Matemáticas 5 PRIMARIA Cuaderno tercer Cuaderno tercer trimestre Unidad ..................... página202 unidad 11 1 ···························· página Unidad ..................... página unidad 12 2 ···························· página 1010 Unidad ..................... página unidad 13 3 ···························· página 1818 unidad 14 4 ···························· página 2626 Unidad ..................... página unidad 15 5 ···························· página 3432 Unidad ..................... página
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11
Longitud
Múltiplos del metro 1 Completa.
8 km 5 8.000 m
•
•
21 km 5 21.000 m
•
•
2,5 km 5 2.500 m
•
•
•
•
•
•
0,8 km 5
•
2
800
700 m 15 hm 5 1.500 m 9,3 hm 5 930 m 3,45 hm 5 345 m 7 hm 5
•
m
Expresa en metros. •
•
•
km
hm
dam
m
•
•
•
3
60 m 13 dam 5 130 m 2,9 dam 5 29 m 2,75 dam 5 27,5 m 6 dam 5
5.025 m 9,2 km y 8 m 5 9.208 m 12 hm y 8 m 5 1.208 m 0,95 hm y 43 m 5 138 m 35 dam y 5 m 5 355 m 2,9 dam y 0,8 m 5 29,8 m 5 km y 25 m 5
Expresa en la unidad indicada. En dam
12 m 5
•
321 m 5
•
4,5 m 5
•
0,9 m 5
•
1,2 dam 32,1 dam 0,45 dam 0,09 dam
En hm
16 dam 5
•
8 dam 5
•
85 m 5
•
•
9m5
1,6 hm 0,8 hm 0,85 hm 0,09 hm
4 Resuelve. •
La luz recorre 300.000 km en un segundo. ¿Cuántos kilómetros recorrerá la luz en una hora?
300.000 3 60 3 60 5 1.080.000.000 SOLUCIÓN
Recorrerá 1.080.000.000 km.
En km
7 hm 5
•
24 hm 5
•
185 m 5
•
97 m 5
•
0,7 km 2,4 km 0,185 km 0,097 km
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Submúltiplos del metro 1 Completa.
24 dm 5
•
123 dm 5
•
12,3 dm 5
•
3,1 dm 5
•
2
2,4 m 12,3 m 1,23 m 0,31 m
0,15 m 6 cm 5 0,06 m 10,5 cm 5 0,105 m 4,6 cm 5 0,046 m 15 cm 5
14 mm 5 0,014 m
•
•
•
•
•
•
•
•
7 mm 5 0,007 m
31,3 mm 5 0,0313 m 9,4 mm 5 0,0094 m
Expresa en metros. •
•
•
m
dm
cm
mm
•
•
0,33 m 32 cm y 78 mm 5 0,398 m 23,1 cm y 24 mm 5 0,255 m 0,95 dm y 43 mm 5 0,138 m 12,4 cm y 49,8 mm 5 0,1738 m 2 dm y 13 cm 5
3 Resuelve.
La yarda es una unidad inglesa de medida de longitud que equivale a 91,4 cm. ¿Cuántos metros son 200 yardas?
El grosor de una carta de una baraja es de 0,5 mm. ¿Qué grosor, en centímetros, tiene una baraja de 40 cartas?
91,4 3 200 5 18.280 18.280 : 100 5 182,80
SOLUCIÓN 4
0,5 3 40 5 20 20 : 10 5 2
Son 182,80 m.
SOLUCIÓN
Su grosor es 2 cm.
RAZONAMIENTO. ¿Cuánto mide Álvaro? Observa el dibujo y calcula.
m c 5 3
m c 5 7 y m
m c 5
2,35 2 1,75 5 0,6
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Relaciones entre las unidades de longitud 1
Completa el esquema.
100
1.000
3
km
3
dam
hm
: 100
2
dm
m
: 1.000
Expresa en la unidad indicada. En dam
3
mm
cm
En m
35,5 dam
•
3,4 hm y 15 m
•
21,8 km y 230 dm
•
27,8 m y 95 cm
2.182,3 dam
2,875 dam
•
0,5 hm y 3,2 dm
50,32 m
•
7,4 dm y 35 cm
1,09 m
•
32,5 cm y 12 mm
0,337 m
Utiliza el cuadro y expresa cada medida en la unidad que se indica. RECUERDA
El trazo rojo indica la unidad dada, el trazo verde indica la unidad a la que pasamos . km
9,65 hm en m
hm
dam
m
9
6
5
3
2
9
0
3.290 cm
1
2
9
1,29 m
4
3
32,9 m en cm 12,9 dm en m 54,3 m en hm
0
5
dm
cm
mm
965 m
0,543 hm
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11 5
Observa el ancho de cada objeto y calcula.
FRIGORÍFICO LAVADORA
LAVAVAJILLAS
MUEBLE
60 cm
45 cm
1 m y 35 cm
¿Se puede poner el lavavajillas y el mueble, uno al lado del otro, en un espacio de 1,50 m?
¿Se puede poner el mueble y el frigorífico, uno al lado del otro, en un espacio de 2 m?
0,45 1 1,35 5 1,80 1,80 > 1,50
SOLUCIÓN
1,35 1 0,80 5 2,15 2,15 > 2
No se puede.
SOLUCIÓN
¿Qué espacio, como mínimo, se necesita para colocar la lavadora, el mueble y el lavavajillas, uno a continuación del otro?
0,60 1 0,45 1 1,35 5 2,40
SOLUCIÓN
Se necesitan 2,40 m.
25
33,75
No se puede.
Marta coloca el frigorífico, el mueble y la lavadora en un espacio de 3 m de largo. ¿Cuántos centímetros le sobran?
0,80 1 1,35 1 0,60 5 2,75 3 2 2,75 5 0,25
SOLUCIÓN
En un almacén hay colocados 25 muebles y 10 lavadoras, uno a continuación del otro. ¿Qué longitud en metros ocupan?
1,35
80 cm
Le sobran 25 cm.
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Estimaciones 1
2
Escribe la unidad de medida que usarías para medir estas longitudes. longitudes.
metros
•
La altura de una torre.
•
El largo de un folio.
•
El grosor de una moneda.
•
La distancia entre dos ciudades.
•
La altura de un bebé.
•
El largo de un autobús.
centímetros milímetros kilómetros
centímetros metros
Escribe dos objetos cuya cuya longitud expresarías con cada unidad. unidad. R. L. Metro
Centímetro
Kilómetro
3 Resuelve. •
Para empapelar una habitación, habitación, Antonio tiene tiene 6 rollos. Después de empapelarla, le sobra un rollo y 6,5 m de otro. ¿Cuántos metros de papel utilizó si cada rollo tiene 35 m?
4 3 35 1 35 2 6,5 5 168,5 SOLUCIÓN •
Utilizó 168,5 m.
El coche de Marcos gasta 6,5 litros de gasolina cada 100 kilómetros. ¿Cuántos litros de gasolina gastará en un trayecto de 1.200 kilómetros?
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11
Problemas 1
Lee y resuelve.
Las embarcaciones están clasificadas por categorías, dependiendo de la distancia a la que pueden alejarse de la costa. En la tabla aparecen las distintas categorías y la distancia a la que pueden alejarse. Cate Catego gorí ría a de de la la emb embar arca caci ción ón
Mill Millas as desd desdee la la cos costa ta
1.ª categoría
Sin límite
2.ª categoría
60 millas
3.ª categoría
25 millas
4.ª categoría
12 millas
5.ª categoría
5 millas
6.ª categoría
2 millas
¿A cuántos kilómetros de la costa puede alejarse una embarcación de 2.ª categoría, si una milla marina es igual a 1.852 m?
1 milla marina ▼
1.852 m
¿A cuántos kilómetros de la costa puede alejarse una embarcación de 2.ª categoría más que una embarcación de 3.ª categoría?
1.852 : 1.000 5 1,852 60 3 1,852 5 111,12 SOLUCIÓN
A 111,12 km.
Una embarcación de 4.ª categoría se encuentra a 9,26 km de la costa. ¿A cuántas millas marinas está?
60 2 25 5 35 35 3 1,852 5 64,820 SOLUCIÓN
A 64,82 km.
Una embarcación está a 74,08 km de la costa. ¿De qué categoría puede ser esta embarcación?
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Aplica y repasa Aplica lo aprendido 1
Observa el cuentakilómetros de un coche y calcula. •
¿Cuántos kilómetros lleva recorridos este este coche?
12.678 km.
•
¿A cuántos kilómetros por hora circula este coche?
A 100 km por hora.
•
En este coche se ha revisado el motor cada 5.000 km. ¿Cuántas revisiones del motor lleva hechas?
12.678 : 5.000
SOLUCIÓN •
c 5 2; r 5 2.678
Lleva 2 revisiones.
•
¿Cuántos kilómetros le quedan hasta la próxima revisión del motor?
5.000 2 2.678 5 2.322
SOLUCIÓN
Le quedan 2.322 km.
Un coche recorre 95 kilómetros en una hora. ¿Cuántas horas tardará en recorrer un trayecto de 760 km, si siempre lleva la misma velocidad?
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11
Repasa lo anterior 1 Escribe. En forma de número decimal •
•
•
2
12 5 1,2 10 34 5 0,34 100 36 5 0,036 1.000
•
•
•
2 5 0,2 10 143 5 1,43 100 9 5 0,009 1.000
58 10 189 1,89 5 100
•
5,8 5
•
0,345 5
•
Completa la tabla. Número decimal
Lectura
3,019
3 unidades y 19 milésimas
0,456
456 milésimas 1 unidad y 65 décimas
1,650 1,650
12,09 234,8
3
En forma de fracción decimal
12 unidades y 9 centésimas 234 unidades y 8 décimas
Escribe qué número representa cada cada punto de color. color. 5
5,5
6
345
1.000
234 10 6 0,06 5 100 8.453 8,453 5 1.000 23,4 5
•
•
•
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12
Capacidad y masa
Relaciones entre unidades de capacidad 1
Completa el esquema.
100
1.000
3
kl
3
hl
dal
: 100
2
cl
ml
: 1.000
Expresa en litros.
2.000 ¬ 8 hl 5 800 ¬ 1,2 dal 5 12 ¬ 4,5 kl 5 4.500 ¬ 2 kl 5
3
dl
¬
12 dl 5
•
•
•
•
•
•
•
•
26 cl 5 39 ml 5
123 ml 5
1,2 ¬ 0,26 ¬ 0,039 ¬ 0,123 ¬
0,3 kl 5
•
4,6 hl 5
•
9,8 cl 5
•
Expresa en la unidad indicada. •
En litros
•
•
En decalitros
•
•
•
12.035 ¬ 6,5 hl y 19 ¬ 5 669 ¬ 26,9 dal y 24 ¬ 5 293 ¬ 12 kl y 35 ¬ 5
2,64 dal 4,5 hl y 92 cl 5 45,092 dal 2,9 kl y 123 ml 5 290,0123 dal 25 ℓ y 14 dl 5
12,7 ml 5
•
300 ¬ 460 ¬ 0,098 ¬ 0,0127 ¬
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5
Utiliza el cuadro y expresa cada medida en la unidad que se indica. kl
12,7 dal en ¬ 5,9 hl en ¬
hl
da l
¬
1
2
7
5
9
0
3,4 kl en dal
3
4
0
15,7 kl en cl
15
7
0
dl
cl
127
340 dal 0
0
0
Natalia compra un bote bote de colonia de 1 ¬ . Al llegar a casa, llena con él dos frascos de 150 ml cada uno. ¿Qué cantidad de colonia le queda en el bote?
2 3 150 5 300 1.000 2 300 5 700 SOLUCIÓN •
Le quedan 700 ml.
Un depósito contiene 1,2 hl de zumo. Primero, se llenan 50 botellas de 1 litro y con el resto de zumo, se llenan botellas de 250 cl cada una. ¿Cuántas botellas se han llenado en total?
(12.000 2 5.000) : 250 5 28 SOLUCIÓN •
¬
590 ¬
6 Resuelve. •
ml
Se han llenado 28 botellas.
Un camión cisterna lleva 3,5 kl de gasoil. En En la primera gasolinera descarga 12 hl y 90 ¬ y y en la segunda descarga el resto. ¿Cuántos litros de gasoil descarga en la segunda gasolinera?
1.570.000 cl
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Relaciones entre unidades de masa 1
Completa el esquema.
100
1.000
3
kg
hg
dag
3
g
: 100
2
Expresa en gramos. •
•
•
•
•
•
3
2.830 g 5,9 hg y 38 g 5 628 g 8,4 dag y 7 g 5 91 g 75 dg y 6 g 5 13,5 g 123 cg y 4 g 5 5,23 g 267 mg y 72 g 5 72,267 g 2,6 kg y 230 g 5
Expresa en kilos y averigua averigua qué paquete pesa pesa más.
dg
: 1.000
cg
mg
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12 5
¿Cuánto cuesta un kilo de cada producto? Observa el dibujo y calcula.
CEBOLLAS
500 g 0,65 €
250 g
MANTEQUILLA
1,50 €
1.000 : 500 5 2 0,65 3 2 5 1,30 €. 1.000 : 250 5 4 1,50 3 4 5 6 €.
125 g 1,25 €
CHOCOLATE
1.000 : 125 5 8 1,25 3 8 5 10 €.
6 Resuelve. •
La carga máxima que puede transportar un camión es de 14 toneladas. En una obra ha cargado 125 sacos de cemento de 50 kg cada uno y 9 vigas de 230 kg cada una. ¿Cuántos kilos más se pueden cargar en el camión?
125 3 50 5 6.250 9 3 230 5 2.070
6.250 1 2.070 5 8.320 14.000 2 8.320 5 5.680
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Cuadro con unidades de capacidad y masa 1
Utiliza el cuadro y expresa cada medida en la unidad que se indica. kl
21,8 dal en ¬
hl
dal
¬
2
1
8
5,93 ¬ en cl
0
7,4 dl en dal 84,9 cl en ¬ kg
cl
ml
218 ¬
5
9
3
593 cl
0
7
4
0,074 dal
0
8
4
9
cg
mg
0,849 ¬
hg
dag
g
dg
0
8
0
0
8,9 dag en cg
8
9
0
0
8.900 cg
35,6 dg en dag
0
3
5
6
0,356 dag
0
9
3
0,8 hg en dg
93,2 cg en g
2
dl
800 dg
2
Utiliza el cuadro de unidades y calcula cuántos gramos pesan en en total.
0,932 g
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12
Problemas 1
Lee y resuelve.
Clase
Peso (en gramos)
A
De 125 a 200
B
De 201 a 250
Antes de empaquetar las manzanas, Juan las clasifica según el tamaño que aparece en la tabla.
•
¿Cuántos kilos pesan, como mínimo, 10 manzanas de clase A?
•
¿Cuántos kilos pesan, como máximo, 8 manzanas de clase B?
0,125 3 10 5 1,25
SOLUCIÓN •
0,25 3 8 5 2
Pesan 1,25 kg.
Carmela compra un kilo de manzanas
SOLUCIÓN •
Pesan 2 kg.
Nerea compra una caja de 2,4 kg con
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Aplica y repasa Aplica lo aprendido 1
Observa la lista de precios y calcula el importe impor te total de cada pedido.
1 kg 1,80 €
1 kg 0,98 € HARINA
ARROZ
SAL
PEDIDO 1
1 kg de arroz 1 kg de sal ite 3 ¬ de ace te 1 ¬ d
inagre
1,80 0,58 8,97 1 04
1 ¬ 2,99 €
1 kg ▶ 0,29 € 2
1 ¬ ▶ 0,26 € ▶ 4
V I N A G R E
1 ¬ 0,75 €
HAZ AQUÍ LAS OPERACIONES
ZUMO
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12
Repasa lo anterior 1 Calcula. •
3 de 658 7
282
2
Completa la tabla.
•
5 de 288 8
180
•
4 de 405 9
180
•
2 de 143 11
26
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13
Área de figuras planas
Área con un cuadrado unidad 1
Cuenta y escribe cuál es es el área de cada figura.
Área 5 63
y 10
Área 5 48
y
20
Área 5 39
y 24
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Unidades de superficie 1 Completa.
2
•
5 m2 5 5 3 100 5 500 dm2
•
10 00 7 m2 5 7 3 1
5
•
10 00 9 m2 5 9 3 1
5
•
10 00 11 m2 5 11 3 1
700 dm2 900 dm2 1.100 dm2
5
•
3 dm2 5 3 3 100 5 300 cm2
•
6 dm2 5 6 3 100
5
•
8 dm2 5 8 3 100
5
15 dm2 5 15 3 100
•
Expresa en la unidad indicada.
402 dm2 2,5 m2 y 6 dm2 5 256 dm2 0,25 m2 y 1,9 dm2 5 26,9 dm2
•
En dm2
•
•
4 m2 y 2 dm2 5
5
600 cm2 800 cm2 1.500 cm2
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Área del cuadrado, el rectángulo y el triángulo 1
Calcula el perímetro y el área de cada figura.
3 cm 12 cm 9 cm
24 cm 27 cm2
48 cm 144 cm2
Perímetro 5
Perímetro 5
Área 5
Área 5
7 cm
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13 4
Observa la medida del lado del del cuadrado grande y calcula. •
El área del cuadrado gris.
6 3 6 5 36
A 5 36 cm2 •
El área del rectángulo amarillo. 12 3 6 5 72
A 5 72 cm2 •
El área del triángulo rojo. rojo.
(6 3 6) : 2 5 18
A 5 18 cm2 12 cm
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Área de figuras compuestas 1
Observa las medidas y calcula el área de cada figura. 8 cm 4 cm
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13
Problemas 1 Resuelve. •
Miguel compra un terreno de 120 m de largo y 40 m de ancho por 216.000 €. ¿Cuánto ha pagado por cada metro cuadrado?
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Aplica y repasa Aplica lo aprendido 1
Lee y resuelve.
Se va a repoblar de pinos un terreno rectangular de 1 km
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13
Repasa lo anterior 1
Escribe la fracción que representan las bolas de cada color. color.
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14
El tiempo y el dinero
El reloj 1
Dibuja las manecillas de cada reloj.
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