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V Subtraction, Multiplication and Division, "Geometrical Figures, Liries. * and Lineal Measurement, At..A

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V Subtraction, Multiplication and Division, MOM ... EDli6MD ii030 430 AUTHOR " Beatty, ;Leslie: And Others TITLE Miftematicas Fara ta Escuela. Primarias Grado Li(Parte 2) Comentario% Traduccion Prelimimalr de la Ecticion en Ingles Revisadtta. (Mathematic's for the Elementary SchoolGrade 14 Part 2Teascher is Commentary. Pre3.tininary Translatiion of the Revised Enclish. Edition). r INSTITuTpN Statford Univ.,. talit;--Sc)foinlnitbema-tics -Study-- Group. .SPONS AG pri Natioaal Science Fountlation, Washingt.on, t.C. PUB DATE. 67 . NOTE' 145Bp.: For teleCte.d document in Spanish, see SE 0 0 1129. A.ANGULGE Spanish, EDRS PRICE. MF01/PC19 Plus Postage. DESCRIPTORS: *.Arithmetic: *Bilingual' Education': ne,mettaty Education: 4Elementariy School. Mthematics: Geometry; ' Grade 14: Instuctiona.1 Materials: *Mathmatics Curriculum: NathOmatics Instruction; *Te?tching , Guides IDENT PIERS *School Mathematics Study Group ABSTRACT This is Part 2 of the teacher os commentary for*the grade41 mathematics pro§ram.. Part 2' includes the ccmmentary for chapterp 6 through 10. Topics covered inclucle addition ana V subtraction, multiplication and division, "geometrical figures, liries. * and lineal measurement, aT..a. .tractiqns. (RH) .1% NE, V *****It*********************************,******************************** .4 ReproauCtions supplied by RDIIS are the best that can be made * * from the original document.' N * ************4********************************************************** . 4 44 4444. , a. ''' 444. 4, NtiAT.EMATIcAgPARA.L ESC:0E1A i'it.111/ARIA,. Grado 4 (Pane 2) Comentario. t. .(Traduccitin ireliminar de la Idicieiven isglis-reviaada) 1, *. **PERMISSION TO REPROD CE THIS U S DO.ARTMENT OF HEALTH. V MATERIAL HAS BEEN GR TED BY EDUCATION IL WELFARE NATIONALINSTITUTE OF EDUCATION 0..ivrks TH)S .DOCUME NT HAS BEEN REPRO- DUCE E x4( TY AS RECEIVE() F ROM i.*!n Niz THF RE ()SON OR ORGANIZA T ION ORIGIN- ATING )T POINTS OF VIEW OR OPINION" "STATED DO YOT NECESSARILY REPRE- TO THE EDUCATIONAL RESOURCES SENT OF F IC lAt. NATIONAL INSTITUTE OF INFORMATION C.FNTFF) (MCI ". # DLKAT ION POSITION OR POL IC`f a- V. a ',a a 4 4 MATEMATICA:S PAll'A LA ESCUELA PRIMARIA Grado 4 (Pine 2) Comentario (Traducción preliminar de la edicini en inglés revisada iléxt9 preparado bajo,la supervisiem del Comite para la.matemitica de la escuela primaria deI irupo de Estudio de la Matemi.tica Escolar: . Leslie Beatty Distrito eseelar de Chula Vista Chula Vista, California E. Glenadine Gibb Colegio.para Maestros del'Estado .de Iowa, Cedar FalId, Iowa W.41. Guy ,,Universidad de Texas S.B.yIackson - Universidad de Maryland Irene Sauble % Escuelas plib4.cas de Detroit Maa. Stone Universidad de Chicago Weavqr Universidad be Boston .112;L: wilder Universidad de Michigan .4;2W - a sos. ® 1967 by The Board ofTruitliteersigtsthe Leland Stanford junior University .Printed in the United Stattipf Ainerica Imp Permission to make verbatim use of material in this book must be secured from the Director of SMSG. Such permission will be planted except in unusual circumstances,Publications incorporating SMSG materials must include both an acknowledgment of the SMSG copyright (Yale Univer . sity or Stanford University, as the case may be) and a disclaimer of SMSG endorsement. Exclusive license will not be granted save in exceptio.nal circumstances, and then only by specific action of the Advismy Board of SMSG. V Financial support for the School Mathematics Study Group ha's been provided by the National Science poundation. Proy9rto de Traducci6n al Espgiol ,Comisi6n Consultiva -t egle, Universidad e Stanford. F. Fet4liniversidad de Columbia o Garcia, Univérsidad de.Puerto Rico S. Max Kramer, San Jose State College' 0 111 .TABLA DE lAS omeritario.Rara Texto dei el maestro estudAante r Oapitulo ' -6. PROPIEDADES Y,TEONIGAS DE LA ADIOION Y.SUSTRACCIdN II .503 Proptisita de'la unidad. ' 503' Aase latemitica* -0 * . 504. Enseftani& de la 1L-1:1aad 508 NombresdiferenZesp9.ra . el misma nilmero . 508,516 297 Rspaso de la adicion 512,516 - 299 His sdbre la adici6n 517,520 --I 300 a Otto m4tododara'sumar. 522,523' 302 4. .Repaso de la,sUstracción 528/531 307 146s sabre la sustracciOn 02,535 308'- &Ira m4odo-Para reStar 537,540 310 5u6ttacc16n con ceros 543 313 Relaci6n de las técnicas 1 de-la ad1ci6d'y la sustraccicin 545,548 315 El lenguaje de los pro- blemas de sustracc16n. 552,555 31/9 Razonamiento en la forma si-entonces 5571558 321 Rebaso 561,563 324 Amplicaci6n ..... 569,571 330 TEONICAS DE LA HULTIPLICAOION' Y LA DIVISION . 575 Prsv6sito de'la unidad . 575 Base matem4tiea 576 Ensetianza (re la unidad 585 Repaso de laimiltiplica- ci6n y la dIvlsión-- Operaciones 334, Multtplicaci6n porxrnil- tlplo.s diez 592,594 339 Mult1pi1cac1611 pormill- t._ tiplosele 597,599, 342 ' 4. -* kjOQmentario pain)! Texto del , CaPitulo el maest.ro estudiante MAs'.intormaclOn acerca. depqMo multiplic . 2 606 345, .kltiplicaci6n denu ergs maS grandes . 609) 6 1 1 , 34& metodo mis torto de 615.0611 '352 Mult1p1.1caci6n,de mimeros menores que 1007-7igor 620,623 355- Determlnación%de productos de dos nlimeros cualesr quierd mayores que (y menores que, 100),. 626,630' 358 Uso de la multlplitaci6A lb4, para resolver problemas en forma d9 cuentQ 636'4637 '36,4 S. Determlnaci6-factores \---desconocidos 64 6451. 367 Una,manera de dividir dos . ,numeros 65 654 373 lets 1nfoimaci6ntacercade la divisl.611. de dos nlimeros **** *** 658- 375 Uso de la divisiOn para resolver"problemal en' forma de cuento s f66,662. 377' Mis pricti6aen la dlvi- , si6n.de'n-ilmeros . 666,670 381 , Determinación de ,cocientes y residuos 674,678 85 Repaiydampliacion . 681,685 388 Ejerci6ios de prictica . 688 2391 Repaso 692 395 CARACTERIZACION DE F1GURAS GEOMETRICAS CORRIENTES 707 Prop6sito de,la unidad. 70 Base matilitica 708 Enseflanza. de-la 'unidad 716 Tus() triingulo y el adril4tero . 0716.718 410 Comparaci6n de segmentos- de recta 722,724' 414, vi 60 Oomen io para Texto. del el mstro estuaiante Oapitulo ) Triingulos iseafaeles yequiliteros 728)730 418 Angulos 'rectos 733,734, 421 Rectingulos y 'cuadrados "09,740 Ito Superficies' 743,761 429. Prisma rectangular 744,763 431 Priama,triangular' 747,767 45 Pir4m14e. .... 7480771 439 Oilindrd 751,773 441 Cono 754,777, 445 Superficie esf4rica 756,779 447 Cubo 758 Tetraedrp 759 Artatas y cams 781 449 MEDIOION LINEAL 783.2. Prop6sit.(5 de la unidad 783 pase matemitica' 6 784 Enseanza de la unidad . 797 Oomparación de tamahos 798,800 451 Comparación,de tamaflostn contar .... - 862 453 Uso de un compis pare comparar segmentos . 808 459 , edición de segmentos 81o,8 1 146i 1J:9c, de un compis-para modir segmentos recti- 813 .463 Medici6n con;la aproxima- 'cit4n de una unidad 815 465 Udd de unidades.normali- - Was de longitud 818,820 468 Escalas de . 826,827 474 USO4e.esca s .de medida 831 La esgala en pulgadas y la .escala'encentimetros . 83Z Otras unidades.normaliza- das 836,837 482 CombinaciOn*de longitudes 842 487 Perimetro 849,850 494 ,0 \-) i-Comentario pare. Texto del- Capitulo el maestro .estudiante Perimetros 'de poligonos 855 '.499 Meterminaoi6n de peri- metros .. a. 859 503 10. EL CONCEPTO DE IRTMERO RACIONAL863 _Prop6sito de la u4dad . 863 Una nota.para'el maestro 864 Base, matemitica Materiales . 879 Ensetanza.de la unUlad 885 , La idea de ntimer6 raeionai 885;889 506 Unt nueva. elase Nde 'Inimeros 893,894' 510 WiMeros ragianales mayores que pno . 902,905 Nombrei diferehtes para ,e1 MiBmo niimero . 911,013 524 0rdenaei6n de'los nilmeros raeionales 923,924 534 Una nueva clase de nombres930,932 540 Uo de los nximeros racionales 938,939 *546 lUerciePlas de prietiea 945 552 Repaso 949 556 S. viii \ OapItulo 4 0 ,PROPlEDADES Y TEbNICAS DE LA AD1CION YLi SUSTRACCIONII PROPOSITO DE-LA UNIDAD Ayudar a los estudiantes a Comprender tecnicas para sumar yreitarnUmeros'con numerales Ps varios digites, haeiandoles entender cOmo esas te,9nicaa dependen delas prepiedades devnuestro sistema denumeraci6n, dp las propiedades corimatativa y asociativa'de adici6n. - ) 2.*-4,0Pudar a los.estudiantes a'darsecuent'a de que si conocen . las combinations's bisicasde la adiciOn y 1as propiedades ., y-restar nil- . de la:"adiei6n y lasustiacci6n,pu*Sden.suar . i meros cuyos numerales eontenganvp..rioq-digitos. Iyudar a los esiu#antes a lograr destreza enL. adieicin y laAustracci6m,'Io midmo que en la comprobapión de los - resultados de diehas operaciones. Ayudar a-los' tatudianteh aperfaecionar su habilidad pava resolver prob emas mediante elempieo de enunciados.mate- mkticos en ea os que requierA Ia'adici6n y lasustracOión d9 niimeroi cuyossnumerales tienenyarioa digitos, dand9 preferenciaos. Aprender a decidircuindo se debe emplear la suOtmecion. Los alumnoe que ya hayan aprendido aemplear perfectamente las tecnicas ge adici6n la,.sustrac?i6n podrin:completar ripidilmente la primera mitad de esta upidad. Gtros alumnOs :deberin estudiailik cOn misdetenimiento. Sin embargo, la ex- plicaciem de los"concei4os fundamntales que seemplean en las t4onicas es importante y nd debe descuidose conninglin grupo. \porl contrario, debedetrsele.preferencia.' La explisepi6nide èsoa conceptos y'el desarrollo pela habilidS'd para rdsolver 'problemas son los obfetivos principales de es,taunidad. 4 4. 503 - 4 9, si* BA.SE MATEMATIOA 4 I. respuesta a_li.pregunta: %cal es lasuma (WI> y 2?", es 5 + 2. Generalmente, se considera lipe la pregunta significat ds el numeral decimal cle Iasuma de 5 S'T 2?" Para esta preguntal la'respuesta es 7. Anilogamentel la respuesta a: "4Que,ntlmer9 hay quesumar a 4 para que la suma sea- 7?", es 7 - 4.. EiiP.resado como un numeral decimal, '/"(- 4 'es 3. La expbesitin.892 +7367 es una respuesta cotrecta a la., pregunta:1-"Ouil'es lasuma de 892y3679", pero; geneisl-t mente no esla tap conveniente. .Se espera qtiese de como respuesta,el numeral decimal 1,259. Luego,akraprender proceso de la adici6n, un objetiv90o imporiante es escribir uña suma eomo 892 + 367en la forma,de un Auieral decimal. Si los alimeros que se stIman son 42 5i, 37, el'resul'cado es 7 decenas y 9 unidafles.
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