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Libro del Docente Soy de quinto 1a edición, 2010.
Martínez, Olga EDIBA LIBROS S.A.
Libro del Docente es material complementario del libro Soy de quinto.
ISBN 978-987-583-193 978-987-583-193-3 -3
Av. Forest 579 (C1427CEO) Ciudad Autónoma de Buenos Aires Tel: 011-4554- 9800/7577 /8688 - Fax: 011 -5256-635 2 Mail:
[email protected] © 2010 Editorial Ediba SRL Queda hecho el depósito que establece la ley 11.723.
Libro de edición argentina. Todos los derechos reservados. No se permite la reproducción parcial
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ÍNDICE Índice ................. .................................... ...................................... ...................................... ...................................... ...................................... .......................Página ....Página 2
Páginas iniciales Soy de 5to con vos .................. ..................................... ...................................... ...................................... ....................................Pág .................Página ina 4 Narradores Narrador es de cuentos. Los dinosaurios ¿Dónde están?..................Página 5 Los niños de este ciclo................................. ciclo.................................................... ....................................... ................................Página ............Página 6
Áreas de aprendizaje Lengua (Prácticas del Lenguaje) Fundamentación del área .................. Fundamentación ...................................... ....................................... ......................................P ...................Página ágina 7 Proyectoss didácticos ................. Proyecto .................................... ...................................... ...................................... .....................Páginas ..Páginas 8 a 16
Ciencias Sociales Fundamentación del área ................... Fundamentación ....................................... ........................................ ...................................Pági ...............Página na 17 Proyectoss didácticos................................... Proyecto didácticos...................................................... ...................................... ....................Páginas .Páginas 18 a 26
Ciencias Naturales Fundamentación del área .................... Fundamentación ....................................... ....................................... ...................................Pági ...............Página na 27 Proyectoss didácticos ................... Proyecto ...................................... ...................................... ..................................Pági ...............Páginas nas 28 a 36
Matemática Fundamentación del área ................... Fundamentación ...................................... ....................................... ....................................Pági ................Página na 37 Proyectoss Didácticos ................................................... Proyecto ...................................................................... .....................Páginas ..Páginas 38 a 46
Solucionario de Matemática Proyecto 1: ................. .................................... ....................................... ....................................... ....................................Pági .................Páginas nas 48 y 49 Proyecto 2: ................... ...................................... ...................................... ...................................... ...................................Pág ................Páginas inas 50 a 53 Proyecto 3: .................. ..................................... ...................................... ...................................... ....................................Pá .................Páginas ginas 54 a 56 Proyecto 4: ................... ...................................... ...................................... ...................................... ...................................Pági ................Páginas nas 57 a 59 Proyecto 5: ................. .................................... ...................................... ...................................... .....................................P ..................Páginas áginas 60 y 61 Proyecto 6: .................. ..................................... ...................................... ...................................... ....................................Pá .................Páginas ginas 62 a 64 Proyecto 7: ................. .................................... ...................................... ...................................... .....................................P ..................Páginas áginas 65 y 66 Proyecto 8: ................... ...................................... ...................................... ...................................... ...................................Pági ................Páginas nas 67 y 68 Proyecto 9: ................. .................................... ...................................... ...................................... .....................................Pá ..................Páginas ginas 69 y 70
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En estas páginas, querido docente, encontrarás una nueva, práctica y dinámica propuesta pedagógica, que te acompañará enriqueciendo tu tarea de aula en este ciclo lectivo.
Yo Soy de 5to es el libro pensado por y para el maestro/a argentino; un maestro que entiende que la educación no se fortalece desde una única mirada, sino que por el contrario es necesario indagar y buscar nuevos horizontes que nos permitan transferir óptimamente los contenidos y acompañar a nuestros alumnos en su formación integral como personas, más allá de los obstáculos cotidianos que deben enfrentar. Como somos conscientes de la realidad del aula, pensamos en crear un producto diferente, que contemple a los verdaderos actores del sistema educativo, que los haga sentir protagonistas y partícipes de la etapa educativa que atraviesan.
Yo Soy de 5to es una propuesta de trabajo que tiene como propósito, además de contemplar las necesidades de los niños y del docente, contribuir al fortalecimiento de la calidad educativa, guiar y estimular el proceso de enseñanza y de aprendizaje en un contexto donde se dé paso al “recorte de la realidad”, “al desarrollo de los procesos cognitivos”, a la “interdisciplina” “interdisci plina” y a la “intercultu “interculturalidad”. ralidad”. En cada una de las páginas de este libro se plantean verdaderas verdader as situaciones didácticas en las que el docente deberá poner en juego sus decisiones didácticas, con el propósito de que los niños desarrollen habilidades y estrategias estrategi as de aprendizaje y de pensamiento que les permitan desempeñarse y resolver desafíos en el ámbito escolar y social del cual forman parte. La tarea en el aula no es sencilla y el docente debe recurrir de manera permanente a todas las estrategias le permitan optimizar optimizar el aprendizaje aprendizaje de
La sociedad actual exige una educación fortalecida en valores sin dejar de lado la formación académica, la preparación concreta y acorde para abordar el futuro de manera sólida, y es la escuela, a través de sus docentes, quien tiene que hacer frente a esta demanda. Desde ese lugar este manual te permite el abordaje de todos los contenidos planteados en los NAP (Núcleos de Aprendizajes Prioritarios) y en los Nuevos Diseños Curriculares, con una mirada y una actitud de reflexión frente a las diversas situaciones problemáticas a resolver, y donde el docente es el orientador que encauza y reencauza, cada vez que lo considera oportuno y necesario, con distintas estrategias estrategi as el proceso de enseñanza y de aprendizaje.
Yo Soy de 5to es un verdadero desafío, porque presenta un esquema de trabajo basado en el abordaje permanente de variadas situaciones concretas de aprendizaje que ponen en juego las habilidades, las destrezas y la reflexión. Por eso estamos seguros y somos conscientes conscientes de que esta propuesta en particular reúne todos los elementos necesarios que, hoy por hoy, no deben estar ausentes en al aula en el momento de la transposición didáctica. Este proyecto educativo fue pensado, analizado, discutido y plasmado para vos con el esmero, la atención, la dedicación, el esfuerzo, la creatividad y la calidad del equipo interdisciplinario interdisciplinario de EDIBA LIBROS. Es nuestro deseo que disfrutes esta propuesta y que te permita, con una nueva mirada, recorrer el camino de la noble tarea de enseñar.
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“NARRADORES DE CUENTOS CUENTOS”” Área: Prácticas del Lenguaje Modalidad: aula-biblioteca-salón de usos múltiples.
Propósito general
Recrear oralmente diversas obras que forman parte de la literatura universal.
Fundamentación Este proyecto tiene como finalidad que los niños recopilen una serie de cuentos tradicionales pertenecientes a la literatura universal para luego narrarlos con diferentes propósitos y a distintos auditorios a fin de que engrosen el repertorio de los textos de lectura habitual en clase. Es la intención del mismo que los niños: Preparen y sostengan breves exposiciones orales para comunicar lo aprendido, intercalando lecturas y utilizando apoyos visuales que colaboren con la comprensión del auditorio. ◆
◆ Participen progresivamente progresivamente del proceso de evaluación de los proyectos y actividades propuestos por el docente: acordando acordan do y siguiendo criterios para realizar la indagación, exponer sus resultados y participar de otras situaciones de construcción de conocimientos.
PROPUESTA DE ACTIVIDADES Conversar con los niños acerca de la Conversar intención de esta actividad. ◆ Comunicarles que recopilarán cuentos tradicionales y que los registrarán registra rán de manera individual en un soporte a su elección. ◆ Acordar las pautas de la metodología de trabajo: •buscar los cuentos en la biblioteca de la escuela; •consultar con el docente acerca de la ◆
acompañe la narración (puede ser un títere que represente al protagonista de la historia, una serie de secuencias, una maqueta representativa del relato, entre otros); •determinar un día semanal en el que se pondrá en práctica la actividad de contar cuentos.
Sugerencia: una vez afianzado el proyecto en el transcurso del tiempo, programar diferentes fechas para presentar los cuentos a distintos destinatarios: niños de otros grados, padres, directivos del colegio, entre otros. Por turnos los niños narrarán su cuento y mostrarán el material que acompaña. Se sugiere considerar la adecuación del espacio para crear un clima de narración acorde, es decir tener prevista la llegada de los invitados en un clima de distensión a través de una música suave que invite a la relajación y a la escucha atenta. El docente oficiará de presentador y moderador, pautando los silencios y animando al aplauso una vez que los niños hayan relatado. Evaluación: Se establece a través de la narración de los textos que buscaron, con intervención directa del docente a fin de determinar el grado de comprensión e interpretación y la responsabilidad con la tarea propuesta.
LOS DINOSAURIOS ¿ DÓNDE ESTÁN? Área: Prácticas del lenguaje, Ciencias Naturales Modalidad: aula, patio, salón de usos
múltiples.
Propósito general
espacios concretos desarrollaron la vida, qué lugares actuales se reconocen como el hábitat y por qué en la actualidad sorprende la figura de los dinosaurios. Paraa desarrollarlo los niños deberán: Par ◆ Reconocer, con seguridad y autonomía crecientes, las obras en las que se encuentra encuentran n materiales vinculados con los temas en estudio y los lugares físicos o virtuales a donde dirigirse para hallarlas. ◆ Utilizar diversos sistemas de organización y búsqueda. ◆ Explorar rápidamente la obra apoyándose en diversos indicadores con el fin de localizar la información buscada.
PROPUESTA DE ACTIVIDADES
◆ Solicitar a los niños que exploren, busquen e investiguen acerca del tema propuesto. ◆ Traer a la clase el material recopilado y compartirlo. compartirlo. ◆ Realizar observaciones que permitan descubrir las características generales y particulares de los dinosaurios.
Pedirles que averigüen acerca de sus movimientos y de su desplazamiento. ◆
Realizar una puesta en común de la información, destacando y comparando: la forma de desplazamiento, los lugares que habitaron, la forma de alimentación. ◆
◆
Seleccionar la información a utilizar.
◆ Preparar, en grupos, un informe sencillo para exponer oralmente lo investigado. ◆ Proponer la confección de maquetas utilizando todo tipo de materiales para ilustrar el tema en el momento de la exposición grupal.
Sugerencia: Organizar una muestra con maquetas confeccionadas confeccionadas por los
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LOS NIÑOS DE ESTE CICLO Los niños de este ciclo, cuyas edades oscilan entre los 9 y 11 años, se caracterizan caracterizan por atravesar atravesar la etapa del “pensamiento concreto cooperativo” y se preparan para ingresar en el “pensamiento formal operacional”, por lo que es de suma importancia tener en cuenta y conocer ciertas características para acompañarlos en su crecimiento. Además requieren de una cuota importante de afectividad y de límites claros y permanentes.
Características generales La estabilidad y la coherencia son reemplazadas por una organizació organización n conceptual. ◆
El marco conceptual conceptual se aplica a objetos en el mundo. ◆
Las cualidades físicas se ven como constantes, a pesar del cambio en tamaño, peso y volumen. ◆
◆
La asimilación es la incorporación de lo nuevo.
La acomodación es la reorganización de los pensamientos. ◆
El comportamiento emocional tiende a estabilizarse.
Las frustraciones afectivas afectivas son obstáculo de su autonomía y de su autoestima. ◆
Sus habilidades y valores se extienden para incluir los de su barrio, club y escuela. ◆
Los niños de este ciclo prefieren: Docentes realistas, que manifiesten claramente sus ideas. ◆
Docentes que pauten con seriedad los límites no obstante dejen entrever una mirada justa y comprensiva comprensi va ante las dificultades. ◆
A los niños de este ciclo les agrada: ◆
que se interioricen y participen en sus proyectos;
que los adultos se equivoquen para analizar su reacción; ◆
que sus docentes participen en actividades escolares y extraescolares; ◆
◆
que confíen en sus posibilidades;
◆
El sentido de justicia, sociabilidad y solidaridad se amplía.
que les asignen tareas que evidencien y pongan de manifiesto la responsabilidad; ◆
◆
El juego es parte fundamental de su vida y le permite el desarrollo de su personalidad.
contar sus historias personales y las de sus amigos; ◆
◆
◆
La autonomía forma parte de su crecimiento.
El grupo de pares y la lealtad, el compromiso y la solidaridad para con el mismo le proporciona gusto y
que la docente plantee el juego como estrategia porque les permite manifestar otro aspecto de su personalidad. ◆
◆
Para estos niños:
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Fundamentación El área de Prácticas del Lenguaje abarca contenidos curriculares de las tradicionales Lenguaje o Lengua; su denominación refleja una concepción que privilegia como objeto de enseñanza las prácticas mismas-hablar y escuchar, leer y escribir- sobre los contenidos lingüísticos escolares -sustantivo, oración...-. Toda práctica se adquiere “en la práctica”. Formar a los niños/as como hablantes, lectores y escritores significa crear las condiciones didácticas que les permitan ejercer como tales desde su ingreso en la escuela. Los niños/as tienen que apropiarse de las prácticas en contextos donde se justifique ejercerlas: ejercerlas: donde haya haya que argumentar argumentar en defensa defensa de un punto punto de vista al
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Proyecto nº 1 ¡Cumplir las normas! Propósito general: Despertar el interés por hablar, escuchar, leer y escribir en distintas situaciones, con distintos propósitos y a diferentes interlocutores, a través de las posibilidades que ofrece la lengua para comunicarse eficazmente.
Indicadores de avance: •Avanzar en la lectura sin detenerse ante cada dificultad, para construir un sentido global del texto antes de analizarlo parte por parte. •Hacer anticipaciones sobre el sentido del texto y buscar índices que permitan verificarlas o corregirlas. corregirlas. •Resolver dudas sobre el significado de palabras, expresiones expresio nes ambiguas o desconocid desconocidas as apelando al contexto, relacionándolas con otras palabras.
Ejes
En torno a la
•Recurrir a la escritura para apoyar la comprensión mientras leen. •Utilizar estas escrituras para reconstruir el sentido de lo leído o para repasar el contenido sin tener que releer el texto completo.
Formación de actitudes positivas Aceptación del otro, el trabajo cooperativo en el aula, el cuidado del espacio propio y ajeno en el entorno escolar; las normas de convivencia; la metodología de estudio.
Mes: marzo.
Contenidos -Lectura, prelectura y poslectura. -El cuento tradicional: El lobo y las siete cabritas . -Comprensión lectora.
Propuesta de actividades -Anticipar el contenido del texto a partir del título o de las imágenes del mismo. -Leer con diferentes propósitos y comentar lo leído.
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Proyecto nº 2 Todos a leer Propósito general: Hacer uso de las prácticas del lenguaje en forma oral y escrita ajustándose ajustándose a cada registro registro,, a través través de la lectura comprensiva, de la exploración del vocabulario y de la escritura con diferentes propósitos.
Indicadores de avance: •Hacer anticipaciones sobre el sentido del texto y buscar índices que permitan verificarlas o corregirlas. corregirlas. •Resolver dudas sobre el significado de palabras, expresiones expresio nes ambiguas o desconocid desconocidas as apelando al contexto, relacionándolas con otras palabras, buscando en el diccionario, etc. •Identificar en el texto las marcas que ayudan a reconstruir las ideas del autor. •Elaborar textos escritos para comunicar diversos aspectos de los nuevos conocimientos adquiridos,
Ejes
atendiendo al género, el registro, el soporte, la información que se incluirá y la que se obviará, el el orden de presentación de la información, antes y durante la escritura, tomando en cuenta los propósitos y los destinatarios del texto. •Observar, comparar, comentar y reflexionar acerca de los usos orales y escritos de la lengua y de la adecuación de los mismos a sus intenciones comunicativas.
Formación de actitudes positivas: Respeto por el trabajo de los otros, actitudes de solidaridad y compañerismo para fortalecer el clima de trabajo en el aula.
Mes: abril. Ortografía: Usos de adv-, inv-, env-, conv-.
Contenidos
-Lectura, hipótesis, comprensión. -Lectura de: Las aventuras de Don Quijote de la En torno a la Mancha. literatura -Los héroes: Aquiles. -Para leer: El sonido de la historia.
Propuesta de actividades -Leer con diferentes propósitos. -Hipotetizar sobre la lectura. -Comprender lo leído y comunicarlo. -Realizar la lectura de diferentes textos para reconocer el marco narrativo. -Reconocer en distintas situaciones los
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Proyecto nº 3 ¡Rodeados de información! Propósito general: Leer diferentes tipologías textuales y descubrir la intención del emisor interpretando y comentando el material leído en distintos soportes utilizando su propio vocabulario; reescribir textos aplicando las convenciones de uso y seleccionando la clase de palabras adecuadas.
Formación de actitudes positivas:
Indicadores de avance: •Hacer anticipaciones sobre el sentido del texto y buscar índices que permitan verificarlas o corregirlas. corregirlas. •Resolver dudas sobre el significado de palabras, expresiones expresio nes ambiguas o desconocid desconocidas as apelando al contexto, relacionándolas con otras palabras, buscando en el diccionario, etc. •Preparar y sostener breves exposiciones orales para comunicar lo aprendido, intercalando lecturas y
Ejes
utilizando apoyos visuales que colaboren con la comprensión del auditorio. •Releer y revisar el texto mientras lo escriben hasta alcanzar un escrito que les resulte satisfactorio y adecuado a los propósitos y los lectores. •Colaborar con la revisión de los textos de otros compañeros. •Tomar críticamente las sugerencias recibidas y decidir sobre su incorporación a la versión definitiva. Valoración de la identidad nacional, participación activa y entusiasta en las diferentes situaciones de aprendizaje.
Mes: mayo. Ortografía: Usos de bu-, bus-, bur-, sub-, ab-, ob-, obs-.
Contenidos
-Formación de valores. En torno a la -Fábula: La zorra y la perdiz. literatura -Lectura y comprensión: Ulises, el héroe griego.
Propuesta de actividades -Leer la fábula y renarrarla secuencialmente a través de una serie de imágenes. -Conversar -Convers ar y comunicar la opinión acerca de los valores que se ponen de manifiesto en el texto. -Leer noticias y crónicas en distintos soportes.
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Proyecto nº 4 No todo lo que reluce es oro Propósito general: Hacer uso de las prácticas del lenguaje en forma oral y escrita ajustándose ajustándose a cada registro registro,, a través través de la lectura comprensiva, de la exploración del vocabulario y de la escritura con diferentes propósitos.
Formación de actitudes positivas:
Indicadores de avance: •Avanzar en la lectura sin detenerse ante cada •Avanzar dificultad, para construir un sentido global del texto antes de analizarlo parte por parte. •Hacer anticipaciones sobre el sentido del texto y buscar índices que permitan verificarlas o corregirlas. corregirlas. •Utilizar diversos sistemas de organización y búsqueda. •Explorar rápidamente la obra apoyándose en diversos indicadores con el fin de localizar la información informació n buscada.
Ejes
Contenidos -La secuencia narrativa: leyenda El camalote.
En torno a la literatura
•Encarar y sostener la lectura profunda de los textos de estudio, asumiendo asumiendo una actitud centrada en definir los aspectos importantes. •Observar, comparar, comentar y reflexionar acerca de los usos orales y escritos de la lengua y de la adecuación de los mismos a sus intenciones comunicativas.
-Superestructura narrativa. -El marco y los sucesos. -La anécdota: características características narrativas.
Respeto por el trabajo de los otros, actitudes de solidaridad y compañerismo para fortalecer el clima de trabajo en el aula.
Mes: junio. Ortografía: Adjetivos terminados en –oso, -osa y en –ivo, -iva.
Propuesta de actividades -Leer diferentes textos para reconocer el marco narrativo y los sucesos. -Contar anécdotas respetando el orden secuencial. -Reconocer en distintas situaciones los elementos que forman parte del acto comunicativo. -Hablar con distintos propósitos a distintos interlocutores, empleando diferentes registros.
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Proyecto nº 5 Palabras y más palabras Propósito general: Promover situacion situaciones es que generen interés por la lectura de diferentes textos y que permitan la reflexión acerca del uso de la lengua; comentar comentar lo leído y escribir textos sencillos conforme a una estructura, teniendo en cuenta el vocabulario y la revisión ortográfica.
Indicadores de avance: •Avanzar en la lectura sin detenerse ante cada •Avanzar dificultad, para construir un sentido global del texto antes de analizarlo parte por parte. •Hacer anticipaciones sobre el sentido del texto y buscar índices que permitan verificarlas o corregirlas. corregirlas. •Resolver dudas sobre el significado de palabras, expresiones expresio nes ambiguas o desconocid desconocidas as apelando al contexto, relacionándolas con otras palabras, buscando en el diccionario, etc.
•Identificar en el texto las marcas que ayudan a reconstruir las ideas del autor. •Controlar la propia comprensión identificando lo que resulta ambiguo, confuso o incomprensible. •Observar, comparar, comentar y reflexionar acerca de los usos orales y escritos de la lengua y de la adecuación de los mismos a sus intenciones comunicativas.
Formación de actitudes positivas: Valoración de la identidad nacional y compromiso en la construcción de un futuro compartido; la libertad y la responsabilidad en la escuela, en la familia y en el entorno social.
Mes: julio. Ortografía: Prefijos hipo-, hiper.
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Proyecto nº 6 Todos somos diferentes, pero podemos compartir Propósito general: Afianzar el desarrollo como hablantes, oyentes, lectores y escritores con distintos propósitos y en diferentes circunstancias; leer e interpretar los textos en cuestión.
Indicadores de avance: •Utilizar diversos sistemas de organización y búsqueda. •Avanzar •Avanz ar en la lectura sin detenerse ante cada dificultad, para construir un sentido global del texto antes de analizarlo parte por parte.
Ejes
Contenidos
•Hacer anticipaciones sobre el sentido del texto y buscar índices que permitan verificarlas o corregirlas. corregirlas. •Resolver dudas sobre el significado de palabras, expresiones expresio nes ambiguas o desconocidas apelando al contexto, relacionándolas con otras palabras, buscando en el diccionario, etc.
Formación de actitudes positivas: Actitud de constancia para el trabajo y el estudio; respeto y comprensión en las diferencias; valoración de nuestros antepasados por el compromiso que manifestaron con nuestro país.
Mes: agosto. Ortografía: Grupos: -gen-, -gia, -gía, -gio, -gión.
Propuesta de actividades
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Proyecto nº 7 Mi libertad termina donde comienza la libertad del otro Propósito general: Leer poesías, descubrir la intención del autor, reconocer el formato textual y los recursos propios de las mismas; descubrir la importancia de los textos expositivos-argumentativos; revisar la ortografía como estrategia de escritura.
Indicadores de avance: •Utilizar diversos sistemas de organización y búsqueda. •Avanzar •Avanz ar en la lectura sin detenerse ante cada dificultad, para construir un sentido global del texto antes de analizarlo parte por parte. •Hacer anticipaciones sobre el sentido del texto y buscar índices que permitan verificarlas o corregirlas. corregirlas. •Resolver dudas sobre el significado de palabras,
expresiones ambiguas o desconocidas apelando al expresiones contexto, relacionándolas con otras palabras, buscando en el diccionario, etc. •Identificar en el texto las marcas que ayudan a reconstruir las ideas del autor. •Preparar y sostener breves exposiciones orales para comunicar lo aprendido, intercalando lecturas.
Formación de actitudes positivas: El cuidado de los espacios naturales; el respeto por el entorno y sus componentes; el diálogo y la aceptación de las diferencias como base sólida de un buen compañerismo; la escucha y aceptación de la opinión de los pares.
Mes: septiembre. Ortografía: Verbos terminados en –ger, -gir.
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Proyecto nº 8 Explican el origen de todo Propósito general: Leer comprensivamente con distintos propósitos recreando lo leído o escuchado y reflexionar acerca de las prácticas del lenguaje en los textos trabajados; revisar la ortografía, la concordancia y el uso de conectores como estrategia de escritura.
Indicadores de avance: •Avanzar en la lectura sin detenerse ante cada •Avanzar dificultad, para construir un sentido global del texto antes de analizarlo parte por parte. •Hacer anticipaciones sobre el sentido del texto y buscar índices que permitan verificarlas o corregirlas. corregirlas. •Resolver dudas sobre el significado de palabras, expresiones expresio nes ambiguas o desconocid desconocidas as apelando al contexto, relacionándolas con otras palabras, buscando en el diccionario, etc.
•Identificar en el texto las marcas que ayudan a reconstruir las ideas del autor. •Controlar la propia comprensión identificando lo que resulta ambiguo, confuso o incomprensible. -Observar, comparar, comentar y reflexionar acerca de los usos orales y escritos de la lengua y de la adecuación de los mismos a sus intenciones comunicativas.
Formación de actitudes positivas: Diálogo como instrumento que favorece la no violencia; actitudes actitudes pacíficas frente a las opiniones en contrario.
Mes: octubre. Ortografía: Los homófonos.
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Proyecto nº 9 Ayudar, no es dar lo que nos sobra, sino lo que tenemos Propósito general: Leer comprensivamente y con distintos propósitos para expresarse con coherencia en forma oral y escrita y reflexionar reflexionar acerca acerca del buen uso de de la lengua como como medio de comunicación comunicación..
Indicadores de avance: •Utilizar diversos sistemas de organización y búsqueda. •Explorar rápidamente la obra apoyándose en diversos indicadores con el fin de localizar la información informació n buscada. •Encarar y sostener la lectura profunda de los textos de estudio, asumiendo asumiendo una actitud centrada en definir los aspectos importantes de acuerdo con los propósitos.
antes de analizarlo parte por parte. •Hacer anticipaciones sobre el sentido del texto y buscar índices que permitan verificarlas o corregirlas. corregirlas. •Resolver dudas sobre el significado de palabras, expresiones expresio nes ambiguas o desconocidas apelando al contexto, relacionándolas con otras palabras, buscando en el diccionario, etc. •Identificar en el texto las marcas que ayudan a reconstruir las ideas del autor. •Controlar la propia comprensión identificando lo que resulta ambiguo, confuso o incomprensible. •Recurrir a la escritura para apoyar la comprensión mientras leen.
Formación de actitudes positivas: Actitud de valoración por el legado cultural; solidaridad, respeto, diálogo, compañerismo, cooperación, esfuerzo y amabilidad como pilares fundamentales del trabajo en el aula.
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Proyecto nº 1 La aventura de comenzar Propósito general: Explorar la metodología de trabajo en el área y comprenderr la ubicación espacial. comprende
Indicadores de avance: •Diferenciar los actores sociales de su entorno directo e indirecto.
•Registrar, sistematizar y comunicar informaciones y conclusiones en diferentes soportes. •Ubicarse en tiempo y espacio. •Reconocer a la Argentina en el espacio como su territorio.
Formación de actitudes positivas: El compromiso y el esfuerzo en las tareas asignadas; la tolerancia y la comprensión en el trabajo diario; la escucha atenta; el diálogo como vehículo de las
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Proyecto nº 2 Empezamos recordando Propósito general: Explorar los modos de vida y organización de los primeros habitantes de la Argentina y reflexionar acerca de la formación de los virreinatos y de la vida en la colonia.
Indicadores de avance:
•Reconocer acontecimientos relevantes. •Usar nociones temporales, tales como antes de, después de, durante, mientras tanto, al mismo tiempo y unidades cronológicas tales como año, década y siglo.
Formación de actitudes positivas: Solidaridad y respeto en el trabajo diario; el cuidado personal y del entorno; aceptación de los errores; confianza en sus propias posibilidades; la escucha atenta; el diálogo en los acuerdos y opiniones.
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Proyecto nº 3 Un Cabildo Abierto Propósito general: Comprender la importancia del Primer Gobierno Comprender Patrio, interpretar causas y consecuencias y conocer los diferentes gobiernos que le sucedieron y las revoluciones americanas.
Indicadores de avance:
•Obtener información de diversas fuentes y establecer relaciones entre la información que ellas brindan. •Realizar intercambios orales para dar cuenta de ideas, valoraciones, opiniones y puntos de vista sobre los temas trabajados.
Formación de actitudes positivas: Respeto por el pasado histórico y por los símbolos patrios; aceptación de las diferencias; actitud de
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Proyecto nº 4 Por una patria libre e independiente Propósito general: Comprender la organización social y política del país y Comprender las primeras manifestaciones de libertad e independencia como así también los ideales y esfuerzos de sus protagonista protagonistas. s.
•Usar nociones temporales, tales como antes de, después de, durante, mientras tanto, al mismo tiempo y unidades cronológicas tales como año, década y siglo. •Identificar variadas causas y múltiples consecuenciass de los hechos y procesos sociales consecuencia estudiados.
Formación de actitudes positivas: Respeto por el pasado histórico, por quienes lucharon por la libertad de la patria y por los símbolos patrios;
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Proyecto nº 5
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Proyecto nº 6
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Proyecto nº 7
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Proyecto nº 8
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Página 24 1.
S i s t e ma d e c i m a l
S iste ma chi no
S iste ma eg ipc io
320 1.042 4.205 2.
EGIPCIO
¿En qué sistemas no importa la posición de cada símbolo?
x
¿En qué sistema no se usa el 0?
x
CHINO
DECIMAL
x
3. El sistema egipcio usa más símbolos. ◆Sistema
decimal: 888.
◆Sistema
egipcio:
◆Sistema chino:
Página 25
Página 26
1. El tercer intento. 2. Producción personal. Actividades
1. a. A 2 cm . b. En las intersecciones.
3.
Hay dos posibilidades. c. En cualquier punto de la circunferencia de centro A, que se encuentre dentro de la circunferencia de centro B, sin contar los puntos de intersección. d. Son los puntos extremos de los diámetros dibujados.
A
A
B
2. Producción personal. Página 28 Recortables 1. ◆ 2.520.714 = 2 x 1.000.000 1.000.000 + 5 x
dividendo 45.132
divis or 10
cocie nte 4513
res to 2
◆ 13.60 13.608.425 8.425 = 13 x 1.000.0 1.000.000 00 + 6
3.759
100
37
59
x 100.0 100.000 00 + 8 x 1.000 1.000 + 42 x 10 10 + 5
268.345
10
26.834
5
◆ 7.243 7.243.968 .968 = 7 x 1.000.000 1.000.000 + 2 x
32.816
1.000
32
816
100.000 + 2 x 10.000 + 7 x 100 + 1 x 10 + 4
100.000 100.0 00 + 4 x 10.000 10.000 + 3 x 1.000 1.000 + 9 x 100 100 + 6 x 10 + 8
52
2.
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Página 28 3.
53 =
534 =
5.342 =
4. Producción personal. Página 29 1.
3. Egipcio: 7 símbolos
23.486.597 - 1 23.486.597 - 10 4. 23.486.597 - 100 100 23.486.597 - 1.000 23.486.597 - 10.000 23.486.597 - 100.000 23.486.597 - 1.000.000 2.
7.777.777 - 77.700 7.777.777 + 1.111.111
Chino: 13 símbolos
A
Decimal: 10 símbolos
C
5. 32 de 1.000.000 1.000.000;; 8 de 100.000 100.000;; 7 de 10.000 10.000;; 9 de 1.000 1.000;; 1 de 100 100;; 5 de 10 10 y y 6 de 1.
Página 30 1. ◆ 7x 1.000.000 + 8x 100.000 + 3x10.0 00 + 62 NO ◆
20+600+30.000 + 80 0.000 + 7.000.000 Sí
◆
7U de millón + 8 C de mil + 3 D de mil + 62 D Sí Sí
◆
700.000 + 8 + 30.0 00 + 620 NO
4. B
A
C
2. a. Ju J ugador
Puntos
Se lee
Agustín
18.061.900
Dieciocho millones sesenta y un mil novecientos novecientos..
T i a g o
42.600.715
Cuarenta y dos millones seiscientos mil setecientos quince.
Bautista
9.009.006
Nueve millones nueve mil seis.
Facundo
30.712.080
Treinta millones setecientos doce mil ochenta.
Manue l
25.000.439
Veinticinco millones cuatrocientos treinta y nueve.
b. Bautista, Agustín, Manuel, Facundo y Tiago.
c. Tiago, Facundo y Manuel tienen más de veinte millones de puntos y menos de veinte millones Agustín y Bautista.
3. Es posible, porque el sistema decimal es posicional y el egipcio no. 53
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Entre multiplicaciones y ángulos
3 Página 34
Página 31 ◆
1. a. En cada estante acomodan
Los cuadros correctos son: el 3, el 6 y el 8.
Página 32 1.a. Personal. b. Podrán ver la función sentados 864 espectadores. 2. Habrá lugar para 1.080 24 x 36 + 6 x 36
3. 5 funcione s
2 5 funciones
80 funciones
comidas
$3 00
$1 .500
$ 4.80 0
a lojamiento
$2 75
$1.3 75
$4 .40 0
transporte trans porte
$125
$625
$2.000 $2.00 0
Página 33 a. trajes 2
c ap as
x
2
en la cabeza
x
3
combinaciones
=
12
b. No. Página 35 4. a. Con esa cantidad de sobrecitos, pueden maquillar a los artistas durante 11 días. b. Quedan 2 sobrecitos. 5. a. Tiene razón Ana. b. Porque necesita un perchero más para guardar las 9 que sobran. ◆ Los problemas de las páginas 34 y 35 se parecen en que se resuelven empleando divisiones.
Página 37 6. a. Es correcta la forma en que lo resolvió. La explicación debe producirla cada uno. b. Porque es más fácil multiplicar por 10 y luego por 5. c. 428 x 12 = 428 x (10 + 2) = 428 x 10 + 428 x 2 = 4.280 +856= 5.136 7. a. Producción personal. b. 88 x 101 = 88 x 100 + 88 = 8.888 50 x 99 = 50 x 100 - 50 = 4.950 ✖ Puesta en común
1. conmutativa 2. conmutativa 3. asociativa 4. asociativa 5. asociativa 6. distributiva 7. distributiva 54
22 videos y sobran 8 videos. b. Completarían 22 estantes y sobrarían 8 videos. c. Se resuelven con la misma cuenta, pero el significado de los números es diferente. Uno es de reparto y el otro de partición. par tición. 2. a. Le alcanzará para 41 funciones. b. Debería tener 8 remeras más. c. Con sumas: debe sumar tantas veces 12 como le sea posible, hasta acercarse a 496 . Con restas: restando 12 a 496 tantas veces como se pueda. Multiplicando: multiplicando 12 por otro número aproximadamente, hasta acercarse lo más posible a 496. Dividiendo: dividiendo 496 por 12. 3. El valor de la cuota con el plan 1 es de $4.925. El valor de la cuota con el plan 2 es $3.950.
Página 36 1. Los cálculos son: 6x8
8x6
2. Puede hacer 8 x 2 x 5
u
8 x 5 x 2. 3. Sol pensó que 2 x 8 es igual a 16 y Lucía que 4 x 4 es igual a 16. 4. 320 x 14 = 320 x 2 x 7 850 x 45 = 850 x 5 x 9 5. Es incorrecta porque 2 x 4 no es 24, sino 8. La forma correcta es: 957 x 3 x 8 ó 957 x 4 x 6
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Página 38
Página 41
1. Sólo Katia llegó al resultado correcto. 2. a. Yaki b. 954 : 6 = 954 : 3 : 2 3. (V) (F) (V) 4.
1. Que todos suman 180°. 2. 70º
180 : 18 = 180 : 9 : 2
110 10º º
180 : 18 = 180 : 9 + 180 : 2 180 : 18 = 90 : 18 + 90 : 18 180 : 18 = 180 : 10 : 8
3. Sí y medirá 90° cada uno. 4. = 140°. 5. Sí, es verdad.
Página 39
Página 42
1. Hizo 19 paquetes de masitas. 2. a. No. b. Para averiguar el resto de la división, hay que
1. Lo que dice Pablo es correcto. 2. Los ángulos amarillos. 3. amarillo: 65° ; verde: 115°; rojo: 115° 4. Sí, es verdad.
hacer: 6 x 27 = 162 , y luego 165 – 162 = 3 3. 26 x 13 + 7 = 345 (D= d x c + r).
4. a
c
b
1 2 6 15 6
8
73 14 3
5
Página 44
d
8
6
6
9
a. En el C hay más de una solución (dividendo: 48 a 55 y resto 0 a 7). b. La cuenta que no tiene solución es la D. Porque el resto no puede ser mayor al divisor. 5. Hay varias posibilidades pero como el resto tiene que ser menor que el divisor, éste se considerará a partir del número 5 en adelante.
Recortables 1. a. Deberá colocar 37 sillas en cada fila. b. De 18 formas distintas (2 x 3 x 3 = 18). 2. La caja le alcanza para 18 días. Deberá tomar 11 servilletas más de una nueva caja para completar lo necesario para el día siguiente.
3.
32 x 184
184 x 4 x 8
184 x 30 + 184 x 2
4. a.
140 : 14 = 70 : 14 + 70 : 14
V
Página 40
140 : 14 = 140 : 10 + 140 : 4
F
1. a. Mauro contestó correctamente. b. Producción personal. Se espera que se tenga
140 : 14 = 140 : 2 : 7
V
140 : 14 = 140: 10 : 4
F
en cuenta que deben tener un lado y un vértice en común.
2. Mide 60°. 90º
3. ß = 30°
60º
b. Divisor 7 y resto 0.
sí
Divisor 3 y resto 8.
no
Divisor 4 y resto 6.
no
Divisor 6 y resto 2.
sí
Divisor 5 y resto 4.
sí
55
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Página 44
Página 46 1. A y C. 2. Sí, es correcto, porque descompone en multiplicaciones el divisor. 3. 79 x 4 = 80 x 4 – 4 = 316
Recortables 5. a. 135º
61 x 9 = 60 x 9 + 9 = 549 8 x 31 = 8 x 30 + 8 = 248
color azul
color verde
4. 94 15 4
color rojo
color amarillo
6
6
23 4 18
7
0
13
No es posible completar la segunda cuenta, el resto es mayor que el divisor. 5. adyacentes consecutivos
b. Respuesta: Ángulo verde = 135° Ángulo azul = 45° (adyacente al verde 180º - 135º = 45°). Ángulo rojo = 45° (opuesto por el vértice al azul, miden igual) . Ángulo amarillo = 135° (opuesto por el vértice al verde, miden igual).
opuestos por el vértice
Página 45 1.
manteles
4
platos
x
2
centros
x
combinaciones
=
2
16
mesas mantel rojo plato redondo Velas
Flores
mantel blanco
plato cuadrado Velas
plato redondo
Flores Velas
Flores
mantel azul
plato cuadrado Velas
2. 31 veces. 288 : 18 = 16 3. 288 : 16 = 18 A partir del resultado de una multiplicación se puede obtener el resultado de sus divisiones exactas.
Flores
4.
plato redondo Velas
Flores
DETALLE
Carpeta Manual Lapicera Cartuchera
5. Producción personal. 56
mantel negro
plato cuadrado Velas
Flores Velas
CANTI DA DAD
32 11 26 40
plato redondo Flores
plato cuadrado Velas
Flores
PR EC ECIO UNITAR IO IO
PRECIO TOTAL
16 47 5 8
512 51 7 130 32 0
Tot otal al
1.47 9 1.479
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Para jugar y aprender
4
Página 48 1.Producción personal. Se espera que reconozcan y nombren los conocimientos usados.
2.a. No, porque no cae dando saltos de a 2, ni de a 3. b. Sí, porque atrapa a los que saltan de 2 y de 3. Es el mejor lugar de los cuatro. c. Sí, atrapa a los que saltan de 2 en 2. d. Sí, atrapa a los que saltan de 3 en 3.
3.a. 6, 12, 18, 24, 30. b. 1, 5, 7, 11, 13, 17, 19, 23, 25, 29 .
22, 24, 26, 28 y 30. Conejo de Flavio: 5, 10, 15, 20, 25 y 30. b. Coinciden en el 10, 20 y 30. c. No, porque no es múltiplo de 10. d. Producción personal.
Página 50
1.Múltiplos de 4: Múltiplos de 9: Múltiplos de 6:
8 27 18
20 54 54
4 36
1) a. 90 Bolsitas
2. Múltiplos de 5: 5 10 15 20 25 30 35 40 45 50 Múltiplos de 8: 8 16 24 32 40 Múltiplos de 10: 10 20 30 40 50 3. 24
48
En grupo
◆Los múltiplos son infinitos porque los
números por los que se puede multiplicar a otro son infinitos. ◆El 0 es múltiplo de todos los números porque todo número multiplicado por 0 da 0.
Página 51
1
caramelos en la bolsa
30
2
3
5
6
10
15
30
15
10 10
6
5
3
2
1
b. No se puede, pues sobran bombones. 2. a. Hicieron divisiones. b. Usaron 3 bolsas. c. Sí. Podrían haber hecho 147 – 3 –3 –3 –3 etc., hasta llegar a 0 (es decir, restándole 49 veces 3).
3. a. Es verdad, porque quiere decir que 13 entra un número exacto de veces en 1.196. b. 95.
Página 52
4. D 48= [ 1, 2, 3, 4, 6, 8, 12, 16, 24, 48] 48 x 1 = 48 16 x 3 = 48
2.a. Conejo de Ale: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20,
3. a. 8, 16, 24, 32, 40, 48, 56, 64, 72 y 80. b. Llega justo al 96 y al 1.232.
Página 49
✖
Atrapar al conejo II 1. Producción personal.
24 x 2 = 48 12 x 4 = 48
6 x 8 = 48
5. No son divisores de 15: 9 y 10 .
1. No es posible, porque todo número multiplicado por un número par da como resultado un número par.
2. El número equivocado es 556 , pues no termina
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Página 53 múltiplo de 2
5. 25 48 10 12
6.
múltiplo de 5
múltiplo de 6
múltiplo de 10
x x x x
x
x x
x
6 es divisor de
sí
666 66 6
x
526 52 6 192 19 2
múltiplo de 3
no
x
a. No. b. Es múltiplo de 10. Por ejemplo: 10 Otros: 20, 30, 40, etc .
x
7. Hay muchas opciones: a. Que sea divisible por 2: puede terminar en 0,
porque...
2 ó 4. b. Que sea divisible por 3: cualquier combinación no es divisible por 2 y 3 a la vez. pues sus cifras suman 12. c. Que sea divisible por 5: debe terminar en 0 ó 5. es divisible por 2 y 3 a la vez. d. Que sea divisible por 10: debe terminar en 0. es divisible por 2 y 3 a la vez.
x x
Página 54
Página 55 4. a. Necesitará 4 estantes. b. Colocará 6 mantitas y 5 camitas en cada estante.
1. Se volverán a encontrar dentro de 48 días.
5. a. Podrá armar 12 bolsas como máximo. b. Cada bolsa tiene 3 cepillos y 4 champúes antipulgas.
2. Cada 12 horas. 3. Cada 24 horas. ◆El múltiplo común mínimo
de 5, 10 y 6 es 30.
◆
Divisores de 24: 1 - 2 - 3 - 4 - 6 - 8 - 12 - 24 Divisores de 36: 1 - 2 - 3 - 4 - 6 - 9 - 12 - 18 - 36 Divisor común mayor: 12
Página 56 1. a. Los dos intentos son correctos. b. Porque ambos puntos se hallan a igual distancia de los otros vértices (centros de circunferencia).
2 cm
2. a. posible b. imposible c. imposible 3.◆ 4 cm, 7 cm y 4 cm. 4 cm, 7 cm y 6 cm. ◆ 4 cm, 7 cm y 8 cm. ◆ 4 cm, 7 cm y 10 cm. ◆
Página 57
3 cm
3 cm 4 cm, 7 cm y 5 cm. ◆ 4 cm, 7 cm y 7 cm. ◆ 4 cm, 7 cm y 9 cm.
◆
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Página 58 Actividades en tu carpeta
1. 40°, 60°, 125º 2. a. Marcos. b. El ángulo de 80° debe estar comprendido entre los lados mencionados.
40º
60º
3. Es posible construir más de un triángulo con la misma medida de sus
4 cm
ángulos, cambiando la medida de sus lados.
Página 60 6.
Recortables
es posible
L ad o 1
L ad o 2
La do 3
8 cm
4 cm
3 cm
3. No se llega justo al 0. a. No. b. No.
3 cm
7 cm
6 cm
x
6 cm
6 cm
6 cm
x
4. Las cuentas A, E y F son exactas.
7 cm
7 cm
14 cm
2. ◆ A 2.707 debo sumarle 3 = 2.710 . ◆
3.415 15. A 3.411 debo sumarle 4 = 3.4
no es posible
x
x
860 es divisible por 5 porque termina en 0. 6.800 es divisible por 10 porque termina en 0. 7.152 es divisible por 3 porque, sus cifras sumadas dan un múltiplo de 3.
π
β
Ω
es posible
60 º
6 0º
60 º
x
5. a. Cada 14 días.
1 00º
3 5º
35 º
x
80 º
4 0º
90 º
x
45 º
9 0º
45 º
b. Se pueden armar 6 bandejas como máximo. En cada una habrá 3 sándwiches y 4 empanadas.
Página 61 1. a. No, porque se puede multiplicar a un número infinitas veces. b. Es correcto.
3. a. 12 cm. b. 4 tiras celestes. 5 tiras violetas.
x
Página 62 1. 13 es divisor de 247 247 es múltiplo de 19
19 es divisor de 247 247 es múltiplo de 13
2. La cifra que falta es 0 (el número es 510 ). 3.a. 72 x 1 = 72
2. Cada 12 segundos.
no es posible
18 x 4 =7 2
36 x 2 = 7 2 12 x 6 = 72
2 4 x 3 = 72 8 x 9 = 72
b. D 72 { 0, 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72} 4. No, es un divisor común, pero no es el mayor. El mayor divisor común es 21 .
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Todo por partes Página 65
Página 63 La figura intrusa es la A porque es la única que no está dividida a la mitad.
1. a. Así lo pensó Dana:
Página 64
1 2
1.
1 6
6 9
1
+
2
+
1 2
+
1 2
+
es incorrecto porque
el entero no se forma con 6 de esas partes. En cambio, en el segundo sí, pues 4 partes de las pintadas forman un entero.
2.
5
,
5 8
,
4 6
b. Es verdad.
1 2 3
del papel entero, se debe dividir en dos para encontrar 1 y 3 luego repetirlo. Posible construcción:
2
4
2 +
2
Otra forma de reparto
1
para cada uno,
para cada uno
2
para cada una.
2
1
3. Una forma puede ser 2
2
1
para cada una.
2. Una forma de reparto
.
3. Como la pieza representa
c. 2
1
Reparto de Katia:
2 2 3
y
1
para cada uno.
4
para cada uno.
para cada uno
2
para cada uno
2 3
para cada uno
Otra forma puede ser dividir cada chocolatín en 3 partes y a cada uno se le reparten 8 . 3
8 3
4. a. 2 tiritas. b. 2
tiritas.
c. 3 tiritas.
tiritas.
d.
1 2 1 1 4
para cada uno
Página 67 1. a. La estrategia de Ana es incorrecta, porque si tienen igual
Página 66
numerador, la mayor es la que tiene menor denominador.
b. 3
1.a. No, porque todas representan la misma parte del entero. b. Fracciones equivalentes.
2.b. Es incorrecto.
4 3
0
1
8
c.
x2 3
6
3
6
3
3
3
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Página 69
Página 68
1.a. Porque 10 representa 1 y al restarle a 40,
1. Nico no llegó: 7 . Vero, sí 9 . 8 9 2. Llegó al entero porque al sumar obtiene 10 .
4 3 o sea 4 , lo que da representa . 4 4 b. Representa 1 . 2. 20 páginas. 4 3.a. 4 masitas. b. Tenía 12 masitas.
10
3.a. Sí.
b. Faltan 4 . 18
d.Sobran 2 .
c. Sí.
16
4.a. 5 . b. 2 . 7 7 Página 70
2.Este triángulo es...
1. No es posible construir un triángulo equilátero rectángulo ni equilátero obtusángulo, porque al construirlos, el lado opuesto al ángulo (recto u obtuso) debe ser mayor para llegar a tocar el lado y formar el vértice.
Obtusángulo
Acutángulo
Rectángulo
Isósceles
Escaleno
c m 4
Equilátero
50º 4 cm
Página 72 1. a.
Página 73 5. 1 de 90 =15
b.
c. 4 5 2.a. 3 , 5 b. 1 , 3
...según sus lados: isósceles. ...según sus ángulos: acutángulo.
6
4 de 80 = 40 8
2 de 90= 60 3
2 de 250 =100 5
1. 2.
5 para cada uno 4
6. 8 , 4 5 5 4 , 3 , 5 2 6 4
3.a. 3 + 4 + 5 = 12
18 18 18 18 b. 12 - 9 = 3 16 16 16 c. 1 + 2 + 3 = 1 + 10 + 12 = 23 20 4 5 20 20 20 20 d. 2 - 3 = 10 - 9 = 1 15 3 5 15 15 e. 3 + 1 - 3 = 3 + 4 - 6 = 1 8 8 4 2 8 8 8
60º
30º 4 cm
1 1 para 4 cada uno
Página 74 1. No, porque no está dividido en partes iguales. 2 = 6 2. 5 = 15 18 12 6 4 6 12 3 = = 4 8 2 3.a. Laura. b. 8 c. 1
3. 1 4
7 8
0
3 2 1
2
4.a. 19 b. 1 . Es decir: 3 flores. 20
20
5. Es un triángulo isósceles,
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Expresiones decimales
6
Página 75 Producción personal.
Página 76 2.
1. a. 100 figuritas. b. 50 son de Batman. 100 c. Son 10. d.
20 del total. 100
7 2
= 35
7 2
4 25
= 16
6 = 20
10
100
= 350 100
30 100
7 2
= 3.500
1 8
=
1.000
Es verdad porque no es posible pasar de octavos a décimos, centésimos o milésimos. ◆
3. Damián dice que 43 también se puede escribir de estas formas: 100
4 + 3 430 43 + 43 10 100 1.000 50 50 ◆ La tercera opción es incorrecta. La explicación es personal. Sin embargo pueden deducir: 4 + 3 reemplazar por una fracción equivalente 40 + 3 = 43 . 100 100 100 10 100 Luego
430 es equivalente a 4.300 y a 43 . 10.000 1.000 100
Página 77 1. a. Producción personal. 1 b. 100
4.300 10.000
Página 78 1. b. En la 1.a y en la 2.a vuelta gana Juan y en la 3. a pierde.
2. a. Es verdad, porque son expresiones equivalentes.
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Página 80 1. Todas, menos la D.
3. a. Le falta... 2,5 - 3,30 - 1,8 - 3,5. b. Le sobra... 1,85 - 5,90 - 0,50 - 0,50.
2. 4,02. 4.
5 + 7 10 100
4 + 5 10
0,67
5,36
4,60
4,5
0,57
460 100
4,60
5. Para que aparezca en el visor 2,36 con una s ola operación,hay que restarle 1,1. Para que aparezca en el visor 4,66 con una s ola operación,hay que sumarle 1,2.
Página 81 1. a. Paola, porque ubicó
2.
correctamente respetando el valor posicional de cada número.
b. Les alcanzó y les dieron de vuelto $8,75.
3.
0,63 + 0,37 = 1 0,05 + 0,95 = 1 0,75 + 0,25 = 1 0,005 + 0,995= 1 0,18 0, 18 + 0,8 0,82 2=1 0,075 + 0,925= 1
Actividades en tu carpeta Actividades ◆ Se equivocó porque no respetó el valor posicional de cada cifra. El resultado correcto es:
0,4 + 0,8 = 1,2
En el visor leo...
Ten engo go que que hac hacer er... ...
...para ...par a que apar aparezca ezca... ...
6, 5
+ 0, 5
7
9, 0 5
- 0, 05
9
4, 9 3
+ 0, 07
5
0, 0 8
+ 1,92
2
3 , 07
+ 0,93
4
Página 82 1. Grupo 1: D y A Grupo 2: D, A, F y E Grupo 3: D y E Grupo 4: C y B
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Página 86 Recortables 1.
4.
Fracción
Número decimal
6 10 92 100 15 1.000
132 100 8 100 42 10
8,13
Se lee...
0,6
Seis décimos.
5. Sólo éstas
0,92
Noventa y dos centésimos.
0,015
Quince milésimos.
son las diagonales de un rombo:
1,32
Un entero, treinta y dos centésimos.
0,08
Ocho centésimos.
4,2
Cuatro enteros, dos décimos.
3. 2,60
2,61
2,62
6.
2,63
2,64
2,65
2,66
Diagonales que Lados se cortan opues opuestos tos por la mitad paralelos paral elos
Tie iene ne......
2, 6 7
2,68
2,69
2 , 70
Ángulos Diagonales de opues opuestos tos igual medida medida iguales iguale s
4 ángulos rectos
Cuadrado
Sí
Sí
Sí
Sí
Sí
Rectángulo
Sí
Sí
Sí
Sí
Sí
Paralelogramo
Sí
Sí
No
Sí
No
Trapecio
No
No
No
No
No
Sí
Sí
No
Sí
No
Rombo
Página 87 1. 1,60 =
16 10
=
160 100
0,05 =
5 100
=
50 1.000
2. Máximo.
3. 3 + 1,5 = 4,5 6 - 3,50 = 2,5
2,25 + 1,25 = 3,5 45 - 5,5 = 39,50
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Parte por parte
7
Página 90
Página 89
1.a. Cuentas Perlas
1
Piedritas
4
Cadenas 3
x 1 $0,05 $1,05 $0,65 $8 $8,95
x 10 $0,5 $10,5 $6,5 $89,5
x 100 $5 $105 $65 $895
b. La coma se corrió a la derecha un lugar al multiplicar por 10 y dos
1 2 4 3
lugares al multiplicar por 100 .
c.
2
8,95 x 1.000 = 8.950 0,65 x 1.000 = 650
1,05 x 1.000 = 1.050 0,05 x 1.000 = 50
d. Según la cantidad de ceros que acompaña a la unidad (10, 100, 1.000), la coma decimal se correrá uno, dos o más lugares.
2. Página 91 1.a. 45,50 : 10 = 4,55
7,25 x 10 = 72,5 0,98 x 10 = 98 9,8
12,058 x 100 = 120,58 1205,8 0,06 x 100 = 6
3,14 x 1.000 = 3.140 0,0019 x 1.000 = 19 1,9
45,50 : 100 = 0,455
b. La coma se corre a la izquierda tantos lugares como ceros tenga el divisor.
2. 78,35 : 10 = 7,835 1.290,6: 1.000 = 1,2906 2,6 : 100 = 0,026 4,18 : 10 = 0,418 3. a. 175 : 1.000 b. 175 : 10
Página 93 1. a. Porque el primer factor tiene dos decimales y el segundo uno, en total son tres que corresponden a los milésimos. b. La cantidad de decimales en cada factor.
2.
12,3 x 4,8 = 59 59,04 1,23 x 48 = 59,04 12,3 x 48 =590,4 123 x 4,8 = 590,4 123 x 48 =5.904
3. Ninguno de los dos. El resultado correcto es
171,4.
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Página 95
Página 96
1.a. Porque divide por un lado la parte entera e ntera y, por otro, la parte decimal. 2.a y b. Producción personal. 3. 76,02 : 3 = 25,34
1.a. Ana: 8,6 Federico: 9 Lucas: 8,8
Página 98
b.Federico será el abanderado.
1. a. Producción personal. b. Sí. 2. Comprobará que suman 360º.
2.a. 1.458 libros. b. 243 libros.
Actividades en tu carpeta Es correcta la afirmación.
1,23 x 7 = 8,61 4,20 : 3 = 1,4 6,25 x 12 = 75
Página 97
Página 99
1. a. 0,1 = 1:10 b. 0,01 = 1:100 c. 2,27 = 227:100 d. 0,4 = 4:10 e. 4,5 = 45:10 f. 6,009 = 6.009 : 1.000 2. 24 x 0,25 0,25 = 6 ó 24 x 18 = 432 , faltan 6 para 438 3. Hay infinidad de posibilidades. Pueden hacerlo por medio de operaciones inversas. 4. 48,26
-8
40,26
- 0,2
40,06 - 0,06
40
- 40
0
1. b: 40º
m: 110º
2. c: 50º e : 60 º
b : 1 30 º f:1 20º
a:50º g:60º
3. a: 40º Página 100 1.
: 100
781,3
7,813
x 10
78,13
-57,66 20,47 + 57,73
78,2
Página 102 1.
2. $25,87 3. Cada paquete: $1,68
Número
Cálculo
Resultados
2,45
x 100
245
8,6
: 10
0,86
12 cajas: $504 ◆ Todos los paquetes:
14,09
x 10
140,9
2,625 kg.
17,3
: 1.000
0,0173
6
: 10
0,6
◆
2. Debe mencionar la medida de lados y ángulos.
4. Producción
Página 103
5. a = 48º
1. a. Kiosco: 20 : 100 = $0,20
personal.
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En forma proporcional Página 107
Página 105 ◆
1. 90 porciones de almendrado.
3.
bolsas
1 00
2 00
300
50
cucuruchos
500
1. 0 0 0
1. 5 0 0
250
P o te s K i l o s 10 20 5 10 15 30 25 50 40 80 50 100
x2
4.
Conserva la proporción la foto n.º 3.
Página 106 2.
8
A l f a j o r es
3
6
9
12
15
18
Tapas
9
18
27
36
45
54
x2
a. Necesitan el triple de tapas y el cuádruple. b. Para 12 alfajores 3+9, para 15 alfajores 6 + 9 ó 3 + 12. Y para 18, 3 + 6 + 9 ó 3 + 15, etc. c. No es necesario averiguar cuántas tapas lleva un alfajor para completar la tabla.
5. cubanitos (cajas) Dulce de leche (metros)
Página 108 Página 109
20
4
24
40
60
80
75
15
90
1 50
2 25
30 0
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Página 111 1. a. Chi Chicos cos
Porcen Por centaj taje e%
40 20 10
100% 50% 25%
c. Para hallar el 25% deberá dividir el total por 4. 2. Le faltan 62 figuritas, el 75%. 3. Golosina preferida prefer ida
b. Es verdad. Página 112 1. a. Centímetros Met r o s
2. a.
Centímetros (mapa) 2 cm 4 cm 1 cm 1 2 cm 5 21 cm
1 2
2 4
3 6
Km (reales) 300 km 600 km 15 0 k m 75 k m 825 km
b. 375 km están representados por 2,5 cm. Página 115 1. El perímetro es: P1 = 11 cm, P2 =9 cm, P3 = 8 cm y P4 = 11 cm. 2. Cuadrado: 0,65 cm cada lado.
Chocolate
Dulce de leche
Frutil Fru tilla la
Vain ainill illa a
Porcentaje
40%
30%
20%
10%
Cantidad de chicos
12
9
6
3
4.a. 30 b. 25 c. 2 d. 80 e. 80 f. 350
Página 113 1. a. La bandera de Diana. Explicación personal. b. Necesitan igual cantidad. Explicación personal. 2. a. Figuras A y B. b. Figuras A y C. Página 114 1. a.Es verdad, ambas tienen igual superficie. b. Producción personal. c. Producción personal. d.Los perímetros de las figuras de Ezequiel no son iguales, la B es mayor m ayor.. 2. Ambas tienen razón. A las dos les da distinto porque emplearon diferente unidad de medida. Actividades en tu carpeta: Trabajo personal. Página 118 Recortables
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Una cuestión de medidas Página 122
Página 121
1. a. Respuesta personal. b. No, necesita una unidad más grande. 2. Los dos dicen lo mismo, porque son expresiones equivalentes. 3. Fede y Nico.
Con la figura número 4 se armó el cubo.
Página 123 1. 0,04 m; 4 cm , 40 mm. 2. Para armar una tira de 2
9
cm mm
3.
metros, necesito 20 tiras de 1 dm o 200 tiras de 1 cm o 200 tiras de 10 mm.
6
3
9
2,5
42,3
60
30
90
25
423
a. Sí. b. Le contestaría que también es directamente proporcional. c. Es verdad, porque nuestro sistema métrico es decimal. 4. a. 4 m, 80 cm = 480 cm = 4.800 mm b. 1 m, 2 dm, 3 cm = 123 cm = 1.230 mm = 1 m, 23 cm Página 124
1. Aumentó 33,8 kg 2. Respuesta personal. 3. ◆ Piojo (mg) Barco (t) ◆ Gomitas (g ) ◆
Página 125 1. a. b.
de kg a dag? (x 100) ◆ de mg a dg? (: 100)
de kg a g? (x 1.000) ◆ de mg a g? (: 1.000)
◆
◆
0,039 kg - 0,39 hg - 3,9 dag - 39 g - 390 dg - 3.900 cg - 39.000 mg
2.
g
6
28
09
0 015
36
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Página 129 1. a. Sí, la ruleta es un juego de azar. b. La lotería, el loto, los dados, las cartas, etc. 2. a. Dos (cara y ceca). b. No podemos saber quién ganará la próxima vez porque es azarosa.
3. Podemos predecir quién ganará porque no interviene el azar, pues Nico hizo trampa y se conoce el resultado de antemano.
Página 130 1. a. Seguro C. Imposible B. Probabl Pro bablee A.
2. Suceso: a Imposible, b Probable, c Probable, d Seguro, e Imposible, f Seguro. Página 132 1. Se puede armar: un prisma de base cuadrada. ◆ una pirámide de base cuadrada. ◆ un prisma de base triangular. 2. Se puede armar un cubo con los desarrollos A, C y D. ◆
Página 131 1. a. Sí, porque unos tienen caras planas y otros curvas. b. La esfera, el cilindro y el cono. c. El prisma de base pentagonal. d. La cantidad de aristas es mayor que la cantidad de vértices.
2. a. Cono. b. Es cierto. Prisma de base triangular, prisma de base cuadrada y prisma de base pentagonal.
Página 134 Recortables 1. 6,959 km y 695.900 cm. 2. 18 dag , 1,150 kg, 15 hg, 2.500 g y 2,6 kg.
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