RECOPILACIÓN DE EJERCICIOS
4°
BÁSICO
Nombre: 4° www.matematicasip.cl 2016
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IMPORTANTE
Este cuaderno de trabajo es una obra colectiva, realizada a partir de la recopilación de ejercicios de distintas fuentes, teniendo por único fin ser un texto de ejercitación para los alumnos SIP. Este cuaderno de trabajo fue creado sin fines de lucro. Prohibida su reproducción comercial
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MATEMÁTICA CUARTO AÑO BÁSICO Cuaderno de Trabajo
4°
epartamento de
atemática SIP
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4ª EDICIÓN Departamento de Matemática SIP - 2016 RECOPILACIÓN EJERCICIOS Y CORRECCIONES
Asesoras Asesoras y Profesores de de la SIP COORDINACIÓN
Asesoras de Matemática Marcia Muñoz , Oriana Bustos y María Luz Montes EDICIÓN
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ESTIMADOS ALUMN@ speramos que este cuadernillo Matemático te ayude a enriquecer
“E
tu gusto por las matemáticas, a comprender la realidad, te facilite la selección de estrategias para resolver problemas y contribuya al
desarrollo de tu pensamiento crítico y autónomo.
Aprender matemática te proporciona herramientas conceptuales para analizar la información cuantitativa presente en las noticias, opiniones, publicidad y diversos textos, aportando al desarrollo de tus capacidades de c omunicación, razonamiento y abstracción e impulsando el desarrollo de tu pensamiento intuitivo y la reflexión sistemática.”
El equipo de asesoras del departamento de Matemática SIP SIP quiere agradecer el compromiso del equipo de profesores que, día a día, se esfuerzan por contribuir a que nuestros alumnos con sus aprendizajes enriquezcan la comprensión de la realidad. Muy especialmente, queremos agradecer a un grupo de profesoras que durante el 2012 se reunieron en numerosas oportunidades a generar los ejercicios que son parte de este cuadernillo, con la prolijidad y compromiso que las caracteriza ASESORA Oriana Bustos Fuentes PROFESORAS PARTICIPANTES
Marcela Acosta Moraga
(Escuela Eliodoro Matte Ossa)
Giselle Álvarez Neira
(Colegio Presidente Alessandri)
Yannina Guerrero Cornejo
(Colegio Jorge Alessandri Rodríguez)
Ana Cecilia González Olguín
(Escuela Arturo Matte Larraín)
Carmen Gloria González Rodríguez (Colegio Guillermo Matta)
Irma Muñoz Bravo
(Colegio Arturo Toro Amor)
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ÍNDICE
MES
TEMA
N° DE PÁGINA
MARZO 1
Números hasta el 10.000
…………………………………………….…
1 – 8
MARZO 2
Adición y sustracción hasta el 10.000
………………………………………………
9 – 15
MARZO 3
Multiplicación
………………………………………..…… .
16 – 24
ABRIL 1
Líneas, figuras 2D y sus elementos
………………………………………….……
25 – 32
ABRIL 2
Multiplicación
……………………………………………....
33 – 40
MAYO 1
Sistema Monetario
……..………………………………..……..
41 – 49
MAYO 2
Números y Patrones
……………… .…………………………….
50 – 58
MAYO 3
Unidades de Tiempo
……………………………………………....
59 – 67
JUNIO 1
Unidades de longitud y peso
……………………………………………….
68 – 74
JUNIO 2
Figuras 3D y sus elementos
……………………………………………….
75 – 86
JUNIO 3
División como repartición
……………………………………………….
87 – 94
JULIO 1
División exacta e inexacta
………………………………………………
95 – 102
AGOSTO 1
Fracciones
……………………………………………….
103 - 109
AGOSTO 2
Fracciones y decimales
………………………………………………
110 - 116
AGOSTO 3
Ecuaciones e inecuaciones de un paso ……………………………………………….
117 - 124
SEPTIEMBRE 1
Movimientos, simetría y perímetro
……………………………………………….
125 - 135
OCTUBRE 1
Tablas, pictogramas y gráficos
……………………………………………….
136 -146
OCTUBRE 2
Volumen
……………………………………………….
147 - 157
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MARZO NUMERACIÓN HASTA 10.000
1
El número 3.024 se lee: A) Trescientos veinticuatro B) Tres mil veinticuatro C) Tres mil doscientos cuatro D) Tres cero veinticuatro
2
Al ordenar de menor a mayor los números 3.874 – 3.478 – 3.748. A) 3.478 < 3.748 < 3.874. B) 3.478 < 3.874 < 3.748. C) 3.748 < 3.874 < 3.478. D)
3
3.874 < 3.748 < 3.478.
¿Qué número se forma con 6 decenas, 4 unidades de mil, 8 unidades y 7 centenas?
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4
Observa la imagen. ¿Cuántos estudiantes hay en el curso de Carmen? Hoy asistimos a clases
A) 51 estudiantes. B) 41 estudiantes. C) 37 estudiantes. Retrocederé 7
D) 33 estudiantes. espacios
5
Observa la imagen
37 compañeros y faltaron 4
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6
Observa la recta numérica cuyas marcas están a la misma distancia entre sí.
5.099
5.101
5.102
¿Cuál es el número que falta en el rectángulo? A) 5.000 B) 5.098 C) 5.097 D) 5.100
7
¿Qué números siguen en la secuencia?
9 - 11 - 12 - 14 - 15 - ____- ____ A) 16 – 17 B) 17 – 18 C) 18 – 20
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9
Teresa y sus amigos ayudaron a cosechar las manzanas del árbol de su abuelo. La tabla presenta la cantidad de manzanas que cosechó cada uno.
NOMBRE
CANTIDAD DE MANZANAS
María
5 340
Rafael
5 304
Nicolás
5 314
Teresa
5 324
¿Qué niños cosecharon la mayor y menor cantidad de manzanas? A) María
y Nicolás
B) Rafael y Teresa C) Nicolás y Rafael D) María
10
y Rafael
¿En qué opción los números están correctamente ordenados? A) 6 009 < 6 090 > 9 600 B) 4 001 < 2 002 < 6 600 C) 4 810 < 5 180 < 6 801
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12
Observa la secuencia numérica. ¿Cuál es la regla que se aplicó para obtener cada uno de los números?
10.010 – 9.000 – 7.990 – 6.980 – 5.970 A) Se restan 1.000 B) Se restan 1.010 C) Se restan 1.020 D) Se restan 1.030
13
Observa la siguiente tabla, que muestra las montañas más altas de América del Sur.
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14
El número formado por 2 C y 7 UM es : A) 2.700 B) 7.200 C) 7.020 D) 7.002
15
Observa la imagen
Juanita tiene:
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17
Escribe el número que completa la secuencia.
9.990 - 8.990 A) 8.000 B) 7.990 C) 6.990 D) 6.900
18
¿Cuál es el antecesor de: 5.699 más 8? A) 5.668 B) 5.670 C) 5.706
- 6.990
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20
PREGUNTA DE DESARROLLO
Escribe dos números que cumplan con cada condición: A) Tiene 4 dígitos y la suma de todos ellos es 15.
B) Es un número entre 8230 y 8320. El dígito de las unidades es el doble del dígito del dígito de las decenas.
C) Es un número impar de 4 dígitos. El dígito de las centenas es 6 y el de las unidades de mil es la mitad del dígito de las centenas.
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MARZO ADICIÓN Y SUSTRACCIÓN HASTA EL 10.000
1
¿Cuál es el resultado de?
879 + 409 = A) 1.298 B) 1.288
2
C)
470
D)
479
Tengo 6 decenas más que 467. ¿Cuál es el resultado?
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4
¿Qué número debo poner para completar la igualdad? A) 122 B) 222
178 + ______ = 300
C) 278 D) 121
5
¿A qué número le agrego 80 para obtener 1.560? A) 1.640 B) 1.480 C) 1.520 D) 1.570
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8
Una bebida vale $ 340 y un queque vale $80 menos que la bebida. ¿Cuál es el precio de un queque? A) $ 420 B) $ 260 C) $ 340 D) $ 360
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11
Don José pesa 110 kilos y el médico le indicó que debe bajar 38 kilos, deberá cambiar sus hábitos alimenticios y hacer ejercicio tres veces a la semana. Después de hacer este tratamiento. Según el médico, ¿cuántos kilos debiera pesar Don José? A) 38 kilos B) 62 kilos C) 72 kilos D) 88 kilos
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14
El 4º año A necesita comprar dos escobillones y una pala para su curso, hicieron una colecta y reunieron $3.600, después d espués de comprar la pala y los escobillones les quedó $ 1.300. ¿Cuánto dinero gastaron en la compra de ambos productos? A) $ 2.300 B) $ 2.600 C) $ 4.900 D) $ 4.902
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17
La señora Isabel fue a pagar sus cuentas. Al llegar a la casa quiso saber cuánto dinero había gastado. Ayúdale a sacar la cuenta. CUENTA PAGADA Luz Agua Telefonía Total pagado
A) $ 1.334 B) $ 8.149
VALOR PAGADO $ 8.809 $ 4.540 $ 3.609
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20
PREGUNTA DE DESARROLLO Observa la siguiente sustracción
6 4 0 0 -
0 9 5 0 5
1) ¿Qué número representa la
?
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MARZO MULTIPLICACIONES
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3
¿Cuál de las siguientes imágenes representa 5 x 4?
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5
Camila observa los siguientes dibujos. ¿Cuál de ellos representa la expresión 2 x 7?
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7
Tomás tiene el triple de láminas que José. José tiene 15 láminas. ¿Cuántas láminas tiene Tomás?
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10
María Isabel resuelve la siguiente multiplicación multiplicación :
5 x 10 =
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15
¿Cuál es la figura que sigue en la serie?
A) B) C) D)
16
Si en cada fila y columna deben sumar el mismo número, ¿Cuál es el número que completa el cuadrado mágico?
4
11
9 8 A) 1 B) 2 C) 7
6 5
3
10
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17
Si para armar la figura figura 1 con palitos de fósforos usamos 3, 5 para la figura 2 y 7 para la figura 3, ¿Cuántos palitos necesitamos para armar la figura 5?
A) 9 palitos B) 11 palitos C) 15 palitos D) 17 palitos
18
¿Cuál es el número que completa la serie?
1
2
3
5
A) 14 B) 15 C) 21 D) 22
19
¿Cuál es el séptimo número de la serie?
1 A) 45 B) 38 C) 31
1
1
2
2
8
13
?
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20
PREGUNTA DE DESARROLLO En cada fila hay un cilindro que no tiene número. Encuentra el número que falta y señala el patrón de formación.
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MAYO UNIDADES DE TIEMPO
1
Observa la información acerca de la triatlón y luego responde las preguntas 1, 2 y 3 El Triatlón es un deporte individual y de resistencia. Consiste en tres disciplinas deportivas que deben ser realizadas una después de la otra: natación, ciclismo y carrera a pie. Es uno de los deportes más duros que existen en el panorama competitivo internacional actual. Existen varios tipos de triatlón que se diferencian en cuanto a las distancias que hay que recorrer en cada una de las disciplinas. A continuación se entrega información respecto de 3 tipos diferentes de triatlón.
La trayectoria total de las 3 pruebas de natación es:
A) 3 800 m B) 4 000 m C) 6 300 m
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2
¿Cuántos metros más largo es el trayecto realizado en bicicleta que el trayecto realizado a pie para la prueba de triatlón olímpico? A) 8 500 m B) 9 500 m C) 38 500 m D) 30 000 m
3
Javier seleccionó parte de la información conocida para la prueba de media distancia. Realizando una operación aritmética, ha logrado saber que la diferencia entre lo que se recorre caminando y lo que se recorre nadando en dicha prueba es: A) 8 500 m B) 17 500 m C) 18 500 m D) 38 200 m
4
María participó en un triatlón y obtuvo los tiempos se ñalados en la tabla. ¿Cuánto tiempo demoró en toda la prueba?
NATACIÓN CICLISMO CARRERA A PIE A) 4 080 segundos B) 3 600 segundos
8 min.
20 min.
40 min.
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5
Observa los resultados en minutos y segundos de tres atletas en una triatlón:
ATLETA ATLETA
NATAC NATACII N
CICLIS CICLISMO MO
CARRERA CARRERA
A
08: 51
24:22
13:28
B
10:40
22:05
14:05
C
08:12
24:12
13:55
El atleta ganador fue: A) Deportista A B) Deportista B C) Deportista C D) Deportistas A y C
6
Este es el calendario de diciembre: El cumpleaños de María es el 2 de diciembre. Ella debe hacer un viaje exactamente 3 semanas después. ¿Cuándo debe viajar María?
L 3
M 4
M 5
J 6
V 7
S
D
1
2
8
9
10 11 12 13 14 15 16
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7
José tiene 9 años y medio y Loreto 120 meses. ¿Cuál de los dos niños es mayor? A) José B) Loreto C) Tienen la misma edad D) No se puede saber.
8
9
¿Cuál de los siguientes relojes marca más de las 2:10 horas?
Si un reloj se adelanta 5 minutos cada día, ¿Cuántos días deben transcurrir para que lleve 35 minutos adelantados? A)5
B)6
C)7
D)8
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11
El tiempo estimado en ducharte es: A) 5 segundos B) 5 horas C) 15 horas D) 5 minutos
12
Alicia está en el cine viendo una película que dura 2 horas. ¿Qué información se necesita para saber a qué hora la pasan a buscar al cine? A) Qué película está viendo Alicia B) A qué hora empezó la película C) Cuánto tarda en llegar a la la casa D) Cuánto cuesta la entrada al cine.
13
Dos horas puedes demorarte en: A) Peinarte B) Viajar de Santiago a Valparaíso C) Lavarte los dientes D) Recorrer Chile de Norte Norte a Sur.
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15
Patricia miró la hora y su reloj marcaba lo siguiente: 45 minutos después Patricia recibe una llamada. ¿Qué hora marca el reloj cuando Patricia recibe la llamada? A) 12:55 B) 12:30 C) 12:45 D) 12:40
16
Observa el calendario y marca la alternativa correcta LUNES MARTES MIÉRCOLES
JUEVES
VIERNES SÁBADO DOMINGO
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30
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17
Juan Pablo todo los días necesita 10 minutos para ducharse, 15 minutos para desayunar y 15 minutos para llegar a su trabajo. ¿A qué hora debe levantarse Juan Pablo para llegar al trabajo todos los días a las 8:00 de la mañana? A) 7: 20 B) 7: 40 C) 7: 45 D) 7: 50
18
Jorge practica fútbol seis días a la semana. Él practica 3 días, 45 minutos cada uno. Él practica 3 días, 20 minutos cada uno. En horas y minutos, ¿Cuál es el tiempo total que Jorge practica fútbol los 6 días a la semana? A) 2 horas 20 minutos B) 2 horas 55 minutos C) 3 horas 5 minutos D) 3 horas 15 minutos
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20
PREGUNTA DE DESARROLLO Completa: A) El año siguiente al año 1 999 es ………………………………………… B) Si hoy es jueves, mañana será …………………………………………… C) El primer día de la semana es ……………………………………………. D) El mes siguiente de agosto es ……………………………………………. E) El pe núltimo mes del año es ……………………………………………… F) Si hoy es miércoles, en 2 días más será ………………………………… G) Si ayer fue sábado, en 4 días m ás será ………………………………… H) Si hoy es martes, en 7 días más será …………………………………… I) Si hoy es viernes, en 14 14 días más ser á …………………………………. J) Hace 3 días fue sábado, en dos días más será …………………………
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¡DESAFÍA A TU MENTE!
A este relojero se le revolvieron las manecillas de los relojes y las puso al azar.
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JUNIO UNIDADES DE LONGITUD Y PESO
1
En un corral de gansos hay 2 envases que juntos miden 54 centímetros de longitud, uno es más pequeño que el otro. La diferencia entre ambos envases es 6 centímetros. ¿Cuál es la longitud del envase más pequeño?
A) 18 cm. B) 24 cm. C) 30 cm. D) 48 cm.
2
A Esteban se le quebró en dos partes su regla de 30 cm. Si una parte mide 18
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4
Si un kilo de reineta cuesta $3.200. ¿Cuánto costará 500 gramos de reineta? A) $ 800 B) $ 1.200 C) $ 1.600 D) $ 3.000
5
El Volcán Villarrica tiene una altura de 2.847 metros. Esto equivale a: A)
28 kilómetros y 47 metros
B)
2 kilómetros y 847 metros
C) 284 kilómetros y
7 metros
D) 2.000 kilómetros y 847 metros
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7
Rafael, Maite y su profesora son los encargados de organizar una fiesta en la escuela. Para calcular cuánta guirnalda comprar, varios niños midieron e l ancho de la sala de clases, pero anotaron distintos resultados. ¿Cuál resultado podría ser el correcto? A) 50 centímetros B) 5 metros C) 5 centímetros D) 50 milímetros
8
Una caja es 5 veces más larga que alta. Si tiene 30 cm. de alto. ¿Cuánto mide su largo? A)
15 centímetros
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10
El edificio más alto de Chile mide aproximadamente apr oximadamente 200 metros de altura. El más alto del mundo está en Dubai y mide, aproximadamente, 800 metros de altura. ¿Cuánto veces más alto es el edificio de Dubai que el de Chile? A)
3 veces
B)
4 veces
C) 600 veces D) 1.000 veces
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14
Liliana visita a un amigo que vive cerca de su casa, en bicicleta. Una vuelta completa de las ruedas recorre 163 cm. Las ruedas dieron 40 vueltas. ¿Cuál es la distancia a la que vive su amigo? A)
123 cm
B)
203 cm
C)
652 cm
D) 6.520 cm
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17
Rodrigo mide 39 cm. menos que su hermano Fernando. Si Fernando mide 1 metro y 68 centímetros ¿Cuánto mide Rodrigo? A) 39 cm. B) 1m y 29 cm. cm. C) 131 cm. D) 1m y 39 cm
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20
PREGUNTA DE DESARROLLO El paralelepípedo tiene las siguientes medidas: a= 9 cm., b= 4cm. y c= 3cm
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JUNIO FIGURAS EN 3D Y SUS ELEMENTOS
1
Carolina observó un cuerpo geométrico y dibujó sus vistas.
De frente
Desde arriba
De un lado
¿A qué cuerpo geométrico corresponde lo que observo Carolina?
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3
Valentina observa una torta en el almacén. ¿Cuál es la vista que tiene valentina desde la posición en que ella se encuentra observándola?
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4
Observa la imagen
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5
El siguiente dibujo corresponde a la vista desde arriba de: A) Un cono
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8
“Es un poliedro que tiene caras laterales que son triángulos y su base cualquier polígono”.
Esta descripción corresponde a:
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10
Observa la figura:
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19
A Natalia le pidieron 7, 5 metros de cinta para hacer un trabajo manual. Si su mamá tiene 5 metros de cinta ¿Cuántos metros de c inta le falta a Natalia? A) 12, 5 metros B) 3, 5 metros C) 2, 5 metros D) 2
20
metros
PREGUNTA DE DESARROLLO Tomás tiene una autopista que mide 0,7 metros de largo y su hermano tiene una que mide 1,55 metros. Ellos desean unirlas. Si la habitación en la que están jugando mide 2 metros y medio de largo. ¿Podrán unirlas? Justifica tu respuesta
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AGOSTO ECUACIONES E INECUACIONES DE UN PASO
1
¿Qué número falta para completar la igualdad?
64 - ____ = 28 A) 36 B) 44 C) 46 D) 92
2
Observa
3x
x 2 = 54
¿Qué valor debe tener el
para que se cumpla la igualdad?
A) 6 B) 7 C) 8 D) 9
3
Gabriel pensó en un número y lo dividió por 8 y le dio como resultado 2. ¿Qué número pensó Gabriel? A)
4
B)
8
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4
¿En cuál de las siguientes expresiones el número 3 cumple la igualdad? A) 21: _____ = 7 B) 21 x 7 = _____ C) _____ x 21 = 7 D) _____ : 7 = 21
5
Estos números están ordenados
38.989
39.898
39.889
¿Qué signos deben ir en los rectángulos?
6
A)
> , >
B)
< , <
C)
> , <
D)
< , >
¿Qué número podría escribirse en el recuadro para que se cumpla la relación de orden?
2.000 A) 180 B) 200
> 3.500 - 1.700
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7
En la siguiente multiplicación, ¿qué número está tapado?
44 x
= 4.400
A) 10 B) 11 C) 100 D) 101
8
¿Qué número dividido por 4 da como cociente 16? A) 4 B) 8 C) 16 D) 64
9
Enrique tiene 15 años menos que su hermano José. Si José tiene 17 años. ¿Cuántos años tiene Enrique? A) 2 años B) 12 años C) 15 años D) 32 años
10
¿Cuál es el dígito que falta para completar la igualdad? A) 102 B) 118
18 + ___ = 50 + 70
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11
Para que se equilibre la balanza
¿Cuál podría ser el peso de la
?
A) 5 kilos B) 14 kilos C) 15 kilos D) 27 kilos
12
Adivina el número que tiene escondido Carlita. Si mi número lo aumento en 18, resulta A) 35
el número 53. ¿Qué número es?
B) 45 C) 61 D) 71
13
Para aprobar un curso de tejido, Estela debe tejer 250 gorros. Si ya ha tejido 129 gorros. ¿Qué operación permite descubrir cuántos gorros le quedan por tejer? A) 250 - 129 B) 250 + 129
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14
Descubre: si el antecesor del antecesor es 76, el número oculto en la nube es:
A) 74 B) 75 C) 77 D) 78
15
Si a cada figura se le asignan los siguientes valores
Calcula el valor de la siguiente expresión
A)
20
B)
68
C)
590
D) 5.900
¿?
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17 ¿Cuánto vale cada flor? A) 3 B) 5 C) 7 D) 15
18
Matías obtuvo 7,2 puntos al terminar un juego que tenía 3 etapas. Si en la pr imera etapa obtuvo 3,6 puntos y en la segunda etapa obtuvo 1,9 puntos. pu ntos. ¿Cuántos puntos obtuvo en la tercera etapa? A)
1,7 puntos
B)
5,5 puntos
C) 12,7 puntos D) 15,7 puntos
19
¿Qué números deben ir en el
y
para que se cumpla la expresión de
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20
PREGUNTA DE DESARROLLO Observa la imagen
¿Cuántos
equivalen a
= _________
? Justifica tu respuesta
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¡DESAFÍA A TU MENTE!
Divide la figura en 6 partes. La suma de los números de cada parte debe ser la misma
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SEPTIEMBRE MOVIMIENTOS, MOVIMIENTOS, SIMETRÍA, ÁNGULOS, PERÍMETRO Y ÁREA.
1
¿Cuál de las siguientes imágenes nos muestra un ángulo recto?
A)
B)
C)
D)
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3
Observa los siguientes ángulos e indica cuáles de ellos corresponden a ángulos agudos.
A) Ángulos 1 y 7 B) Ángulos 2, 4, 7 C) Ángulos 3 y 6
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5
Observa la imagen.
Esta imagen representa el movimiento de: A) Rotación B) Traslación C) Congruencia D) Reflexión
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7
¿Qué alternativa muestra el movimiento de reflexión?
A)
C)
B)
D)
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9
¿A cuál de las siguientes letras NO se le puede trazar un eje de simetría vertical?
A) Letra M B) Letra X C) Letra E D) Letra Y
10
¿Qué figura tiene más de 1 eje de simetría?
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C) 36 cm. D) 81 cm.
12
En qué figura no está trazado correctamente el eje de simetría.
A)
B)
C)
D)
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14
Calcula el perímetro de esta figura.
A) 16 cm B) 38 cm C) 44 cm D) 73 cm
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16
¿Cuánto mide el área de un cuadrado de 5 unidades de lado?
A) 5 unidades cuadradas B) 10 unidades cuadradas C) 20 unidades cuadradas
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18
Observa la siguiente imagen.
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20
PREGUNTA DE DESARROLLO Observa el modelo y realiza realiza dos dibujos “donde” o “de manera que “ambos tengan la misma superficie del modelo inicial. Indica el área o superficie de cada una de las figuras.
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¡DESAFÍA A TU MENTE!
Completa los números que faltan en cada pirámide. Para subir un peldaño debes sumar los dos
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OCTUBRE TABLAS, PICTOGRAMAS Y GRÁFICOS DE BARRA.
1
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3
Observa el gráfico y responde las preguntas 3 y 4.
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5
De acuerdo al siguiente gráfico, responde las preguntas: 5, 6 y 7
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6
¿Quién tiene el doble de pulseras que Sabrina? A) Florencia B) Carla
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9
¿Qué afirmación es correcta? A) Carla tiene 5 pulseras menos que Florencia
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