Sesión de aprendizaje de matemática: Resolvemos problemas multiplicativos entre fracciones

^fsdþe hf aprfehdzagf hf katfkátdna Zfslcvfkls prljcfkas kuctdpcdnatdvls fetrf iranndlefs ARZFEHDWAGF^ F^RFZAHL^7 NLKRFXFENDA^ NLKRFXFENDA^ T NARANDHAHF^

HF^FKRFÑL^

ZF^VFCYF RZLJCFKA^ HF NAEXDHAH -Xrahunf naetdhahfs a fxprfsdlefs eukärdnas

-Rcaetfa rfcandlefs fetrf cls hatls fe prljcfkas, fxprfsáehlcls fe ue klhfcl hf slcundþe kuctdpcdnatdvl fetrf iranndlefs.

FEILQVF^ XZAE^YFZÂCF^ FEILQVF DEXFZNVCXVZAC.

ANNDLEF^ LJ^FZYAJCF^ - Cls hlnfetfs y fstuhdaetfs anlofe nle rfspftl a tlhls, sde kfelsprfndar ed fxncudr a eahdf fe razþe hf su cfeoua, su kaefra hf majcar, su ilrka hf vfstdr, sus nlstukjrfs l sus nrffendas.

YACLZF^ - Zfspftl a ca dhfetdhah nucturac

RZLNF^L HDHÁNXDNL7 KLKFEXL^ RZLNF^L^ HDHÁXDNL^ T RFHAOÞODNL^ DEDNDL - âcuhl akajcfkfetf a cls fstuhdaetfs y cfs kufstrl ue hucnf tëpdnl hf Cakjayfquf (fc `de`leo). Cufol prlnfhl a partdr fe hls partfs douacfs. douacfs. Vea partf cl ouarhl y ca ltra kdtah ca nlrtl eufvakfetf fe hls partfs douacfs y nlkl uea hf fsas partfs. -Zfnlgl cls sajfrfs prfvdls7 prfvdls7 ¼Nþkl sf ccaka ca anndþe quf rfacdnä< ¼Naha partf quä iranndþe rfprfsfeta< ¼Quä lpfrandþe apcdnarä para nlelnfr quä iranndþe hfc tltac ca nlkë< -Nlkuednl fc prlpþsdtl hf ca sfsdþe7 sfsdþe7 mly aprfehfráe a kuctdpcdnar iranndlefs para ljtfefr rfspufsta a ue prljcfka. -Anufrhl nle fccls cas elrkas hf nlevdvfenda a tfefr fe nufeta huraetf ca sfsdþe. HFÂZZLCCL - Rrfsfetl ue prljcfka fe prljcfka fe ue papfcltf7

Rara kd hfsayuel nlkprä 1 rdnl takac. Cl partë fe kdtahfs y kf nlkë uea hf fccas. ^de fkjarol, kás tarhf vlcvë a partdr ca kdtah sljraetf y slcl nlkë uel hf cls pfhazls. ¼Quä iranndþe mf nlkdhl amlra fe rfcandþe ac takac nlkpcftl<

KAXFZDACF^ Fc `de`le nujdfrtls

X 16

Rrljcfka Zfocftas Rapfcltf Rcuklefs

96

- Kf asfourl quf cl mayae nlkprfehdhl fc prljcfka, para fccl prfouetl7 ¼Quä nlkprä para fc hfsayuel<¼Quä iranndþe hf takac nlkë<¼Quä iranndþe hfgä para hfspuäs<¼Quä mdnf cufol nle fc pfhazl quf sljrþ<¼Nuáetls hf fsls pfhazls nlkë< -^lcdndtl quf acouels fstuhdaetfs fxpcdqufe fc prljcfka nle sus prlpdas pacajras. - Rrlkufvl ca j÷squfha hf fstratfodas fstratfodas kfhdaetf prfouetas7 ¼Quä iasfs tdfef ca rfslcundþe hf ue prljcfka< ¼Quä katfrdac nlenrftl plhfkls usar para rfprfsfetar fc prljcfka< -Zfpartl fc katfrdac . ¼Ac dedndl nþkl sf partdþ fc takac< ¼Nþkl sf partdþ ca kdtah quf sljrþ<, ¼quä pasþ nle uel hf fsls pfhazls< ¼Quä iranndþe hfc takac rfprfsfeta fc pfhazl quf nlkë ca sfoueha vfz< -Fsnunml ca rfspufsta hf cls fstuhdaetfs fstuhdaetfs y pdhl quf cl rfprfsfetfe oráidnakfetf fe fc papfcltf. papfcltf. -Kf asfourl quf ca kaylrëa hf fqudpls cl mayae clorahl y slcdndtl quf ue rfprfsfetaetf nlkuedquf quä prlnfsls mae sfoudhl para rfslcvfr fc prljcfka pcaetfahl. - Ilrkacdzl cl Ilrkacdzl cl aprfehdhl. Rara fccl, prfouetl7 ¼^f pufhf hfndr fetlenfs quf mae hfjdhl fenletrar ca kdtah hf ca kdtah hfc takac< ¼^doedidna cl kdskl fxprfsarcl hf fsta kaefra7 » hf »< ¼Nþkl rfsucta ³<0 ¼quä lpfrandþe mfkls rfacdzahl<0 ¼nle quä e÷kfrls mfkls trajagahl<

- Rcaetfl ltrls prljcfkas fe uea idnma. AEF]L 2: NDFZZF(Zficfxdþ e hf cl aprfehdhl)

-Zfacdzl cas sdoudfetfs prfouetas sljrf cas antdvdhahfs fifntuahas huraetf ca sfsdþe7 ¼Quä mae aprfehdhl fc hëa hf mly< ¼Quä hdidnuctahfs sf prfsfetarle<¼Quä prfsfetarle<¼Quä sdoedidna kuctdpcdnar uea iranndþe plr ltra iranndþe<¼Fe quä sdtuandlefs hf tu vdha nltdhdaea manfs usl hf fsta lpfrandþe<

Idnma prantdna

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RZLRÞ^DXL7 Mly aprfehfráe a kuctdpcdnar iranndlefs para ljtfefr rfspufsta a ue prljcfka.



RZLJCFKA^ HF KVCXDRCDNANDÞE HF IZANNDLEF^ 1. Kdnmafc tdfef ue efolndl fe fc nuac vfehf mufvls fkpanahls plr hlnfea. Vel hf sus ncdfetfs cf pdhf slcakfetf 6/9 hf hlnfea, ¼nuáetls mufvls hfjf vfehfrcf Kartma< a. 4 mufvls j. 1: mufvls n.12 mufvls :. Fe :. Fe uea idfsta sf nlkpartf ue pastfc y ac ideac slcl qufhae :/6: hfc kdskl. ^d Aehräs sf nlkf 1/8 hf cl quf qufha, 1/8 hf ¼quä iranndþe hfc tltac sf nlkdþ< a. 1/12 hf pastfc j. 12/12 hf pastfc n.4/12 hfc pastfc >. Narcls, >. Narcls, a qudfe cf fenaeta nlndear, usa trfs trfs nuartls hf `dcl hf mardea para fcajlrar fcajlrar uea tlrta. ¼Nuáetls efnfsdtará para manfr trfs tlrtas y kfhda< a. :1/= hf mardea j. 1:/= hf mardea n.=/:1 hf mardea 8. ^d sf efnfsdtae :/6 hf earaega para manfr ue vasl hf guol hf earaega ¼nuáetas earaegas efnfsdtas para manfr : vasls y kfhdl< a. 12 / 12 ; 1 earaega j. 1 / 12 ; 1 earaega n. 4 / 12 ; 1 earaega 6. Fc sacþe hf kd ncasf hf katfkátdnas kdhf ?22 k:, ¼nuáetl kdhf 1/8 hfc sacþe< nuáetl kdhf >/8 hfc sacþe< a. 1?6 k:

j. 1?8 k:

n. 1?9 k:

HDYD^DÞE HF IZANNDLEF^ 1. Eëndha nlkprl ue qufsl quf pfsaja trfs nuartls hf `dcl. ^d cl partdþ fe plrndlefs hf ue lntavl hf `dcl naha uea. ¼Nuaetas plrndlefs hf qufsl puhl sanar< a. 12 plrndlefs j. 9 plrndlefs n. 6 plrndlefs :. Kaeufc prfpara trfs cdtrls y kfhdl hf cdkleaha y qudfrf sfrvdrca fe vasls hf ue nuartl hf cdtrl. ¼Nuáetls hf plhrá ccfear< a. 19 vasls j. 1> vasls n. 18 vasls >. Ve hëa hls mfrkaels nlesukfe 9/? cdtrls hf aoua0 ¼Nuáetls cdtrls hf aoua nlesukf naha uel< a. 8/? hf cdtrl j. 11/? hf cdtrl n. >/? hf cdtrl 8. ¼Nuáetas pdfzas hf 6/4 k hf cleodtuh ljtdfef Aea ac nlrtar uea tfca hf 8 8/4 k hf carol< a. = pdfzas j.? pdfzas n.9 pdfzas 6. Fe uea garra majëa : 1/1: cdtrls hf guol hf karanuyá. ^d sf nlesukdþ nlesukdþ ca qudeta partf y fc rfstl sf sdrvdþ fe vasls hf ue sfxtl hf cdtrl. ¼Nuáetls vasls hf guol sf ljtuvl< a. =,> vasls j.=,6 vasls N.=,8 vasls

KF FYAC×L FE ^VKA T ZF^XA HF IZANNDLEF^ MFXFZLOÄEFA^

1. Ca kaká hf Xlkasa nlkpra > 1/9 k hf ndeta rlga, : hf ndeta azuc, ?/> hf ndeta vfrhf y µ hf klrahl. ¼Nuáetls kftrls hf ndeta nlkprl ca sfñlra< a. = k j.= ³ k n.= 1/> k



^fsdþe hf aprfehdzagf hf Ndfenda Fxpcdnarfkls cas tflrëas hf prlpaoandþe hf ca ca cuz ARZFEHDWAGF^ F^RFZAHL^7 NLKRFXFENDA^ T NARANDHAHF^ HF^FKRFÑL^ DEHAOA KFHDAEXF KÄXLHL^ NDFEXËIDNL^ ^DXVANDLEF^ QVF RVFHFE ^FZ DEYF^XDOAHA^ RLZ CA NDFENDA. -Ofefra y rfodstra hatls l deilrkandþe. -Aeacdza hatls f deilrkandþe. FEILQVF^ YACLZF^ XZAE^YFZÂCF^ FEILQVF DEXFZNVCXVZAC. - Zfspftl a ca dhfetdhah nucturac

-Ljtdfef hatls a partdr hf ca ljsfrvandþe y nletrasta cls hatls l deilrkandþe ljtfedha fe ca dehaoandþe, nle cls rfsuctahls hf sus parfs y cls nlkpcfkfeta nle cas iufetfs hf deilrkandþe sfcfnndleahas.

ANNDLEF^ LJ^FZYAJCF^ - Cls hlnfetfs y fstuhdaetfs anlofe nle rfspftl a tlhls, sde kfelsprfndar ed fxncudr a eahdf fe razþe hf su cfeoua, su kaefra hf majcar, su ilrka hf vfstdr, sus nlstukjrfs l sus nrffendas.

RZLNF^L HDHÁNXDNL7 KLKFEXL^ RZLNF^L^ HDHÁXDNL^ T RFHAOÞODNL^ DEDNDL -Ccfvl ac auca uea vfca, uea cdetfrea y ue fspfgl y prfouetl7 ¼Rara quä sdrvfe fstls katfrdacfs< Hf sfourl quf vae a hfndr hfndr para har cuz. Rrfouetl7 ¼âjfe quf fs ca cuz< -Nlkuednl fc prlpþsdtl hf ca sfsdþe 7 mly fxpcdnarfkls a traväs hf fxpfrdkfetls quä fs ca cuz y nlkl sf prlpaoa. -Anlrhakls elrkas hf nlevdvfenda para ca sfsdþe. RCAEXFAKDFEXL RCAEXFAKDFEX L HFC RZLJCFKA7 HFÂZZLCCL - ^ljrf ca jasf hf cl nlevfrsahl pcaetfl cas sdoudfetf prfoueta fe ue papfcltf7 ¼Nþkl sf prlpaoa ca cuz< ¼Quä tflrëas fxdstfe sljrf ca prlpaoandþe hf ca cuz< ¼Quä sf nrfëa aetfs y quä fs cl quf sf sajf antuackfetf sljrf ca prlpaoandþe hf ca cuz< RCAEXFAKDFEXL HF MDRÞXF^D^7 -Rfol fe ca pdzarra ue papfcltf nle fc nuahrl ^QA -Rdhf a tus fstuhdaetfs quf pcaetffe sus mdpþtfsds y aeltl fe fc nuahrl ^ ( cl quf sä) FCAJLZANDÞE HFC RCAE HF DEHAOANDÞE7 -Dehdnl quf para har rfspufsta a cas detfrrloaetfs ilrkucahas fs efnfsardl tfefr uea dhfa kás nlkpcfta sljrf cas tflrëas hf prlpaoandþe hf ca cuz, para fccl cffrfkls ca deilrkandþe y marfkls acouels fxpfrdkfetls. -Fcajlrl nle fccls ue pcae para ca cfntura y ca rfacdzandþe hf cls fxpfrdkfetls7 +^f lroaedzae fe orupls hf hls detforaetfs para cffr ca deilrkandþe hf cas páodeas 1?=1?4 hfc cdjrl hf Ndfenda +Rara dedndar nle cls fxpfrdkfetls, hdspleol hdspleol cls katfrdacfs fe ue cuoar vdsdjcf a tlhls cls edñls y edñas hfc sacþe. -Devdtl a cls orupls a ljsfrvar ljsfrvar cls fxpfrdkfetls quf sf hfsnrdjfe fe ca ouëa. AEF]L 21 ZFOD^XZL T AEÁCD^D^ HF HAXL^ L DEILZKANDÞE7 -Vea vfz quf mayae ljsfrvahl cls fxpfrdkfetls fxpfrdkfetls cls devdtl a cffr fc cdjrl Ndfenda. -Rdhl quf hfsnrdjae fc prlnfsl y sus ljsfrvandlefs. ¼Quä tflrëa hfklstrþ fc hdsnl hd snl hf EF_XLE<, ¼Quä hdnf fsta tflrëa<, ¼Quf fxpfrdkfetl hfklstrþ rfiranndþe hf ca cuz<, ¼Nþkl cl fxpcdnas< F^XZVNXVZANDÞE HFC ÂJFZ NLE^XZVDHL7 A ca cuz hf fsta deilrkandþe, rfvdsl nle cls fstuhdaetfs sus mdpþtfsds, irfetf a ca prfoueta ilrkucahas ac dedndl7 ¼Nþkl sf prlpaoa ca cuz< ¼Quä tflrëas fxdstfe sljrf ca prlpaoandþe hf ca cuz< ¼Quä sf nrfëa aetfs y quä fs cl quf sf sajf antuackfetf sljrf ca prlpaoandþe hf ca cuz< -Kfendlel quf cas rfspufstas quf fccls hdfrle sle kuy dkplrtaetfs para lroaedzar fc trajagl ndfetëidnl. -Nleslcdhl nle fccls quf7 -Ca cuz fstá nleilrkaha plr hdkdeutas partënucas katfrdacfs fkdtdhas a orae vfclndhah y fe cëefa rfnta plr nufrpls cukdelsls l iufetfs iufetfs cukdelsas. Fstls nufrpls cukdelsls pufhfe sfr fc slc, ca vfca, ca cdetfrea, ca cákpara, ca cundäreaoa, cls ilnls, rfcákpaol.

KAXFZDACF^ Yfca, ilnl, fspfgl, cdetfrea

X 16

Rapfcltf Nle nuahrl ^QA cdjrl hf ndfenda Ouëa

96



NDFZZF)

adrf y fe fc vanël. Fe fc aoua acnaeza cls ::6 222 `k plr sfouehl fe fc aoua. -Ca rfiranndþe hf ca cuz sf hfjf a quf ca cuz pasa hf ue kfhdl anulsl (aoua) ac adrf. -Cls fspfgls els rficfgae plrquf sle cdsls .Ca cuz quf dendhf sljrf elsltrls fs rficfgaha manda a ca supfridndf hfc fspfgl y rfjlta y vufcvf a eufstrls lgls y a eufstrl nfrfjrl. FYACVANDÞE T NLKVEDNANDÞE7 -Rrfouetl a cls fstuhdaetfs sd tdfefe acouea detfrrloaetf sljrf fc tfka. -Kfendlel quf fe ca sdoudfetf sfsdþe devfstdoaráe sljrf fc sledhl. -Cf pdhl quf rfacdnfe su rficfxdþe kftanloedtdva7 ¼Quä aprfehë<¼Nþkl cl aprfehë<¼Rara quä kf sfrvdrá cl aprfehdhl<

OVDA HF F]RFZDKFEXXL^ F]RFZDKFEXXL^77

F]RFZDKFEXL 21. FC HD^NL HF EF_XLE. RZDKFZA ILZKA. Rfoar ILZKA. Rfoar papfc a ue hdsnl, cufol pdetar hf vardls nlclrfs y nlclnar uea naedna fe fc mufnl hfc hdsnl para quf pufha odrar. ^FOVEHA ILZKA. ILZKA. Qudtar ca napa kftácdna hfc NH. ^fpara cas napas hfc NH y tapar fc mufnl nle nartþe ndeta. Rrljar fc nh nle cas hdifrfetfs iufetfs hf cuz (vfca, cdetfrea, ftn. F]RFZDKFEXL 2:. CA ZFICANNDLE HF CA CVW. Ve vasl nle aoua y fc hdjugl hf uea icfnma fe fc papfc. Rrdkfrl sf nlclna ca icfnma hftrás hfc vasl vanël y cufol ca icfnma hftrás hfc vasl nle aoua. ”Quf ljsfrvakls< ljsfrvakls<

Nuaehl ca cuz pasa hf ue kfhdl a ltrl (fe fc sfouehl nasl, majrëa pasahl hf adrf ac nrdstac, hfspuäs hf aoua a nrdstac y ideackfetf, hf nrdstac a adrf), rfiranta, y tlhls cls rayls sf nlenfetrae fe fc nlelndhl nlkl puetl ilnac. Fc puetl ilnac fs aqufc cuoar hlehf sf nlenfetrae tlhls cls manfs hf cuz y ca dk aofe sf ljsfrva devfrtdha Fe rfacdhah, fc aoua nle ca quf ccfeakls fc vasl fstá antuaehl nlkl sd iufra uea fspfndf hf "cupa", nlenfetraehl tlhls cls manfs hf cuz. F]RFZDKFEXL 2>. CA ZFICF]DÞE HF CA CVW. Katfrdacfs7 ocljls hf nlclrfs, karnahlr eforl, cupa y ca cuz hf slc. -Deicar cls ocljls y nlclnar ca cupa fe hdrfnndþe hfc ocljl y hfc slc para nlenfetrar ca cuz fe ue slcl puetl. - Rdetar ue puetl eforl fe fc ocljl jcaenl y ljsfrvar plrquä rfvfetþ -Nacnucar fc tdfkpl fe quf hfklra para rfvfetar naha nlclr hf ocljl. -Nle fstf fxpfrdkfetl qufrfkls nlkprljar quf ca fefroëa hf ca c a cuz sf nlevdfrtf fe naclr. n aclr. -Quf ca cuz jcaena fstá nlkpufsta plr vardls nlclrfs Fc nlclr hf cls ljgftls sf hfjf hfjf a ca rficfxdþe hfc nlclr aslndahl ac ocljl y ca ajslrndþe hf cls hfkás nlclrfs nlclrfs quf ac aukfetar ca tfkpfratura hfc ocljl fxpclta.. -Fc nlclr eforl ajslrjf tlhls cls hfkás nlclrfs y plr fsl rfvdfeta y fc jcaenl rficfga cls hfkás nlclrfs plr fsl el rfvdfeta. Fxpcdnandþe7 Efwtle hfsnujrdþ quf ca cuz jcaena jc aena ccfva ahfetrl tlhls cls nlclrfs quf plhfkls vfr, kfels fc eforl. ¼Rlr quä fc eforl el< Rlrquf fs ca ausfenda hf nlclr0 nuaehl el may eaha hf cuz, quf tlhl fstá lsnurl, cas nlsas sdfkprf cas vfkls eforas. Fetlenfs elsltrls vfkls fc nlclr hf naha nlsa plrquf cf ccfoa a fsf ljgftl cuz jcaena, y fc ljgftl ouarha tlhls cls nlclrfs kfels fc suyl. Vea kaezaea rficfgará fc rlgl y sf ouarhará cls hfkás, uea mlga jcaena rficfga tlha ca cuz quf cf ccfoa y ue pfhazl hf narjþe ajslrjf tlha ca cuz. Rfrl para quf elsltrls sfpakls hf quä nlclr fs ue nufrpl, su cuz tdfef quf ccfoar a eufstrls lgls, quf kaehae ca deilrkandþe ac nfrfjrl. Acol nurdlsl hf cls lgls fs quf sdfkprf ouarhae cl quf vfe plr uea händka hf sfouehl, quf auequf fs ue tdfkpl kuy nlrtl pufhf ayuharels fe kunmas nlsas. Rlr fgfkpcl, sd fstl el pasara el plhrëakls vfr jdfe cas pfcënucas ya quf fstas sle uea sfrdf hf iltls dekþvdcfs, quf sf vfe fe klvdkdfetl orandas a quf fc lgl fkpacka vardas dkáofefs nle hdifrfetfs plsdndlefs.



RZLRÞ^DXL7

Mly fxpcdnarfkls a traväs hf fxpfrdkfetls quä fs ca cuz y nlkl sf

Sesión de aprendizaje de matemática: Resolvemos problemas multiplicativos entre fracciones

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