GUÍA ESENCIAL
matemáticas
4
primaria
Introducción
1
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índice GUÍA PRIMER TRIMESTRE LA LOMCE LOMCE Y SU REFLEJO EN LAS PROGRAMACIONES DIDÁCTICAS DIDÁCTICAS .......................... ................................................ ............................................ .......................... ....
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ASÍ ES TU GUÍA ...................................... ............................................................ ............................................ ............................................ ............................................ ............................................ .............................. ........
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ASÍ ES TU LIBRO ........................................... ................................................................. ............................................. ............................................. ............................................ ............................................ ...................... �� ÍNDICE DE CONTENIDOS ......................................... ............................................................... ............................................. ............................................. ............................................ ................................. ........... �� COMENZAMOS ........................................................ .............................................................................. ............................................. ............................................. ............................................ ................................. ........... �� UNIDAD � .............................................. .................................................................... ............................................ ............................................ ............................................ ............................................ .............................. ........ �� UNIDAD � .............................................. .................................................................... ............................................ ............................................ ............................................ ............................................ .............................. ........ �� UNIDAD � .............................................. .................................................................... ............................................ ............................................ ............................................ ............................................ .............................. ........ �� UNIDAD � .............................................. .................................................................... ............................................ ............................................ ............................................ ............................................ .............................. ........ �� REPASO TRIMESTRAL............................................................. ................................................................................... ............................................ ............................................ ......................................... ................... ��� PROYECTO PROYECTO ......................................... ............................................................... ............................................ ............................................. ............................................. ............................................ ................................. ........... ���
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La LOMCE y su reflejo en las programaciones didácticas Introducción La LOMCE, Ley Orgánica de Mejora de la Calidad Educativa (12/2013), conlleva cambios significativos respecto a la LOE, especialmente relacionados con la manera de programar las unidades didácticas. En concreto, aparecen nuevos conceptos (estándares de d e aprendizaje, indicadores de logro) y se revisan otros, como la lista de competencias básicas.
Elementos de continuidad A) Objetivos. La Objetivos. La LOMCE formula una serie de Objetivos Generales de Etapa en torno a los cuales han de articularse los contenidos impartidos en todas las materias y cursos. Desaparece, por tanto, el nivel de concreción que aportaban los Objetivos Generales de Área. De ahí que en las programaciones de aula, los objetivos específicos de cada unidad hayan de vincularse directamente desde el plano más general. Estos Objetivos Generales de Etapa no serán sometidos a modificación por parte de las comunidades autónomas. B) Contenidos. La Contenidos. La nueva Ley hace un tratamiento diferenciado según el tipo de materia: troncales ofrece un desglose pormenorizado de los contenidos. Sin embar► Para las materias troncales ofrece go, no ofrece la secuenciación por cursos, sino que les corresponde a las comunidades autónomas determinar su distribución a lo largo de la etapa. específicas el Ministerio no ha especificado contenidos co ntenidos concretos, sino que ► Para las materias específicas el serán determinados por las distintas administraciones autonómicas. Estas serán las encargadas de adecuar los contenidos a las peculiaridades y necesidades de cada Comunidad, y de adaptarlas para que contribuyan al cumplimiento de los objetivos y a la adquisición de las competencias y destrezas previstas para la etapa educativa. C) Criterios de evaluación. Los evaluación. Los criterios de evaluación constituyen el elemento vertebrador alrededor del que se articulan los procesos de aprendizaje y de evaluación. Frente a las leyes educativas anteriores, la nueva Ley organiza los criterios de evaluación en bloques de contenidos. En consecuencia, y aunque no haya una correspondencia directa entre contenidos y criterios, parece clara la vinculación de ambos elementos. Este hecho es especialmente importante en las materias específicas, ya que el desglose de cont enidos ofrecido por las comunidades autónomas deberá garantizar una vinculación con los criterios de evaluación, de modo que serán estos los que en buena medida condicionen el desarrollo de los contenidos. D) Competencias básicas. La básicas. La homogeneización del sistema educativo europeo impulsa la asunción de una serie de competencias básicas ent endidas como el conjunto de destrezas aplicab les a diferentes entornos. Las competencias básicas constituían la gran novedad educativa en los últimos años. En la nueva Ley continúan presentes como uno de los elementos que ha de ser trabajado y evaluado, en este caso a través t ravés de los estándares de aprendizaje, cuya formulación permite una vinculación con las competencias. La LOMCE define siete competencias clave: 1. Comunicación lingüística. 2. Competencia matemática y competencias básicas en ciencia y tecnología. 3. Competencia digital. 4. Aprender a aprender.
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Principales novedades A) Estándares de aprendizaje. Constituyen el elemento más novedoso de las nuevas programaciones. La LOMCE los define como la expresión de lo que un alumno debe saber y saber hacer en una determinada materia y nivel educativo, constituyendo descripciones precisas del conocimiento, las destrezas, competencias y otras capacidades que la escuela debe promover. Estos estándares están fijados por la Ley, tanto para las materias troncales como para las específicas, y representan la referencia básica para la evaluación: es el elemento que se evalúa, y que sirve como guía para las escuelas, como marco de referencia para su trabajo y como expresión de los requisitos del aprendizaje. Por ello, la vinculación entre los estándares de aprendiza je y los criterios de evaluación es clara. B) Indicadores de logro. Son descriptores del estándar de aprendizaje, expresiones cuantitativas o cualitativas que permiten medir el nivel de adquisición de los estándares y, en consecuencia, de los criterios de evaluación. En este caso, son los equipos docentes quienes determinan qué indicadores de logro se utilizan para valorar el grado de consecución de los estándares de aprendizaje.
Las nuevas programaciones de aula Con estas novedades, las nuevas programaciones de aula, como las que ofrecemos en el proyecto Savia, deberán incluir los siguientes apartados: ►
►
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Presentación. Una Presentación. Una vinculación de la unidad didáctica al currículo inicial, especificando cuál va a ser su función en la adquisición de contenidos y de criterios de evaluación. Objetivos. Se Objetivos. Se formularán objetivos específicos para cada unidad vinculados a los Objetivos Generales de Etapa ofrecidos por la Ley. Competencias clave. Se especificarán las competencias básicas que van a ser trabajadas, evaluadas y registradas, relacionándolas con los estándares de aprendizaje. Contenidos. Se Contenidos. Se detallarán y secuenciarán los contenidos de la unidad, pero utilizando como referencia los contenidos de la materia ofrecidos por las Administraciones, que condicionan la distribución y profundización de las mismas. Criterios de evaluación. Deberán evaluación. Deberán corresponderse con los fijados por las Administraciones para el bloque de contenidos incluido en la unidad. Estándares de aprendizaje. Se aprendizaje. Se seleccionará un número de los estándares de aprendizaje que la propia Administración vincula a los criterios de evaluación. Hay que ten er en cuenta que, aunque no son una enumeración de mínimos, han de guiar el proceso de aprendizaje. Indicadores de logro. Para cada estándar de aprendizaje, el docente fijará un número variable descriptores, que deberán ser observados, registrados y evaluados a de indicadores de logro o descriptores, lo largo de la unidad. Metodología. Se Metodología. Se especificarán las orientaciones metodológicas que guiarán el proceso de enseñanza y aprendizaje a lo largo de la unidad, intentando en la medida de lo posible prever las necesidades materiales, las posibles dificultades, la temporalización, etc.
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La guía, un recurso esencial para el aula La Guía esencial de Savia ofrece Savia ofrece ideas y propuestas novedosas, a la vez qu e asocia los recursos del proyecto al libro del alumno, lo que permite enriquecer las clases y adaptarlas al itinerario educativo que decida seguir cada profesor. La estructura general de la guía es la siguiente: ►
►
Páginas iniciales, iniciales, en las que se explica cómo utilizar la guía y cómo se estructuran las unidades didácticas del libro del alumno. También se incluye el cuadro de contenidos de la etapa y se indican los principales cambios incorporados a raíz de la LOMCE. Guía de cada unidad didáctica, didáctica, que incluye un mapa visual de todos los recursos, la programación de aula, las orientaciones metodológicas generales y las sugerencias metodológicas sección por sección.
Estructura de la guía de cada unidad didáctica Introducción general Se exponen los contenidos que se van a desarrollar y se hace referencia al valor destacado a lo largo de la unidad. Se incluyen las lecturas recomendadas y el material complementario asociado (cuadernos de trabajo, material de consulta, etc.).
Mapa de recursos de la unidad Se vincula, a través de un esquema intuitivo, cada sección de la unidad con los recursos asociados a cada una de ellas. Se indican recursos digitales para el profesor y para el alumno.
Se diferencia entre los recursos para el profesor y los elementos del material para el aula.
Se señala la tipología de la actividad y el título de cada recurso. Con un grado de detalle suficiente para que el profesor pueda localizar el recurso con facilidad.
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Programación de aula Se parte de dos tablas organizadas con la intención de ofrecer una visión clara y ordenada de los nuevos contenidos curriculares, teniendo en cuenta la complejidad que supone la adaptación a una nueva estructura y al uso de una nueva terminología que conllevan un cambio legislativo. En la primera tabla se vinculan los objetivos de la unidad y las competencias.
En la segunda tabla se relacionan los contenidos con los criterios de evaluación, los estándares de aprendizaje (nuevo nivel de concreción de la LOMCE) y los descriptores establecidos para ligar cada estándar de aprendizaje a las actividades del libro del alumno.
Orientaciones metodológicas Se indican las orientaciones pedagógicas y didácticas generales para el desarrollo de la unidad. ►
►
1. Conocimientos previos de cursos o unidades anteriores que deberían tener los alumnos. 2. Previsión de las dificultades que dificultades que pueden encontrar-
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Tratamiento específico de las inteligencias múltiples En el proyecto Savia se Savia se ofrece una tipología variada de actividades, con el fin de atender a los distintos estilos de aprendizaje de los alumnos. En el mapa de inteligencias múltiples de múltiples de la Guía esencial se referencian las actividades del libro del alumno y las sugerencias metodológicas que potencian cada una de las inteligencias.
Actividades del libro del alumno. Sugerencias metodológicas metodológicas de la Guía esencial.
Actividades tipo.
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Sugerencias metodológicas Sección a sección, se desarrolla una propuesta de sesión orientada a alcanzar los estándares de aprendizaje definidos y a explotar las páginas del libro con actividades complementarias. complementarias.
Estas llamadas marcan actividades en Saviadigital Saviadigital para los alumnos. En las sugerencias metodológicas se indica en qué consisten y cuándo se pueden realizar. : actividad interactiva
Estándares de aprendizaje y aprendizaje y descriptores asociados descriptores asociados a los contenidos.
digitales que Con llamadas a los recursos digitales que se pueden utilizar con los alumnos en el aula para explotar un contenido, activar un concepto, desarrollar un procedimiento... : audio, : video, : actividad interactiva, etc.
Incluye el solucionario de las actividades.
Cada sesión está organizada temporalmente en tres en tres momentos:
La Guía esencial vincula el libro del alumno con el resto de elementos del proyecto: Llamadas a la guía de Aprendizaje cooperativo. •
2
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Así es tu libro El libro de matemáticas de 4º del proyecto Savia se compone de doce unidades que cuentan con las siguientes secciones.
Entrada de unidad Lectura que Lectura que narra, en forma de breve historia, situaciones en las que participan las matemáticas.
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Páginas de contenidos Programa de Agilidad mental: mental: Recuadro de presentación del contenido a través de un contexto y contexto y una pregunta. pregunta. Se destaca la idea principal del epígrafe.
Recuadros Nota y Ten en cuenta para facilitar la resolución de actividades o ¿Sabías qué? que muestra curiosidades matemáticas.
• Mentatletas • Calculadora estropeada • Dados
Actividad o problema de respuesta múltiple en cada epígrafe.
Actividades interactivas en Saviadigital Saviadigital..
Un Taller de matemáticas manipulativas en manipulativas en cada unidad, para reforzar los contenidos mediante la manipulación para atender a los distintos estilos de aprendizaje.
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Secciones de unidad Problemas, Problemas, cuya página izquierda incluye la sección Me entreno antes de resolver con resolver con actividades que entrenan la comprensión de enunciados y enunciados y la comprensión de los mecanismos para la resolución. resolución. La página derecha incluye las secciones Leo, Leo, pienso y resuelvo e resuelvo e Invento un problema, problema, entrenan la resolución.
Problemas para reforzar la resolución de resolución de problemas con contenidos estudiados.
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Sección Matemáticamente Sección Matemáticamente,, con dos partes diferenciadas: Cálculo mental y mental y Retos matemáticos. matemáticos.
Propuesta visual para visual para que el alumno genere la imagen mental y asociarla a cantidades. Se realizan descomposiciones que faciliten los términos al operar.
PRACTICA en Saviadigital Saviadigital para utilizar la estrategia de cálculo mental aprendida. mental aprendida.
Sección Retos matemáticos con actividades para aplicar el razonamiento y razonamiento y la lógica, lógica, y utilizar materiales como el tangram. tangram.
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Sección Repasa las unidades para unidades para que el alumno repase a través de actividades y problemas los contenidos estudiados desde la unidad 1.
Actividad con icono tangram que trabaja el razonamiento y la lógica.
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Secciones trimestrales Repaso trimestral mediante trimestral mediante actividades tipo test y test y contextos competenciales. competenciales .
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Cálculo mental y lógica
Tratamiento de la información
Ponte a prueba
Suma de dos números de 3 cifras
Un mundo lleno de seres vivos Tarea final: Dedos numéricos
22 Suma de números por sumas sucesivas
40 Sumar completando decenas
56 Multiplicar por 5
S E D A D I N U S A L A S A P E R
25 Un juego de construcción Tarea final: Piojillos de papel
43 El armario Tarea final: Quien parte y reparte se lleva la mejor parte 59 Ayuda solidaria
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Contenidos relacionados Con esta entrada se pretende repasar contenidos de 3.º de Primaria de una forma lúdica para los alumnos. Estos son: • Números de hasta seis cifras • Suma y resta • Múltiplos y divisores • Números romanos Todos ellos se van a estudiar de forma ampliada durante el primer trimestre de este curso.
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Soluciones La pirámide universal 11111 111111 1111111 11111111 111111111
× × × × ×
11111 111111 1111111 11111111 111111111
= 123454321 = 12345654321 = 1234567654321 = 123456787654321 = 12345678987654321
El reparto César tiene una cantidad de canicas que es múltiplo de 3 × 5 (puede tener 15, 30, 45, 60, 75...).
Pizarra Respuesta modelo: 40.128 – 6.795 = 33.333.
Matrículas
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unidad
1
Los números. Sumar y restar
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Recursos de la unidad Recursos digitales Recursos para el profesor en USB y www.smconectados.com
Trabaja con la imagen
Otros recursos
Recursos para el alumno en www.smsaviadigital.com
Recursos para el profesor
Unidad 1:
Material para el aula
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Programación Programació n de aula del Proyecto Savia
OBJETIVOS DE UNIDAD
COMPETENCIAS
1. Formar y utilizar números naturales de hasta seis cifras. 2. Comparar y ordenar números naturales de seis cifras. 3. Los números de siete cifras. Los millones.
Comunicación lingüística (Objetivos 1, 2 , 3, 4 y 8)) Competencia matemática y competencias básicas en ciencia y tecnología
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Programación de aula del Proyecto Savia
BLOQUE
CONTENIDOS
CRITERIOS DE DE EV EVALUACIÓN
ESTÁNDARES DE DE AP APRENDIZAJE �*�*�
Propiedad conmutatitva y asociativa.
2. Realizar cálculos numéricos básicos con las operaciones de suma y resta, utilizando diferentes estrategias y pro-
2.1. Utiliza y automatiza algoritmos estándar de suma y resta, estimando la coherencia de los resultados en contextos de resolución de proble-
DESCRIPTORES/INDICADORES •
Identifica y aplica adecuadamente las propiedades conmutativa y asociativa de la suma. - Act. 20
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Programación Programació n de aula del Proyecto Savia
Orientaciones metodológicas 1. Conocimientos previos necesarios Para abordar con éxito los contenidos de esta unidad, los alumnos deberán: • Leer y escribir números naturales hasta el 99.999 para poder hacerlo con números mayores con fluidez. • Identificar los distintos órdenes de unidad de cualquier número de cinco cifras. Conocer el concepto de mayor y menor
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Estándares de aprendizaje y descriptores/indicadores �.�.
Utiliza
y automatiza algoritmos estándar de suma, resta y multiplicación de núme ros naturales, estimando la coherencia de los resultados en contextos de resolución de problemas y en situaciones cotidianas. • Sabe multiplicar por la unidad seguida de uno, dos o tres ceros. • Plantea y resuelve problemas con sumas, restas y multiplicaciones.
Soluciones 28
× 10
× 100
× 1 000
38
380
3.800
38.000
562
5.260
56.200
562.000
3.087
30.870
308.700
3.087.000
62.114
621.140
6.211.400 62.114.000
29 950 → 95 × 10
1.290 → 129 × 10 23.600 → 236 × 100 560.100 → 5.601 × 100 4.702.000 → 4.702 × 1.000 30
a) 9.348 − 543 = 8.805. Le quedan por recorrer recorrer 8.805 kilómetros. b) 10.000 + 9.348 = 19.348. 19.348. Floruno está a 19.348 kilómetros de su casa.
s a c i g ó l o d o t e m s a i c n e r e g u S
Para comenzar...
Durante el desarrollo...
Agilidad mental
3. Se propone trabajar estos dos epígrafes en una sola sesión.
Mentatletas (3 a 5 minutos). 1. Mentatletas (3 Cuatro ejercicios con estas condiciones: Operaciones: Cantidad de números: Tiempo (segundos): Número de cifras:
sumas 3 1 1
Es importante identificar la unidad seguida de ceros con ceros con su expresión en forma de potencia. 10 x
el exponente es el número de ceros que sigue a la unidad.
4. Apoyar la teoría con el tablero SMdecimal.. SMdecimal 103
102
101
1
• Utilizar las tarjetas blancas para escribir las potencias. • Pedir a los alumnos que coloquen las fichas y lean el número obtenido. • Trabajar la composición de números a partir de su expresión en potencias de base 10.
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Estándares de aprendizaje y descriptores/indicadores �.�. Identifica la potencia como multiplicación de factores iguales. • Expresa la unidad seguida de ceros en forma de potencia.
�.�.
Emplea las potencias de en la descomposi ción polinómica de números. • Compone y descompone números naturales utilizando potencias de base ��. Descomponer en potencias de base 10
Soluciones 31 mil: 32
33 25
103; cien mil: 105; cien: 102; diez mil: 104
planeta Arevafina
620.000
62 × 104
planeta Bernaví
5.300.000
53 × 10 5
planeta Garcoiana
226.000
226 × 10 3
planeta Casanar
36.700
367 × 102
planeta Bejareva
125 125.000 .000..000 000
125 125 × 106
× 105 = 2.500.000
7 × 106 = 7.000.000 412 × 104 = 4.120.000 7.456 × 10 3 = 7.456.000 Respuesta modelo: 7.456 × 103 > 7 × 10 6 > 412 × 10 4 > 25 × 10 5 34 A. 3 × 10 4
5. Se pueden formar números mayores juntando tableros.
UMM
CM
DM
UM
C
D
U
Propuesta de actividades para casa Actividad 32 (5-10 minutos aprox.).
Aprendizaje personalizado (Trabajos asignables en Saviadigital)
1.234.567 1 × 106 + 2 × 105 + 3 × 10 4 + 4 × 10 3 + 5 × 102 + 6 × 10 + 7 juntos: actividades 28, 31 y 34. 6. Practicamos juntos: actividades
Para comprender y reforzar
Documento de refuerzo, actividad 7.
Para profundizar
Actividades interactivas de ampliación, Potencias de base 10.
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Estándares de aprendizaje y descriptores/indicadores �.�. Utiliza y automatiza algoritmos estándar de suma, resta y multiplicación de núme ros naturales, estimando la coherencia de los resultados en contextos de resolución de problemas y en situaciones cotidianas. • Multiplica números naturales por una sola cifra. • Multiplica por números de dos o más cifras. • Aplica la propiedad distributiva. • Plantea y resuelve problemas con sumas, restas y multiplicaciones.
�.�. Progresa en el análisis y comprensión del enunciado de los problemas (datos, relaciones entre los datos, contexto del problema). • Interpreta correctamente la información del enunciado en problemas cotidianos. • Sabe qué operaciones debe realizar para resolver un problema. • Encuentra una pregunta que puede resolver con una operación dada.
�.�. Progresa en la utilización de herramientas tecnológicas para la realización de cálculos numéricos, para aprender y para resolver problemas. • Utiliza las TIC como herramientas de aprendizaje y autoevaluación.
Soluciones Me entreno antes de resolver 1
b) Una multiplicación y una suma. a) Una suma y una resta. a) Una multiplicación y dos sumas.
2
b) Dos Dos multiplicaciones y una suma. 12 × 824 = 9.888 7 × 367 = 2.569 9.888 + 2.569 =12.457 En total hacen 12.457 km.
s Para comenzar... Agilidad mental a c i g 1. Problema visual (3 a 5 minutos). ó l o Número de problemas ➝ 1 d o Tiempo ➝ 5 min t e m s Tras Tras ver la animación, plantear las siguientes preguntas: a i c gramos de comida co• Antes de que los cerdos críen, ¿cuántos gramos n e men entre todos en un día? ¿Y en una semana? ¿Cuánta agua r e cabía en los recipientes que se han roto? g u • ¿Cuántas crías con manchas hay en total en los cercados 1, 2 y S 3? ¿Y en el 4, 4, 5 y 6? • ¿Cuántas crías sin manchas hay en total? Utiliza la propiedad
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Soluciones Leo, pienso y resuelvo 1
Al año venden 6.324 perfumes (527 × 12).
2
12 × (7 + 6 + 5 + 9) = 12 × 27 = 324. En total con sumen 324 yogures.
3
C. 269 (25 × 3 + 67 × 2 + 15 × 4)
4
a) 5 × 34 + 3 × 20 = 170 + 60 = 230. En total tienen 230 animales. b) 300 − 230 = 70. Tendrán Tendrán que comprar comprar 70 animales.
Invento un problema 5
Durante el desarrollo... 3. Hacer ver a los niños que para resolver muchos de los problemas se necesita más de una operación. 39, hacerles ver 4. En el primer problema de la página 39, que uno de los datos necesarios para resolverlo es el año, año, que tiene 12 meses. Deben discriminar entre esta información, que no aparece en el texto, y un dato numérico que no necesitan. juntos: actividad 1, pág. 38 y actividades 1 5. Practicamos juntos: actividad y 2, pág. 39. individual: actividad 2, pág. 38 y actividades 4 6. Trabajo individual: actividad y 5, pág. 39.
Respuesta modelo: ¿Cuántos huevos hay en 35 cajas de una docena cada una?
Aprendizaje cooperativo La actividad 5 puede realizarse mediante la estructura giratorio. cooperativa Folio giratorio. Ver guía de Aprendizaje de Aprendizaje cooperativo. cooperativo.
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Estándares de aprendizaje y descriptores/indicadores �.�.
Elabora y usa estrategias de cálculo mental. • Suma números mediante sumas sucesivas.
�.�. Progresa en la utilización de herramientas tecnológicas para la realización de cálculos numéricos, para aprender y para resolver problemas. • Utiliza las TIC como herramientas de aprendizaje y autoevaluación.
Soluciones Cálculo mental 1
2
712 + 134 = 846
343 + 245 = 588
832 + 121 = 953
330 + 346 = 676
451 + 107 = 558
532 + 264 = 796
243 + 135 = 378. Hemos realizado realizado 378 pulseras en total.
Retos matemáticos 1
Respuesta modelo: Marcaría el 100 (215 − 115 = 100), después marcaría el 538 (423 + 115 = 538) y el resultado sería: 100 + 538 = 638.
2
Todas menos el romboide (6 piezas).
s Durante el desarrollo... a c i numérica del CD Taller de matemáticas g 1. Se puede proyectar la recta numérica del ó hasta lograr que los alumnos adquieran la confianza suficiente para l o abordar la estrategia. d o t Observar que aplicamos la descomposición al segundo sumando e 2. Observar porque operamos de izquierda a derecha. m s juntos: actividad 1, Cálculo mental. mental. a 3. Practicamos juntos: actividad i c n 4. Trabajo individual: actividad individual: actividad 2, Cálculo 2, Cálculo mental y mental y actividad 1, Retos ma e r temáticos. e g Para realizar el segundo reto, indicar que utilicen el tangram tangram.. u S
Para terminar…
5. Corregir en gran grupo las
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Soluciones 1
365 × 2 = 730 4.713 × 23 = 108.399 14.705 × 16 = 235.280
2
A. 6 × 6 × 6 = 6 3 B. 11 × 11 × 11 × 11 = 11 4 C. 9 × 9 = 92 D. 15 × 15 × 15 = 15 3
3 4
B. Dos 10 × 10 × 100 = 10.000 < 11.500 No podrán, no tienen suficientes folios.
Vocabulario matemático 5
- El coche de carreras tiene potencia → significa que el coche tiene mucha fuerza. - Escribe 9 en forma de potencia → se refiere a la expresión 32.5
Durante el desarrollo...
1. Esta sesión y la siguiente servirán para preparar la evaluación.
Aprender a pensar Al final de la sesión, puede realizarse la estrategia de pensamiento Mapa mental
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Contenidos relacionados • Lee números de hasta seis cifras (Ud. 1). • Redondea números a la unidad de millar (Ud. 1). • Ordena números de hasta siete cifras (Ud. 1). • Realiza sumas y restas (Ud. 1). • Realiza multiplicaciones (Ud. 2). • Aplica las propiedades conmutativa y asociativa de la multiplicación (Ud. 2). • Aplica la propiedad distributiva (Ud. 2). • Expresa la unidad seguida de ceros como potencia de base 10 (Ud. 2).
Soluciones 1
83.653: ochenta y tres mil seiscientos cincuenta y tres. 5.687: cinco mil seiscientos ochenta y siete. 652.503: seiscientos cincuenta y dos mil quinientos tres. Redondeos a la UM: 83.653 → 84.000 5.687 → 6.000 652.503 → 653.000
2
8 CM + 3 DM + 2 U > 9 DM + 3 UM + 6 C + 5 D +4U 4 UMM + 6 UM + 4 C < 7 UMM + 5 DM + 6 U 12 C + 4 D + 6 U = 1 UM + 2 C + 4 D + 6 U
3
6.081 × 68 = 413.508 83.245 × 46 = 3.829.270 741 × 407 = 301.587
4
5 × 13 = 13 = 5 × 13 21 × (11 (11 + + 25) = 21 × 11 + 21 × 25 32 × (14 × 13) 13) = (32 × 14) 14) × 13
s Durante el desarrollo... a c i g Esta doble página sirve para preparar la evaluación. Se presentan dos ó l itinerarios, según el tipo de evaluación que se quiera realizar. o
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Estándares de aprendizaje y descriptores/indicadores �.�. Utiliza y automatiza algoritmos estándar de suma, resta y multiplicación de números naturales, estimando la coherencia de los resultados en contextos de resolución de problemas y en situaciones cotidianas. • Ordena datos en filas y columnas y los expresa como una multiplicación. • Multiplica números naturales por una o más cifras. • Aplica la propiedad distributiva.
�.�. Progresa en la elaboración de informes sobre el proceso de investigación realizado, exponiendo las fases, valorando los resultados y las conclusiones obtenidos. • Prepara un informe en el que da respuesta a las cuestiones planteadas.
�.�. Progresa en la utilización de herramientas tecnológicas para la realización de cálculos numéricos, para aprender y para resolver problemas. • Utiliza las TIC como herramientas de aprendizaje y autoevaluación.
Soluciones Un juego de construcción 1
No le falta ninguna (4 × 12 = 48).
2
4 × 23 = 92; 135 − 48 = 87; 92 > 87 Sí, le faltan 5 de las pequeñas (92 − 87).
Modelo de entregable Piojillos de papel
3
3 × (12 + 12) = 3 × 24 = 72. Tendrá una altura máxima de 72 centímetros.
4
B. 4 × (12 + 23)
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unidad
3
Dividir
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Recursos de la unidad Recursos digitales Recursos para el profesor en USB y www.smconectados.com
Otros recursos
Recursos para el alumno en www.smsaviadigital.com
Autoevaluación Autoev aluación inicial Trabaja con la imagen
Recursos para el profesor
Unidad 3: Dividir
Agilidad mental. Mentatletas mental. Mentatletas
1. División y sus términos Vídeo. Dividir
Agilidad mental. Calculadora mental. Calculadora estropeada • CD Taller de matemáticas. Bloques matemáticas. Bloques multibase, tablero SMdecimal • Actividad. División Actividad. División de una cifra • Vídeo. Dividir Vídeo. Dividir • Vídeo. Dividir Vídeo. Dividir con fichas Agilidad mental. Mentatletas mental. Mentatletas
2. División de una cifra Taller de matemáticas Dividir con fichas
3. Múltiplos y divisores
• CD Taller de matemáticas. Recta matemáticas. Recta numérica • Vídeo. Divisores con regletas Agilidad mental. Calculadora estropeada
Agilidad mental. Mentatletas
Monedas y billetes
• Refuerzo. Actividad 1 • Repaso. Actividad 1
• Repaso. Actividades 2-5 • Refuerzo. Refuerzo. Actividades Actividades 2, 3 y 8 • Ampliación. Ampliación. Actividades Actividades 1, 2 y 4 Tablero SMdecimal
• Taller de matemáticas. Págs. Págs. 20 y 21 • Repaso. Actividad 6 • Refuerzo. Actividades 4 y 5 • Ampliación. Actividad 3 Regletas
4. Números primos y compuestos
5. Criterios de divisibilidad
Repaso. Actividad 8 • Repaso. Actividad 9 • Refuerzo. Actividades 6 y 7 • Tablero • Regletas
Actividad. Entrénate
Material para el aula
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Programación Programació n de aula del Proyecto Savia
OBJETIVOS DE UNIDAD 1. Dividir por números de una cifra.
COMPETENCIAS Comunicación lingüística (Objetivos 4 y 6)
2. Utilizar la prueba de la división. 3. Calcular los múltiplos y divisores de un número. 4. Diferenciar los números primos y los compuestos.
Competencia matemática y competencias básicas en ciencia y tecnología (Objetivos 1-9) Competencia digital (Objetivo 8)
5. Aprender los criterios de divisibilidad. 6. Discriminar entre varias opciones la solución posible. 7. Desarrollar estrategias de cálculo mental. 8. Utilizar dispositivos tecnológicos para afianzar los contenidos. 9. Comprender la importancia de ser equitativos.
Aprender a aprender (Objetivos 6-9) Competencias sociales y cívicas (Objetivo 9) Sentido de iniciativa y espíritu emprendedor (Objetivos 4, 6 y 8)
BLOQUE
CONTENIDOS
CRITERIOS DE EVALUACIÓN
ESTÁNDARES DE APRENDIZAJE �*�
División de números naturales por números de una cifra.
1. Realizar cálculos numéricos básicos con las operaciones de suma, resta, multiplicación y división, utilizando diferentes estrategias y procedimientos.
1.1. Utiliza y automatiza algoritmos estándar de suma, resta y multiplicación con números naturales, en contextos de resolución de problemas y en situaciones cotidianas.
Automatización de algoritmos. Múltiplos y divisores. Obtención de los primeros
1.2. Conoce y usa la división de números naturales, así como el co-
DESCRIPTORES/INDICADORES •
•
Expresa situaciones de la vida real mediante una división. - Act. 1, 2, 4, 7 y 9 Indica cuáles son los términos de una división. - Act. 3, 5, 9 y 10 - Act. 2. Tarea final , pág. 59
•
Realiza divisiones por una sola cifra.
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Programación de aula del Proyecto Savia
BLOQUE
CONTENIDOS
CRITERIOS DE DE EV EVALUACIÓN
ESTÁNDARES DE DE AP APRENDIZAJE �*�*�
Elaboración y uso de estrategias de cálculo mental.
2. Conocer, elaborar y utilizar estrategias básicas de cálculo mental y aplicarlas a la resolución de problemas.
2.1. Elabora y usa estrategias estrategias de cálculo mental.
3. Utilizar procesos de razonamiento y estrategias de resolución de problemas, realizando los cálculos necesarios y comprobando las soluciones obtenidas.
3.1. Progresa en el análisis y comprensión del enunciado de los problemas (datos, relaciones entre los datos, contexto del problema).
Entender los enunciados y cómo debe ser la solución correcta. Planificación del proceso de resolución de problemas. Análisis y comprensión del enunciado. S A C I S T Á O D M O E T T É A M M , S N E O S S E E C D O U T R I P T C A Y
DESCRIPTORES/INDICADORES •
Suma números mediante la formación de decenas completas. - Act. 1 y 2. Cálculo mental , pág. 56
(Aprender a aprender y sentido de iniciativa y espíritu emprendedor).
Planteamiento de pequeñas inPlanteamiento vestigaciones en contextos numéricos, geométricos y funcionales.
4. Elaborar y presentar pequeños informes sobre el desarrollo, resultados y conclusiones obtenidas.
4.1. Progresa en la elaboración de informes sobre el proceso de investigación realizado.
Utilización de medios tecnológicos en el proceso de aprendizaje para obtener información, realizar cálculos numéricos, resolver problemas y presentar resultados.
5. Utilizar los medios tecnológicos de modo habitual en el proceso de aprendizaje.
5.1. Progresa en la utilización de herramientas tecnológicas para la realización de cálculos numéricos, para aprender y para resolver problemas.
•
Interpreta correctamente la información del enunciado en problemas cotidianos. - Problemas , págs. 54 y 55
•
•
•
Decide cuál es la solución de un problema. - Act. 1 y 2. pág. 54 Encuentra los datos necesarios para responder a una pregunta dada. - Act. 6. Problemas, pág. 55 Prepara un informe en el que da respuesta a las cuestiones planteadas. - Act. 5. Tarea final , pág. 59
(Aprender a aprender y sentido de iniciativa y espíritu emprendedor)
(Competencia digital)
•
Utiliza las TIC como herramientas de aprendizaje y autoevaluación. - Act. interactiva en Saviadigital, págs. 51, 53, 54, 56, 57 y 59
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Programación Programació n de aula del Proyecto Savia
Orientaciones metodológicas 1. Conocimientos previos necesarios Para abordar con éxito los contenidos de esta unidad, los alumnos deberán: multiplicar. • Dominar las tablas de multiplicar. algoritmos de de suma, resta y multiplicación. • Dominar los algoritmos dividir entre entre números de una sola cifra. • Saber dividir unidad de cualquier número natural. • Identificar los distintos órdenes de unidad de
2. Previsión de dificultades dificultades Es posible que los alumnos encuentren algunas de las siguientes dificultades en el estudio de la unidad: divisor. • Les costará distinguir entre múltiplo y divisor. compuestos. • Tendrán dificultades para diferenciar números primos y compuestos.
3. Vinculación con el área de Lengua En la sección Vocabulario matemático se trabajan términos matemáticos desde el punto de vista lingüístico, al mismo tiempo que el alumno va adquiriendo capacidades en el área de Lengua.
4. Programas transversales Aprendizaje cooperativo
Escritura simultánea simultánea por parejas (página 53).
Aprender a pensar
Las partes y el todo (act.1, página 46), Diagrama de flujo (act. 20, página 52) y Qué aprendo, para para qué (Tarea final, página 59).
Edu duccaci ción ón en val alor ores es
Serr eq Se equit itat atiivos os.. Se trata de hacer ver a los alumnos que todo reparto debe realizarse de forma justa.
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Tratamiento Trat amiento de las inteligencias múltiples INTRAPERSONAL
LINGÜÍSTICO-VERBAL
Reflexión sobre los propios pensamientos y emociones Guía esencial:
Lectura individual Libro del alumno: •
El reparto pirata, pirata, pág.44
Sugerencia 4, pág. 77 Reflexionamos, pág. 77, • Sugerencia 79, 81, 83 y 85 •
Resolución de adivinanzas, enigmas, ect. Libro del alumno: •
Act. 1. Retos matemáticos, matemáticos, pág. 56
Autoevaluación y ejercicios de metacognición Libro del alumno:
Adquisición y uso de nuevo vocabulario Libro del alumno: •
Act. 5. Repasa la unidad , pág. 57
•
Valora lo aprendido, aprendido , págs. 57 y 59
Guía esencial: •
LÓGICO-MATEMÁTICA
Práctica de diversas estrategias de aprendizaje Libro del alumno:
Uso de la numeración en actividades de la vida cotidiana Libro del alumno: •
A lo largo de toda la unidad
Cálculo Libro del alumno: •
A lo largo de toda la unidad
Realización de estimaciones y predicciones Libro del alumno: •
Act. 2. Repasa las unidades, unidades, pág. 58
Actividades de clasificación, comparación
Sugerencia Aprender Sugerencia Aprender a pensar pensar , pág. 91
Problemas, pág. 54 Problemas, mental, pág. 56 • Cálculo mental, •
INTELIGENCIAS MÚLTIPLES
INTERPERSONAL Creación de grupos de apoyo al estudio entre los propios estudiantes Libro del alumno: •
Tarea final, final, pág. 59
Guía esencial: •
Sug. 4, pág. 77 y sug. 4, pág. 87
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Estándares de aprendizaje y descriptores/indicadores �.�. Conoce y usa la división de números natunatu rales, así como los correspondientes algoalgoritmos. • Realiza divisiones por una cifra.
Dividir Dividir con fichas Divisores con regletas
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Soluciones 1
Hacen dos grupos con cada una de las las tres partes del tesoro.
2
28 monedas (56 : 2).
3
8 collares y 4 anillos (sobrarían 2 anillos).
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Estándares de aprendizaje y descriptores/indicadores �.�. Utiliza y automatiza algoritmos estándar de suma, resta y multiplicación de núme ros naturales, en contextos de resolución de problemas y en situaciones cotidianas. cotidianas. • Resuelve problemas con contextos cotidianos. natu �.�. Conoce y usa la división de números naturales, así como el correspondiente algoritalgoritmo. • Expresa situaciones cotidianas mediante una división. • Indica cuáles son los términos de una división. • Realiza divisiones por una cifra.
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Soluciones 1
a) 84 : 8 →Dividendo 84 y divisor 8 b) 42 : 6 →Dividendo 42 y divisor 6 c) 26 : 2 →Dividendo 26 y divisor 2 d) 90 : 6 →Dividendo 90 y divisor 6
2
a) 40 : 5 b) 24 : 6
3
4
Dividendo
divisor
cociente
resto
25 : 3
25
3
8
1
16 : 8
16
8
2
0
35 : 4
35
4
8
3
40 : 5
40
5
8
0
Respuesta modelo:
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Estándares de aprendizaje y descriptores/indicadores �.�. Utiliza y automatiza algoritmos estándar de suma, resta y multiplicación de núme ros naturales, en contextos de resolución de problemas y en situaciones cotidianas. cotidianas. • Resuelve problemas con contextos cotidianos. natu �.�. Conoce y usa la división de números naturales, así como el correspondiente algoritalgoritmo. • Expresa situaciones cotidianas mediante una división. • Indica cuáles son los términos de una división. • Realiza divisiones por una cifra. • Sabe utilizar la prueba de la división.
1
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Soluciones 8
9
642 : 7 = 91; resto resto = 5. 924 : 6 = 154; resto = 0→ exacta. 1.406 : 3 = 48; resto = 2. 3.760 : 5 = 752; resto = 0→ exacta. 1.253 : 5 a) La división no es exacta porque sobran 4 latas. b) 250 − 4 = 246. Hacen falta 246 latas más (1.254 + 246 = 1.500 = 250 × 6).
10
2
Dividendo
divisor
cociente
resto
2.632
9
292
4
1.446
4
361
2
33.476
8
4 .184 4.
4
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Estándares de aprendizaje y descriptores/indicadores �.�. Utiliza y automatiza algoritmos estándar de suma, resta y multiplicación de núme ros naturales, en contextos de resolución de problemas y en situaciones cotidianas. cotidianas. • Resuelve problemas con contextos cotidianos.
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Soluciones 13
– De 6 en 6 no sobran coches. El 6 es divisor divisor de 30. – De 4 en 4 sobran coches. El 4 no es divisor de 30. 1) De 5 en 5 no sobran coches porque el 5 es divisor de 30. 2) De 10 en 10 no sobran coches porque el 10 es divisor de 30. 3) De 2
2
sobran coches
el 2
divi-
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Estándares de aprendizaje y descriptores/indicadores �.�. Utiliza y automatiza algoritmos estándar de suma, resta y multiplicación de númenúme ros naturales, en contextos de resolución de problemas y en situaciones cotidianas. cotidianas. • Resuelve problemas con contextos cotidianos.
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