Table Of Content

Mathematics CrosswaCloka chf otrh eC ommonC oreS tatSet andarMdast,h ematGircasd,e 300NA 5 ISBN-1937:8 -0-7836-7849-8 ContribuWtriintgeR ra:n dyG reen CoveIrm age©: R onH iiton/Oreamstime.com 136M adisoAnv enu7et,h F looNre,w Y orkN,Y 10016 T© r20i1u1Tm rLpieuham prLhen airnnigLn"LgC , Coachi sa ni mprionfTt r iumpLhe arn"i ng Alrli ghrtess ervNeodp .a rotft hipsu blicamtaiyob ne r eproduicnew dh oloer i np arstt,o red ina retriseyvsatle omr,t ransmiitnta endyf oromr b ya nym eanse,l ectromneicch,a nical, photocopyriencgo,r doirno gt herwiwsiet,h owurti ttpeenr missfiroonmt hep ublisher. Printientd h eU niteSdt atoesfA merica. 10 9 TheN atioGnoavle rnorAss sociaCteinotnef ro Bre sPtr actiacnedsC ouncoiflC h ieSft ate SchooOlf ficaerrets h es oloew nerasn dd evelopoefrt sh eC ommonC oreS tatSet andards, ©Copyri2g0h1t0 . righrtess erved. All FrequeAnstkleyQd u estiaobnosut th e CommoCno rSet aSttea ndards .I ) Whata rteh Ceo mmonC orSet aSttea ndards?D ot hCeo mmonC orSet aSttea ndafrodcsou ns I I TheC ommonC oreS taSttea ndafrodrs skialnldsc onteknnto wledge? mathemataincdEs n glilsahn guaagret s, YesT.h eC ommonC oreS tandarredcso gntihzaet I grades araes eotf s hargeoda lasn d botcho nteanntds kialrliesm portaThnety. r equire K-12, expectatfiotorhn eks n owledagneds kitlhlast rigorcoounst eanntda pplicaotfki noonw ledge wilhle lspt udesnutcsc eTheedy. a llow studenttsh rouhgihg her-orders ktihliTlnhskeE.i n nggl ishI tou nderstwahnadit s e xpectofet dh ema nd languaagrets st andarredqsu icreer tacirni tical tob ecomper ogressmiovreepl ryo ficiine nt contefnotar l slt udenitnsc,l udcilnags msyitch s understanadnidun sgi nmga themataincds ands torfireosam r ountdh ew orlAmde,r ica's English laanrgtTusea.ag ceh ewrislb leb etter foundidnogc umenftosu,n dational American equippteokd n owe xacwthlaytt h emyu std ot o literaatnudSr hea,k espeThaer ree.m aincirnugc ial helspt udelnetasra nnd t oe stabilnidsihv idualizdeedc isiaobnosuc to nteanrtle e fttos taatned l ocal benchmafroktrsh em. determinaItnai dodni.t tiooc no ntecnotv erage, theC ommonC orSet aSttea ndarredqsu itrhea t Wiltlh Ceo mmonC orSet aSttea ndatredlsl studesnytsst ematicalklnyo walceqduogifer e teachheorwas n dw hatto t each? literaatnudor teh edri sciptlhirnoeusrg eha ding, writisnpge,a kianngdl, i stening. No.B ecautsheeb e sutn derstanodfwi hnagt workisnt hec lassrcooomme fsr otme achtehress,e Inm athemattihceCs o,m monC oreS tate standawridlesls tablissht udennetestd o what Standalradayss olfiodu ndatiinwo hno le learbnu,tt hewyi lnlo td ictatet eachsehrosu ld how numberasd,d itisounb,t racmtuilotni,p lication, teacIhn.s tesacdh,o oalnsdt eachweirldsle cide division, farnaddc etciiomnaTslo,sg .e thtehre,s e howb esttoh elspt udernetasc thh es tandards. elemenstusp poars tt udent'st oal beialrint y anda pplmyo red emandimnagt hc oncepatnsd Whatwil l thCeo mmonC orSet aSttea ndards procedures. meanf osrt udents? TheC ommonC orSe taSttea ndarredqsu ire Thes tandawridlpslr oviadc el eacro,n sistent thastt udednetvse laod pe ptohfu nderstanding understanodfwi hnagit s e xpecotfesd t udent anda biltiora yp plEyn glilsahn guaagreta sn d learnaicnrgo tshsec o untCroym.m ons tandards mathemattionc osv esli tuataisoc nosl,l esgteu dents wilnlo tp revednitff erleenvte olfas c hievement and emploryeegeusl adrol.y amongs tudenbtustt, h ewyi ll enmsourree consisetxepnots utrome a teriaanldls e arning Wilclo mmoans sessmbeedn etvse loped? experietnhcreosu cguhr riculum, instruction, Itw ilbleu pt ot hes tatseosm:es tatpelsat no teachperre paraatnidoo nt,h esru ppofrotsrst udent comet ogetvhoelru ntatrodi elvye laoc po mmon learniTnhge.ss et andawridlhsle lgpi vset udents assessmseynstt ems.t atec-olnesdo rtoinu m thek nowledagneds kitlhlesny e etdo s ucceiend A assessmweonutlb de g roundientd h ef ollowing colleagnedc areers. princiapllleosw:fi oncrgo mpariascorno sstsu dents, schoodliss,t rsitcattsae,ns dn atiocnrse;a ting economiofes sc alper;o vidiinnfgo rmaatnido n supportmionrgee ffecttievaec hainndgl earning; andp reparsitnugd efnotcrso llaegnedc areers. 3 Tabloef C ontents CommonC orSet atSet andaCrodrsr elaCthiaor..nt. ........... .. . .. ............. 6 . . . . . . Domain OperatiaonndAs l gebrTahiicn k.i.n.g. ... 1.1 CommCoonr e 1 StaSttea ndards . 12 Domai1n: D iagnosAtsisce ssmefnotLr e sson1s- 5. ..... Lesso1n Writaen dI nterpErxeptr ess.i.o.ns. ....... .1.4 5.0A.2 Lesso2n Ordeorf O perati.o.n.s. ............. .1..9. 5.. 0A.l Lesso3n EvaluaEtxep ressiwointsGh r oupiSnygm bo.l.s 24 5.0A.l Lesso4n Patter.n .s. .. . . ...... ... ..... . 29 5.0A.3 . . .. . .. . . Lesso5n GraphP atte.r.n.s. ................ .3.5. .5..0.A .3 . 41 Domai1n: C umulatAisvsee ssmefnotLr e sson1s- 5. ..... Domain Numbearn dO peratiionBn ass Tee n. ..... .4 3 2 . 44 Domai2n: D iagnosAtsisce ssmefnotLr e sson6-s1 6. .... Lesson MultiWphloyl eN umber.s. ............. 4.6.. 5 .NBT.5 6 Lesso7n DiviWdheo leN umbers. .. . . . .. ..5 3 . 5..NB T..6 . . . . . . . Lesso8n QuotieanstE sq uatio.n.s. . . ..... .... 59 5.NBT.6 . . . .. Lesso9n Reada ndW ritDee cima.l.s. ..............6.4 5.NBT.l,5.NBT.3.a Lesso1n0 ComparDee cima.l.s. ...............7.1. .5..N.B T.3.b Lesso1n1 RoundD ecima.l.s. ................7.6.. 5...NB.T .4 Lesso1n2 MultiapnldyD ivibdyeP owerosf T en. ......8.1 5.NBT.l,5.NBT.2 Lesso1n3 AddD ecimlas. .. . . . . . .. ..8 8 . 5..NB T..7 . . . . . . . . . . . . Lesso1n4 SubtraDcetc ima.l .s . . . . . ...9 6 . 5..NB T..7 . . . . . . >.. ' . . . .a "0 :.o�.l!l0. iI Lesso1n5 MultiDpelcyi ma.l. s . . . . . .. ..1 40. 5..N BT..7 . . . . . . rJ). . . �I o o .a rJ) £ Lesso1n6 DiviDdeec ima.l .s . . . . . .. .1. 1 1.5 . N.BT .7. . . . . . . . . . . t .. . .1 81 '0ro Domai2n: C umulatAisvsee ssmefnotLr e sson6-s1 6. 0. > C ro 1lI c +J ro Sl ,aS! 4 CommCoonr e StaSttea ndards Domai3n Numbearn dO perations-F.r.a.c.t.i.1o.n12 s . . 122 Domai3n: D iagnosAtsisce ssmefnotLr e sson1s7 -2.4. .. Lesso1n7 EquivalFernatc ti.o.n.s. ............1..42. .5 .NF.1 . Lesso1n8 ImpropFerra ctiaonndsM ixeNdu mber.s. ... 113 5.NF.1 Lesso1n9 AddF racti.o.n.s. ................1.83.. .5..N F.1,5.NF.2 . Lesson SubtraFcrta ctio.n s . . . . .. ..1 64. 5..N F..1 ,5..N F..2 . . . . . . . 20 . Lesso2n1 UnderstaMnudl tipliocfaF triaocnt i.o .n s. . .1. 35 5.NF.5.a,5.NF.S.b Lesso2n2 MultiFprlayc ti.o. n s. . . . .. .... 1 . 85 .5. NF.. 4. . . . . . . . .a,5.NF.4.b, 5.NF.6 Lesso2n3 FractiaosnD si vis.i.o.n. ............1..56. .5 .NF.3 . Lesson DiviFdrea ctions ..............1.0.7. .5..N.F..7...a, 5.NF.7.b, 24 . 5.NF.7.c . 167 Domai3n: C umulatAisvsee ssmefnotLr e sson1s7 -24 ... Domai4n MeasuremaenndDt a t.a. ..........1.97. .. . 108 Domai4n: D iagnosAtsisce ssmefnotLr e sson2s5- 2.9. ... Lesson ConveCruts tomya rUn.i.t.s. .......... .1.38. 5.MD.1 25 Lesson ConverMett riUcn i.t. s . . . . .. .1. 98 .5 .M.D .1. . . . . . . . . 26 Lesso2n7 UnderstaVnodl um.e . . . . ... ..1 59. 5..MD .3.. a,.5. MD..3 .b., . . . . . 5.MD.4, 5.MD.5.a Lesso2n8 Volumseo fR ectanguPlrairs m.s .. . .. ..2 0.1 5 ..MD .4.,5 .M.D .5.b, 5.MD.5.c Lesso2n9 LinPel ot.s. . . . . . . . ...2 0.7 5..M D..2 . . . . . . . . . . . . . . . .. .21 4 Domai4n: C umulatAisvsee ssmefnotLr e sso2n5s- 29 Domain Geomet.r.y. ......................2. 17. . 5 . 218 Domai5n: D iagnosAtsisce ssmefnotLr e sson3s0 -3.4. ... Lesso3n0 CoordinSaytset e.m. ...............2.2..1.5 .6.1 . Lesso3n1 OrderePda i.r.s. .................2.2.7.. 5..6 .2 . Lesso3n2 PlanFei gur.e.s. ................. .2.3.3.. 5..6 .3 Lesso3n3 Triang.l.e.s. ................... .2.3.9.. 5..6..3 , 5.6.4 Lesso3n4 Quadrielraat.l.s. .................2.4.4. .5..6 .3, 5.6.4 . . 250 Domai5n: C umulatAisvsee ssmefnotLr e sson3s0 -3.4. . Glossary 252 . . . . . . . . . . . .. .. . . . . . . . .... . . . . . . . . . . . .. . . SummatiAvses essmeDnotm:a ins 257 1-5. ........... .... MatTho ol.s. ....................... .2.7.3. .......... 5 Common CoreS tatSet andards CorrelatCihoanrt Common Coach CoreS tate Grade 5 Lesson(s) Standard Domain:Op eratiaor,n',,A(J's" l II! g e"b Trhaiinkci ng � '" .,..', ;� ..oj, . Writaen di nterpnruemte riceaxlp ressions. Usep arenthbersaecsk,eo trbs r,a ciensn umeriecxaplr essainodne sv,a luate 5,OA1 2,3 expresswiiottnhhs e ssey mbols. Wristie mpelxep resstihoarntes c ocradl culawtiitnohun msb erasn,di nterpret numeriecxaplr esswiiotnhsoe uvta luatthienmFg.o erx ampelxep,r etshse 5.0A.2 calcul"aatdi8dao nnd 7 ,t hen mubly2t "ia ps2l y( 8+ 7)R.e cogntihzaet 1 3 (189+3 922 1i)st hrteiem aessl arags1e 8 93+2 9 21w,i thhoauvti tnog x calcutlhaietn ed icsautmeo rdp roduct. x Analyzpea tterannsd r elationships. Generattweon umeripcaatlt eursnisnt gw o given rulaepsp.a rIednetn tify relatiobnesthwiepceson r respondinFgo rtomer rdmesrp.ea di crosn sisting ofc orrespotnedrimfnsrg o tmh tew op attearnndsg ,r apthh oer derpeadi rs ona c oordipnlaatneFe o.er x ampgliev,te hnrue l e" Ad3d" a ndt hset arting 5.0A.3 4,5 numbe0r,a ndg ivtehnre u l"eA dd andt hset arntuimnbge0 r,g enerate termisnt hree sulsteiqnuge nacnedos b,s ertvheat tht ee rmisno nes equence 6" artew itchece o rrespotnedriminsntg h oet hseerq uenEcxep.li anoifrnm ally whyt hiisss o. - ' DomainN:u mbera nd Ope fin ;BasTee n ��ti:n Understatnhde p lacvea lusey ste"m . ,:.�' Recogntihzaietn a m ulti-nduimgbieatrd ,i giinot n ep lacree presents 5.NBT.11 0t imeassm ucha si rte presientn htpesl acteoi trsi gahntd ofw haitt 9,1 2 16 represiennt thpsel acteoi tlse ft. Explain piantt htneeu rmnbseo rfz eroosft hper oduwchte nm ultipal ying numbebryp owerosf1 0a,n de xplpaaitnt eirntn hspe l acemoeftn htde e cimal 5.NBT.2 12 poiwnhte na d ecimiasml u ltipolrdi ievdi dbyea dp oweorf1 0U.s ew hole- numbeerx ponetnodt esn optoew erosf1 0'- 5.NBT.3R eadw,r itaen,dc ompadreec imtaolt sh ousandths. Reaadn dw ridteec imtaolt sh ousanudstihnbsga se-ntuemne ranlusm,b er 5.NBT.3.naa mesa,n de xpandfeodr em.,g 3.4,7 .3932 1x0 0 4 x1 0+ 7 x 1 + 39 x = + 9 + 2 + (16()1 6(01)0 60)' Compaxrt ewo d ecixm taol st housbaansdetodhn ms e aninogfts h dei giitns 5.NBT.3.b 10 eacphl acues,i ng and symbotlors e cotrhdre e suolftc so mparisons. =, 5.NBT.4U sep lacvea luuen>, d erst<a tnord oiunngdd e cimtaola sn yp lace. 11 6 Common Coach CorSet ate Grade5 Lesson(s) Standard Performo peratiownist mh ulti-dwihgoilten umberasn d widtehc imaltsoh undredths. 5.NBT.5F luenmtullyt impullyt i-wdhioglnieut m beurssi ntgh set andaalrgdo rithm. 6 Finwdh ole-nuqmuboetri eonfwt hso lneu mbewrist uhp t of our-digit divideannddts w o-ddiigviits uosrisns,gt ratebgaiseeosdn p lacvea luteh,e 5.NBT.6p ropertoifoe pse ratiaonnds/t,oh rre e latiobnesthwiempeu nl tipliacnadt ion 7,8 division. aInldel xupslttarhiacenta el culbaytu isoinne gq uatiroencst,a ngular arraaynsd,/ aorre mao dels. Adds,u btrmaucltt,i apnlddy i,v iddeec imtaolh su ndredutshisnc,go ncrete modelosrd rawinangdss tratebgaiseeosdn p lacvea luper,o pertoife s 5.NBT.7 13-16 operatiaonnds/t,oh rre e latiobnesthwieape dnd itainodsn u btracrteiloant;e thSet ratteoag w yr itmteetnh oadn de xpltahirene asonuisnegd . Usee quivalfernatc tiaosna s S tratetgoya dda nds ubtrafcrta ctions. Adda nds ubtract fwriatuchnt liidokenens o mina(tionrcsl umdiixnegd numberbsyr) e placgiivnegfn r actwiiotnehsq uivaflreanctt iinso uncsah 5.NF.1 waya st op roduacnee quivasluemno trd ifferoeffn rcaec twiiotnlhsi ke 17-20 de no.m lton ras r.o erx amIep ,2 5 1_5 23( ng Ie neI,r a a e_ L "3 + "41 2+ - 12- 1·2 b + d - (a+d b e)) - 8 . bd Solvweo rpdr obleimnsv olavdidnigt ainodsn u btracotffi roanc tions refertroti hnsega mew holien,c lucdaisnegos fu nlidkeen ominaet.ogr.s,, byu sinvgi sufarla ctmioodne losre quatitoorn esp restehnpetr oblUesme. 5.NF.2 192,0 benchmafrrka ctainodnn su mbesre nsoeff racttiooe nsst immaetnet aalnldy assetshsre e asonabloefan nesswse Froser.x amprleec,o gannii znec orrect . res2u lt1 _3 by bs ervtmha g t3 1 "5 + 72' - 7 · 2 0 < Applayn de xtenpdr eviouunsd erstandionfmg usl tiplicaantdid oinv isitoomn u ltiply andd ividfer actions. Interapf rreatc taisdo inv isoifto hnne u merabtyot rh dee nominator a Solvweo rpdr obleimnsv oldviivnigso ifwo hno lneu mbelresa ding (= 5-7 b). toa nsweirnts h feo romff ractoirom nisx endu mberes.,gb .y,u sinvgi sual fractmioodne losre quatitoorn esp restehnpetr oblFeomer.x ampilnet,e rpret � 5.NF.3 ast hree soufld ti vidbiyn gn o3t itnhga tm ultibpyli eedq ua3l,as n dt hat 23 4, � 4 whe3nw holaersse h areeqdu aalmloyn gp eopelaec phe rsohna ass hare 4 ofs izeIf p9e opwlaen ttos haar5 e0 -posuancdok fr iceeq uablylw ye ight, �. howm anpyo unodfsr icseh oueladc phe rsogne tB?e twewehna ttw ow hole numbedrso eyso uarn swleire ? Applayn de xtend pruenvdieorusst anodfmi unlgtsi plitcoma utlitoianpf lrya ctoirwo hno le 5.NF.4 numbebrya f raction. 7 Common Coach CoreSt ate Grade 5 Lesson(s) Standard (continued) DomainN:u mbera ndO perations-Fractions Applayn de xtend prevuinodeurss tandionfgm su ltliipcatainodnd ivisitoomn u ltipalnydd ivide (continued) fractions. Intertphrpeer to duct qa sa p arotfsa p artiotfqi i onnt boe qual (x* ) partesq;u ivalaesnt thlreye ,s uolfat s equenocfoe p eratai onqs b. x -7- S.NFA.aF oerx ampulseea,v isfuaraclt imoond etlos how and 22 (x� =4) � , creaats et ocryo ntfeorxt th iesq uatDioot nh.e same with (x� ()= � ) (gIennr ea(l,x� ()= a�� ). ) 185. Fintdh aer eoafa r ectanwgiltfehr actisoindlaeel n gtbhyts i liiwtni gt uhn it squaroefts h aep propruinaifttre a ctsiiodlnee ngtahnsds, h owt hatth e S.NFA.ba reiast hsea mea sw oulbde f ounbdym ultiptlhyseii ndgle e ngtMhusl.t iply 22 fractisoindlaeel n gtthofs i nadr eaosfr ectanagnlder se,p resfernatc tion produacstr se ctangaurleaars . S.NF.S Intermpurletti pliacssa ctailo(inrn egs izbiyn:g ), Compartihnsegi zoefa prodtuotc htse i zoefo nef actoontr h bea siosft he S.NF.S.a 21 sizoeft hoet hfearc twoirt,h opuetr fortmhiienn gd icamtueldt iplication. Explaiwnhiymn ugl tipalg yiivnengnu mbebrya f ractgiroena tthear1n r esults ina p rodugcrte attheartn h gei vennu mbe(rr ecognmiuzlitnigp libcya tion wholneu mbegrrse atthear1n a sa f amilciaasree )x;p laiwnhiymn ugl tiplying S.NF.S.b 21 ag ivennu mbebrya f ractlieostnsh a1nr esuilnat s prodsumcatl ltehrat nh e givennu mbearn;dr elattihpnerg i ncoifpf lrea cteiqouni valenince to� � *= theef feocfmt u ltiplbyyi1 n.g * Solvree awlo rlpdr obleimnsv olmvuilntgi pliocffa rtaicotnai nodnm si xed S.NF.6 numberes.,gb .y,u sinvgi sual fractoireo qnu amtoitdoeornl essp resent 22 thper oblem. Applayn de xtepnrde viuonudse rstanodfdi invgisst iodo inv iudnei t frbaycw thioolnes S.NF.7 numbearnsd w holneu mbebrysu niftr actions. Interdpirveitso ifao u nn iftr actbiyao n no n-zwehrool neu mbearn,dc ompute sucqhu otieFnotersx .a mpclree,aa ts et ocryo ntfeoxrt andu sea S.NF.7.a (-7-�4,) 24 visufaraclt imoond etlos hotwh qeu otiUesnett h.re e latiboentswheiepn multiplaincdda itviiotsnoi e oxnp ltahiant because (-7-�4 =) / 2 (/x 2=4 �). Interdpirveitso ifao w nh olneu mbebrya u niftr actainodcn o,m pute sucqhu otieFnotersx .a mpclree,aa ts et ocryo ntfeorx t andu sea 5.NF.7.b 4 -7- (k), 24 visufaraclt imoond etlos hotwh qeu otiUesnett h.re e latiboentswheiepn multiplaincdda itviiotsnoi e oxnp ltahiant 20b ecau2s0e 4 -7- W= x (= k4.) Common Core SSttaatned aCrodrsr elCahtairto n 8• Common Coach CoreS tate Grade 5 Lesson(s) Standard DomainN:u mbera ndO perations-Frac(tcioonntsi nued) .. , . . .' - , Applayn de xtenpdr eviouunsd erstandionfmg usl tiplicaantdid oinv isitoomn u ltipalnyd d ivide fractio(ncso.n tinued) Solvree awlo rlpdr obleimnsv oldviivnigso ifuo nnif tr actbiyon nosn -zero wholneu mbearnsdd ivisoifwo hno lneu mbebrysu niftr actei.ognb.sy,, 5.NF.7.ucs ivnigs ual fractainoden q umaotditeoorln essp restehpnert o blFeomr. 24 examphloew,m uchc hocolwaietlaelc phe rsgoenit f p eopslhea rIeb o f � chocoleaqtuea lHloywm? a ny- cuspe rvianrgiesn2 c uposfr aisins? � 3 .. " �T �- Domairi,M:'easuremen'tandD ata .' �' {'J '.'� • A - Convertl ikmee asuremeunnti twsi thian g ivemne asuremesnyts tem. Convearmto ndgi fferenstt-a�nidzmaeerdad s uremuenniwtti st hai n 5.MD.1 givmeena suremseynstt em c(oen.vge5.cr ,tm t o0 .0m5) a,n du set hese 25, 26 conversiinso onlsv miunlgt i-rsetawelop r,lp dr oblems. Represeanntd i nterpdraetta . Makeal inpel ottod ispald aayt sae otf m easuremienfn rtasc toifao u nnsi t Useo peratoinof nrsa ctfiootrnh sig sr adteos olpvreo bleimnvso lving (t�il,,l · 5.MD.2 informparteisoenn itnle idnp leo tFso.er x ampgliev,de inff ermeenats urements2 9 ofl iqiunii dd entbiecaaklef nridst ,h aem ouonftl iqeuaicdbh e akweoru ld contiatfih nte o taamlo uinnta ltlh bee akewresrr ee distreiqbuuatlleyd. Geometrmieca suremenutn:d erstacnodn ceptosfv olumae ndr elavtoel umteo m ultiplication andt oa ddition. Recognviozleu amsea na ttriobfsu otlei d faingduu nrdeesr sctoanncde opftvs o lume 5.MD.3 measurement. A cube wsiitdlhee ng1tu hn it, ac" aulnlietd ciussb aeit,doh" a v"eo nceu bic 5.MD.3.a 27 uniotfv" o lumaen,dc anb eu setdo m easuvroel ume. A solfiidg uwrhei ccha nb ep acked wgiatphosor uo tv erluaspisnn u gn it 5.MD.3.b 27 cubeisss a itdoh avaev oluomefn c ubiucn its. Measuvroel umbeysc ountuinnicgtu beuss,i cnugb iccm ,c ubiicnc ,u bic 5.MD.4 ft, 272,8 andi mprovuinsietds . Relavtoel utmoet hoep eratoifmo unlst iplaincdaa tdidointa inodsn o lrveea wlo rladn d 5.MD.5 mathemaptriocball eimnvso lvvoilnugm e. Fintdh veo luomfea r igrhetc tanpgruilsawmri twhh ole-nusmibdleeer n gths byp ackiinwtgi tuhn ictu beasn,ds hotw hatth veo luimset hsea mea sw ould 5.MD.5.bae f ounbdym ultiptlhyeeid nggle e ngtehqsu,i valbeymn utlltyi ptlhyei ng 27 heigbhytt h aer eoaft hbea seR.e prestehnrte ewfhoollde -nupmrboedru cts asv olumee.sg,t. or, e prestehanest s ocipartoipveeor fmt uyl tiplication. Appltyh feo rmulaIs w ha nd b hf orre ctanpgruilsatmros = x x = x 5.MD.5.fbi nvdo lumoefrs i grhetc tanpgruilsawmris t whh olneu mbeerd glee ngitnh s 28 V V thceo nteoxfst o lvrienawglo rladn dm athematpircoablle ms. 9