ing any
causieti sn otp arotf a certaciunr ricuylouumm i ghbtet eahcing.
xx Note to th• Student
