แบบฝกทักษะการแกโจทยปญหา

5. 250 ก

1 1. ก

2. ก

ก 220

2 ก q

q 250 - 220 = 30

30 250

q100

3 ก

ก q100 = 30

250 q × 250 = 30 × 100

q = 30 × 100250

= 12 12 %

4 12%

12 × 250100

ก 250 250 - 30 = 220 ( ก

12 %

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

ก ก

ก 220 ก ก

ก

250

1 2 ก1 ก ก0 ก ก

100

250

= 30250

2 ก 2 ก ก ก ก ก ก1 ก ก ก ก ก 0 ก ก ก ก ก

ก

30 × 100 100

250

3 ก2 ก ก ก ก ก1 ก ก ก ก ก 0 ก ก ก

250 = 30 30

ก )

4 2 ก ก ก1 ก ก ก0 ก ก ก

74

โดย เพลินพิศ ปฏิเตนัง

ก ก

ก ก

ก ก ก ก ก

ก ก ก ก ก ก

ก ก ก ก ก

ก ก ก ก ก

ก ก ก ก

ก ก ก ก ก

ก ก ก ก ก

ก ก ก

ก ก ก

ก ก ก

แบบฝกทักษะการแกโจทยปญหา

4. ก

1 1. ก2. ก ก

585 65

2 ก n

ก 585 ก 65

585n = 65

100

3 ก

ก 585n = 65

100 585 × 100 = 65 × n

n = 585 ×65

= 900

4 ก 900 ก

585 × 100900 =

( ก )

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

ก ก

ก 585 65 ก

ก ก ก

65

1 2 ก1 ก ก0 ก ก

n 100

65100

2 ก 2 ก ก ก ก ก ก1 ก ก ก ก ก 0 ก ก ก ก ก

ก

65 × n × 10065

900

3 ก2 ก ก ก ก ก1 ก ก ก ก ก 0 ก ก ก

ก 585 65

900

4 2 ก ก ก1 ก ก ก0 ก ก ก

73

โดย เพลินพิศ ปฏิเตนัง

ก ก

ก

ก ก ก ก ก

ก ก ก ก ก ก

ก ก ก ก ก

ก ก ก ก ก

ก ก ก ก

ก ก ก ก ก

ก ก ก ก ก

ก ก ก

ก ก ก

ก ก ก

แบบฝกทักษะการแกโจทยปญหา

3.

ก

1 1.

2. ก

75%

2 ก p

p ก 75 ก

p

24 = 75

100

3 ก

ก p

24 =

75

100

p × 100 = 75 × 24

p = 75 ×

100

= 18 24 18

4

กก 24 18 × 100

24 = 75 ( ก 24

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

ก ก

75%

24 ก

ก

1 2 ก1 ก ก0 ก ก

ก 24 ก 100

75

100

2 ก 2 ก ก ก ก ก ก1 ก ก ก ก ก 0 ก ก ก ก ก

ก

75 × 24

24

100

18

3 ก2 ก ก ก ก ก1 ก ก ก ก ก 0 ก ก ก

18 ก )

18

4 2 ก ก ก1 ก ก ก0 ก ก ก

72

โดย เพลินพิศ ปฏิเตนัง

ก ก

24

ก ก ก ก ก

ก ก ก ก ก ก

ก ก ก ก ก

ก ก ก ก ก

ก ก ก ก

ก ก ก ก ก

ก ก ก ก ก

ก ก ก

ก ก ก

ก ก ก

แบบฝกทักษะการแกโจทยปญหา

2. ก 2 ก ก

ก

1 1. ก

ก 2. ก ก

ก ก

2 ก ก y

ก y ก ก 7 + 3 = 10

ก 7 ก

7

10 = y

100

3 ก

ก y

100 = 7

10

y × 10 = 7 × 100

y = 7 × 100

10

= 70 ก 70

4 ก 70 ก

ก 70 × 10

100

( ก ) ก 70

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

ก ก

ก ก 7 : 3 ก

ก

ก

ก 2 ก ก 7 : 3

1 2 ก1 ก ก0 ก ก

ก 100

= 10 ก 10

100

2 ก 2 ก ก ก ก ก ก1 ก ก ก ก ก 0 ก ก ก ก ก

ก

100 100

10

3 ก2 ก ก ก ก ก1 ก ก ก ก ก 0 ก ก ก

ก 10

= 7

4 2 ก ก ก1 ก ก ก0 ก ก ก

71

โดย เพลินพิศ ปฏิเตนัง

ก ก

ก

ก ก ก

ก ก

ก ก ก ก ก ก

ก ก ก ก ก

ก ก ก ก ก

ก ก ก ก

ก ก ก ก ก

ก ก ก ก ก

ก ก ก

ก ก ก

ก ก ก

แบบฝกทักษะการแกโจทยปญหา

ก ก ก ก

2 ก ก

1.

80 %

1 1.

2. ก 400 ก

80%

2 ก x

x 400

80 100

x

400 = 80

100

3 ก

ก x

400 = 80

100

x × 100 = 80 × 400 x = 80 × 400

100 = 320

4 ก 320 ก

320 × 100

400 = 80

( ก )

320

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

ก ก ก ก

ก ก ก

ก ก

400 ก

ก

1 2 ก1 ก ก0 ก ก

80

100

2 ก 2 ก ก ก ก ก ก1 ก ก ก ก ก 0 ก ก ก ก ก

ก

400 400

100 320

320

3 ก2 ก ก ก ก ก1 ก ก ก ก ก 0 ก ก ก

ก 400

= 80

4 2 ก ก ก1 ก ก ก0 ก ก ก

70

โดย เพลินพิศ ปฏิเตนัง

ก ก ก ก

ก 2

ก ก

ก

ก ก ก ก ก

ก ก ก ก ก ก

ก ก ก ก ก

ก ก ก ก ก

ก ก ก ก

ก ก ก ก ก

ก ก ก ก ก

ก ก ก

ก ก ก

ก ก ก

แบบฝกทักษะการแกโจทยปญหา

4. 15 % ก

1 1) 2) ก

2 ก ก ก

3 ก

ก 21k

21 × 100 k

4 140 ก

140 ×100

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

% ก

ก

15 % ก 21

ก 21 k 21 : k 21

k 15 100 15 : 100 15

100

ก

= 15100

= 15 × k = 21 × 100

15 = 140

140 140

ก 15% × 15

100 = 21 ( ก ) 140

k

21

100

15 =

69

โดย เพลินพิศ ปฏิเตนัง

ก 21

ก

แบบฝกทักษะการแกโจทยปญหา

3.

1 1) 2) ก

2 ก 250 ก 10 ก

3 ก

ก 250z

250

4 2,500 2,500

100

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

10 % 250 ก กก

กก

10 %

ก z ก 250 : z 250

z ก 100 ก

10 : 100 10100

ก

= 10100

× 100 = 10 × z z = 250 × 100

10 = 2,500 ก

2,500 ก 2,500 ก

500 ก 10% 500 × 10

100 = 250 ก ( ก ) 2,500 ก

z

250

100

10 =

68

โดย เพลินพิศ ปฏิเตนัง

ก กก

250 ก

แบบฝกทักษะการแกโจทยปญหา

2. กก

1 1) 2) ก

2 ก

3 ก ก

3,000

4 15,000

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

กก 20 % 3,000 ก

ก

กก 20%

3,000 y 3,000 : y 3,000

y

20 100 20 : 100 20

100

ก 3,000

y = 20100

3,000 × 100 = 20 × y y = 3,000 × 100

20 = 15,000

15,000 15,000

000 20

15,000 × 20 100 = 3,000 ( ก

15,000

y

3,000

100

20 =

67

โดย เพลินพิศ ปฏิเตนัง

ก

3,000

ก )

แบบฝกทักษะการแกโจทยปญหา

ก ก

1. ก ก ก ก ก

1 1) 2) ก

14 ก 2 ก

ก ก ก ก

3 ก

ก 28 ×

ก ก

4 ก 200 28 × 100

200 ก

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

ก ก 2.3

ก ก (b = %

)

ก ก

ก ก 2 28 ก ก ก

ก ก

ก ก ก

ก ก 2 28 ก x 28 : x 28

x ก ก 2 14 ก 100

14 : 100 14100

ก

28x = 14

100 × 100 = 14 × x

x = 28 × 100

14 = 200

ก 200 ก 200

200 ก ก 2 28 100

200 = 14 ( ก ) ก 200

x

28

100

14 =

ก ก 2

ก

66

โดย เพลินพิศ ปฏิเตนัง

14

ก ก 2 28

100

28

แบบฝกทักษะการแกโจทยปญหา

4. ก ก ก ก ก ก ก 6 : 4 ก ก ก

1 1) 2) ก

ก ก

2 ก ก ก ก 6 + 4 ก ก

3 ก

ก y100

y × 10 y ก ก ก ก

4 ก 10 × 40

100 ก ก

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

ก ก ก ก ก ก ก ก ก ก

ก ก ก

ก ก ก ก กก ก 6 : 4

ก ก y ก 100 y : 100 y

100 4 = 10

ก ก 4 ก 10 4 : 10 4

10

ก

= 410

= 4 × 100 = 4 × 100

10 = 40

ก ก 40 ก ก 40

ก 40 ก 10 40

100 = 4 ( ก ) ก ก 40

100

y

10

4 =

ก

ก

65

โดย เพลินพิศ ปฏิเตนัง

ก ก ก ก ก ก ก ก ก ก

ก ก ก ก ก ก ก ก

แบบฝกทักษะการแกโจทยปญหา

3. ก ก 5 ก

1 1) ก ก ก ก2) ก

2 ก ก ก ก ก 5 ก ก

3 ก ก e

100 e × e ก ก ก ก

4 62.5% ก ก

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

ก 3 ก ก ก ก

ก ก ก ก

ก ก 5 ก 3

ก ก e ก 100 e : 100 e

100 5 + 3 = 8

5 ก 8 5 : 8 5

8

ก = 58

× 8 = 5 × 100 = 5 × 100

8 = 62.5

ก ก 62.5 % ก ก 62.5 %

% ก 8 8 × 62.5

100 = 5 ( กก ก 62.5 %

100

e

8

5 =

ก

ก

64

โดย เพลินพิศ ปฏิเตนัง

ก ก ก ก

ก ก ก ก

ก )

แบบฝกทักษะการแกโจทยปญหา

2. ก 870

1 1) ก2) ก

2 ก

3 ก

ก

p ×

ก ก

4

ก

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

870 ก 1,000 ก

ก

ก 870 ก

p 100 p : 100 p

100

870 1,000 870 : 1,000 870

1,000

ก

p100 = 870

1,000

× 1,000 = 870 × 100

p = 870 × 100

1,000 = 87

ก 87 ก 87

87 1,000

1,000 × 87

100 = 870 ( กก 87

100

p

1,000

870 =

63

โดย เพลินพิศ ปฏิเตนัง

ก

ก ก 1,000

ก )

แบบฝกทักษะการแกโจทยปญหา

ก ก

1. 300 ก ก ก ก ก

1 1) ก ก ก2) ก

2 ก

225

3 ก

ก d × ก ก

4 ก 75 ก 300 ×

100 ก

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

ก ก 2.2

ก ก (c % = )

ก ก

ก ก ก ก 225 ก ก ก กก

ก ก ก

300 ก ก ก ก

d ก ก 100 ก ก

d : 100 d100

ก ก 300 ก ก 225 : 300 225

300

ก

d100 = 225

300 × 300 = 225 × 100

d = 225 × 100

300 = 75

ก 75 % ก 75 %

75% 300 ก ก × 75

100 = 225 ก ก ( กก 75 %

100

d

300

225 =

ก

ก

62

โดย เพลินพิศ ปฏิเตนัง

ก ก ก ก

ก ก ก ก ก ก ก 225 ก ก

ก ก

ก ก

ก )

แบบฝกทักษะการแกโจทยปญหา

ก 360 ก c

b c

360 c × 100 c

4 1,200 360 ×

1,200 180 ×

360 1,200 1,200

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

50% ก b = 360

= 50100

= 50100

× 100 = 50 × 360 = 50 × 360

100 = 180

180 360 + 180 = 540

1,200 - 540 = 660 660

360 × 100

200 = 30 ( ก

180 360 × 100

360 = 50 ( ก ก ก = 660 + (360 + 180) = 1,200

660

61

โดย เพลินพิศ ปฏิเตนัง

ก )

ก )

ก

แบบฝกทักษะการแกโจทยปญหา

4. 1,200 ก ก ก

1 1) ก2) ก

ก 50% ก

2 ก ก ก ก

3 ก ก

ก b1,200

b × 100 b

ก

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

ก 30% ก ก

ก

1,200 ก 30% ก

ก b ก b 1,200

30 100

c c ก b

50 ก 100

ก ก 30%

200 = 30100

= 30 × 1,200 = 30 × 1,200

100 = 360

ก 360

1,200

b

100

30 =

ก

b

c

100

50 =

ก

60

โดย เพลินพิศ ปฏิเตนัง

ก 50%

แบบฝกทักษะการแกโจทยปญหา

3. ก 5

1 1) 2) ก

2 ก ก t

ก 5

3 ก

ก

ก ก

4 ก 60

ก

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

1,200 ก

1,200 ก

ก 5

t 1,200 t : 1,200 t

1,200

100 5 : 100 5

100

ก

t1,200 = 5

100

t × 100 = 5 × 1,200 t = 5 × 1,200

100 = 60

ก 60 ก 60 ก 1,200

60 1,200 60 × 100

1,200 = 5 ( ก

ก 60 ก 1,200

1,200

t

100

5 =

ก

59

โดย เพลินพิศ ปฏิเตนัง

ก

ก )

แบบฝกทักษะการแกโจทยปญหา

2. ก

1 1) ก2) ก 2 ก

ก ก

3 ก

ก ก ก

4 ก 90 × 100

450 ก

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

ก 450 20% ก

ก

ก 450

ก q ก 450 q : 450 q

450 20 ก 100

20 : 100 20100

ก

q450 = 20

100 q × 100 = 20 × 450 q = 20 × 450

100 = 90

ก 90 ก 90

ก 90 ก ก 450 100

450 = 20 ( กก 90

450

q

100

20 =

ก

ก

58

โดย เพลินพิศ ปฏิเตนัง

ก

20%

ก )

แบบฝกทักษะการแกโจทยปญหา

ก ก

1. ก 200 ก

1 1) ก2) ก

ก 2 ก

ก m ก 60

3 ก

ก m × 100 ก ก

4 ก 120 120 ×

200 ก

200

m

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

ก ก 2.1

ก ก (a = c % b)

ก ก

60 กก ก

ก ก ก 200

200 m : 200 m

200 100

60 : 100 60100

ก

m200 = 60

100 m × 100 = 60 × 200 m = 60 × 200

100 = 120 ก 120 ก 120

120 ก ก 200 × 100

200 = 60 ( กก 120

200

m

100

60 =

ก

ก

57

โดย เพลินพิศ ปฏิเตนัง

ก

60

ก )

แบบฝกทักษะการแกโจทยปญหา

เลมที่

..........................................................

ก ก ก

ก ก

ก ก 2.1 ก ก 2.2 ก ก 2.3

ก ก

ก ก ก

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

ึ

เลมที่ 2 การแกโจทยปญหารอยละ

.......................................................... ................... ก

ก ก ก ก ก

ก ก

32 32 32 96

ก ก ก 1 40

56

โดย เพลินพิศ ปฏิเตนัง

ก 2

ก ก ก

แบบฝกทักษะการแกโจทยปญหา

ภาคผนวก

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

ภาคผนวก

55

โดย เพลินพิศ ปฏิเตนัง

แบบฝกทักษะการแกโจทยปญหา

ก ก ก ก . (

.2

ก ก ก . (2554). ( 2). ก . (ก : . (2553). ก : ก

. (2553). ก : ก

ก ก

ก ( .). . (

1. ก ก . (2547).

ก : กก

1 ก

ก : ก

1 ก

( 1). ก ก

.

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

ก

. (2554). ก ก

1. ( 3). ก : ก). 1 ก

ก : ก . . (2546). ก ก ก 2

. ). .2

ก . ). .1

ก . . (2547). ก

ก ก ก 2. ก . (2548). ก ก

ก : ก . ก 2 1. (

ก . ก , . (2554). ก

ก 2 ก ก ก ก

ก . . ก , . (2554). ก

ก 2 ก ก ก ก

ก : ก . . ก. (2547). . 2 . ก

54

โดย เพลินพิศ ปฏิเตนัง

ก ก

ก . ก 2.

2 1.

1.

2.

ก

:

ก ก .2

1).

ก

ก ก ก ก 2551.

ก

ก ก ก ก 2551.

ก :

แบบฝกทักษะการแกโจทยปญหา

5. 250 ก

ก

1

1) (1 .............................................................................................................................

2) ก .............................................................................................................................

2 ก ........................................................ ............................................................................................................................. ................................................................................................................................. .......................................................................................................... ............................................................................................................................. ...................................................... .............................................................................................................................

3 ก ............................................................................................................................. ............................................................................................................................................. ............................................................................................................................. ...................................................................................................... ............................................................................................................................. ..................................................

4 ................................................................................................................... ............................................................................................................................. ............................................................... ............................................................................................................................. .............................................................................................................................

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

ก 220 ก

ก

(2 ) 1 )....................................................................................................

.............................................................................................................................ก (1 )...................................................................................

.............................................................................................................................

(2 ) ....................................................................................................................................................................................................................................................................................

.....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................

ก ก ก .............................................................................................................................

.....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................

(2 ) .....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................

53

โดย เพลินพิศ ปฏิเตนัง

ก

).................................................................................................... ................................................................................................................................................

)................................................................................................ ................................................................................................................................................

............................................................................................... .......................................................................................................................................................

................................................................................................................................................... .............................................

....................................................................................................................................................... .................................................................................................

.......................................................................................................................................................

ก ก (2 ) .......................................................................................................................................................

....................................................................................................................................... .......................................................................................................................................................

................................................. .......................................................................................................................................................

.....................................................................................................

.................................... .......................................................................................................................................................

........................................................................................ ....................................................................................................................................................... .......................................................................................................................................................

แบบฝกทักษะการแกโจทยปญหา

4. ก

ก

1

1) (1 .......................................

2) ก ................................................................................................................................................

2 ก ............................................................................................................................. ...................................................................................................... ............................................................................................................................. .................................................. ............................................................................................................................. ............................................................................................................................. ....................................................................................................

3 ก .................................................................................................................. ............................................................................................................................. .............................................................. ............................................................................................................................. ....................................................................................................................................... ................................................................................................................

4 ............................................................................................................................. ............................................................................................................................. ...................................................................................................... ............................................................................................................................. ..................................................

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

ก 585 65

(2 ) 1 )....................................................................................................

................................................................................................................................................ก (1 )................................................................................................

.......................................................................................................................

(2 ) .........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................

ก ก ก ........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................

....................................................................................................................................................................................................................................................................................

(2 ) .....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................

52

โดย เพลินพิศ ปฏิเตนัง

).................................................................................................... .........................................................................................................

)................................................................................................ .......................................................................................................................

....................................................................................................................................................... .................................................

....................................................................................................................................................... .....................................................................................................

.......................................................................................................................................................

....................................................................................................................................................... ...................................................

ก ก (2 ) .....................................

....................................................................................................................................................... .........................................................................................

....................................................................................................................................................... .............................................................................................................................................

.......................................

.......................................................................................................................................................

....................................................................................................................................................... .................................................

....................................................................................................................................................... .....................................................................................................

แบบฝกทักษะการแกโจทยปญหา

3.

24 ก

1 (2 1) (1

.........................................................................................................................................2) ก

.............................................................................................................................

2 ก .................................................................... ............................................................................................................................. ............................................................................................................................................. ............................................................................................................................. ...................................................................................................... ............................................................................................................................. .............................................................................................................................

3 ก ........................................................................................................................................... .................................................................................................................... ............................................................................................................................. ................................................................ ............................................................................................................................. .........................................................................................................................................

4 ............................................................................. ............................................................................................................................. ..................................................................................................................................................... ............................................................................................................................. .............................................................................................................................

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

75%

ก

2 ) 1 )....................................................................................................

.............................................................................................................................ก (1 )...............................................................................................

.............................................................................................................................

(2 ) ....................................................................................................................................................................................................................................................................................

...........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................

ก ก ก .............................................................................................................................

.......................................................................................................................................................

.............................................................................................................................

.......................................................................................................................................................

..........................................................................................................................................................................................................................................................

(2 ) ....................................................................................................................................................................................................................................................................................

......................................................................................................................................................................................................................................................................................................................................................................................

51

โดย เพลินพิศ ปฏิเตนัง

).................................................................................................... ....................................................................................................................................

)................................................................................................ ................................................................................................................................................

................................................................................... .......................................................................................................................................................

....................................................................................................................................... .......................................................................................................................................................

................................................. ....................................................................................................................................................... .......................................................................................................................................................

ก ก (2 ) .........................................................................................................................................

................................... .......................................................................................................................................................

....................................................................................... .......................................................................................................................................................

...........................................................................................................................................

.......................................................................... .......................................................................................................................................................

............................................................................................................................ ..............................................................................................................................................................................................................................................................................................................

แบบฝกทักษะการแกโจทยปญหา

2. ก 2 ก ก

ก

1

1) (1 .............................................................................................................................

2) ก .............................................................................................................................

2 ก .................................................................................................................................. ........................................................................................................... ............................................................................................................................. ....................................................... ............................................................................................................................. ................................................................................................................................ .........................................................................................................

3 ก ............................................................................................................................. ...................................................................................................... ............................................................................................................................. .................................................. ............................................................................................................................. .............................................................................................................................

4 ............................................................... ............................................................................................................................. ........................................................................................................................................ ................................................................................................................. .............................................................................................................................

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

ก ก 7 : 3

ก

(2 ) 1 )....................................................................................................

.............................................................................................................................ก (1 )................................................................................................

.............................................................................................................................

(2 ) .............................................................................................................................

.......................................................................................................................................................

.............................................................................................................................

.......................................................................................................................................................

..........................................................................................................................................................................................................................................................

.......................................................................................................................................................

ก ก ก ..................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................

(2 ) ....................................................................................................................................................................................................................................................................................

.................................................................................................................................................................................................................................................................................................................................................................................................................

50

โดย เพลินพิศ ปฏิเตนัง

: 3 ก

.................................................. ................................................................................................................................................

................................................................ ................................................................................................................................................

.................................................................................................................................................. ............................................

....................................................................................................................................................... ................................................................................................

....................................................................................................................................................... ....................................................................................................................................................

..............................................

ก ก (2 ) .......................................................................................................................................................

................................................. .......................................................................................................................................................

..................................................................................................... ....................................................................................................................................................... .......................................................................................................................................................

........................................................................................ .......................................................................................................................................................

............................................................................................................................................ ......................................

.......................................................................................................................................................

แบบฝกทักษะการแกโจทยปญหา

1.

80 %

1

1) (1 .............................................................................................................................

2) ก ..................................................................................................................

2 ก

............................................................................................................................. ....................................................................................................................................................... ............................................................................................................................. ............................................................................................................................. ................................................................................ ............................................................................................................................. .............................................................................................................................

3 ก ........................................................................................................................................... .................................................................................................................... ............................................................................................................................. ................................................................ ............................................................................................................................. .............................................................................................................................

4

................................................................. ............................................................................................................................. .......................................................................................................................................... ................................................................................................................... .............................................................................................................................

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

400 ก

(2 ) 1 )....................................................................................................

.............................................................................................................................ก (1 )................................................................................................

..................................................................................................................

ก (2 ) .............................................................................................................................

....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................

ก ก ก .............................................................................................................................

.......................................................................................................................................................

.............................................................................................................................

.......................................................................................................................................................

.............................................................................................................................

.............................................................................................................................

(2 ) ....................................................................................................................................................................................................................................................................................

.................................................................................................................................................................................................................................................................................................................................................................................................................

49

โดย เพลินพิศ ปฏิเตนัง

ก

).................................................................................................... ................................................................................................................................................

)................................................................................................ ................................................................................................................................................

....................................................................................................................................................... .........................................................................................................................

.......................................................................................................................................................

....................................................................................................................................................... .......................................................................

.......................................................................................................................................................

.......................................................................................................................................................

ก ก (2 ) .........................................................................................................................................

................................... .......................................................................................................................................................

....................................................................................... ....................................................................................................................................................... .......................................................................................................................................................

...................................................................................... .......................................................................................................................................................

.......................................................................................................................................... ....................................

.......................................................................................................................................................

แบบฝกทักษะการแกโจทยปญหา

ก ก ก

1. ก 2. 3. ก ก4. ก ก ก ก5. ก

.................................................................

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

ก ก ก

2 ก ก

ก 5 1 4

ก ก ก ก ก ก

ก 2

................................................................. ............. ก

48

โดย เพลินพิศ ปฏิเตนัง

1

ก 2

แบบฝกทักษะการแกโจทยปญหา

............................................................................................................................. ................................................................................................................ ............................................................................................................................. ................................................................................ ............................................................................................................................. ................................................ ............................................................................................................................. ............................................................................................................................................. ............................................................................................................................. .............................................................................................................................

............................................................................................................................. ................................................................................................................ ............................................................................................................................. ............................................................................................................................. ................................................................................................................ ............................................................................................................................. ................................................................................ ............................................................................................................................. ................................................ .............................................................................................................................

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

3 ก

.............................................................................................................................

..............................................................................................................................................

.............................................................................................................................

..............................................................................................................................................

.............................................................................................................................

..............................................................................................................................................

..........................................................................................................................................................................................................................................................

.............................................................................................................................

.............................................................................................................................

4

.............................................................................................................................

..............................................................................................................................................

.............................................................................................................................

.............................................................................................................................

..............................................................................................................................................

.............................................................................................................................

..............................................................................................................................................

.............................................................................................................................

..............................................................................................................................................

.............................................................................................................................

47

โดย เพลินพิศ ปฏิเตนัง

.............................................................................................................................................. ..............................

.............................................................................................................................................. ..............................................................

.............................................................................................................................................. ..............................................................................................

.............................................................................................................................................. ..............................................................................................................................

..............................................................................................................................................

..............................................................................................................................................

.............................................................................................................................................. ..............................

..............................................................................................................................................

.............................................................................................................................................. ..............................

.............................................................................................................................................. ..............................................................

.............................................................................................................................................. ..............................................................................................

..............................................................................................................................................

แบบฝกทักษะการแกโจทยปญหา

21 ก

1) .............2) ก

.....................................................................................................................................

............................................................................................................................. ................................................................................................................ ............................................................................................................................. ................................................................................ ............................................................................................................................. ................................................ ............................................................................................................................. ............................................................................................................................. ................................................................................................................ ............................................................................................................................. ................................................................................ ............................................................................................................................. ............................................... ............................................................................................................................. .............................................................................................................................

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

4

15 % ก ก

1

......................................................................................................... ............................................................................................

.............................................................................................................................

2 ก

.............................................................................................................................

..............................................................................................................................................

.............................................................................................................................

..............................................................................................................................................

.............................................................................................................................

..............................................................................................................................................

.............................................................................................................................

.............................................................................................................................

..............................................................................................................................................

.............................................................................................................................

...................................................................................................................... ........................

.............................................................................................................................

..............................................................................................................................................

.............................................................................................................................

.............................................................................................................................

46

โดย เพลินพิศ ปฏิเตนัง

ก

........................................................................ ...............................................................

................................................................................................................................

.............................................................................................................................................. ..............................

.............................................................................................................................................. ..............................................................

.............................................................................................................................................. ..............................................................................................

..............................................................................................................................................

.............................................................................................................................................. ..............................

.............................................................................................................................................. ........................

.............................................................................................................................................. ...............................................................................................

..............................................................................................................................................

..............................................................................................................................................

แบบฝกทักษะการแกโจทยปญหา

............................................................................................................................. ............................................................................................................................. ................................................................................................................ ............................................................................................................................. ................................................................................ ............................................................................................................................. ................................................ ............................................................................................................................. ............................................................................................................................................. .............................................................................................................................

............................................................................................................................. ................................................................................................................ ............................................................................................................................. ................................................................................ ............................................................................................................................. ................................................ ............................................................................................................................. ............................................................................................................................................. ............................................................................................................................. .............................................................................................................................

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

3 ก

.............................................................................................................................

.............................................................................................................................

..............................................................................................................................................

.............................................................................................................................

..............................................................................................................................................

.............................................................................................................................

..............................................................................................................................................

..........................................................................................................................................................................................................................................................

.............................................................................................................................

4

.............................................................................................................................

..............................................................................................................................................

.............................................................................................................................

..............................................................................................................................................

.............................................................................................................................

..............................................................................................................................................

..........................................................................................................................................................................................................................................................

.............................................................................................................................

.............................................................................................................................

45

โดย เพลินพิศ ปฏิเตนัง

..............................................................................................................................................

.............................................................................................................................................. ..............................

.............................................................................................................................................. ..............................................................

.............................................................................................................................................. ..............................................................................................

.............................................................................................................................................. ..............................................................................................................................

..............................................................................................................................................

.............................................................................................................................................. ..............................

.............................................................................................................................................. ..............................................................

.............................................................................................................................................. ..............................................................................................

.............................................................................................................................................. ..............................................................................................................................

..............................................................................................................................................

..............................................................................................................................................

แบบฝกทักษะการแกโจทยปญหา

1) ...........2) ก

...........................................................................................................................................

............................................................................................................................. ............................................................................................................... ............................................................................................................................. ............................................................................................................................. ............................................................................................................... ............................................................................................................................. ............................................................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................... ............................................................................................................................. ............................................................................. ............................................................................................................................. ........................................... .............................................................................................................................

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

3

10 % 250 ก กก

1

........................................................................................................... ......................................................................................................

.............................................................................................................................

2 ก

.............................................................................................................................

..............................................................................................................................................

.............................................................................................................................

.............................................................................................................................

..............................................................................................................................................

.............................................................................................................................

..............................................................................................................................................

.............................................................................................................................

.............................................................................................................................

..............................................................................................................................................

.............................................................................................................................

..............................................................................................................................................

.............................................................................................................................

..............................................................................................................................................

.............................................................................................................................

44

โดย เพลินพิศ ปฏิเตนัง

ก กก

........................................................................... ...........................................................

................................................................................................................................

.............................................................................................................................................. ...............................

..............................................................................................................................................

.............................................................................................................................................. ...............................

.............................................................................................................................................. .................................................................

..............................................................................................................................................

.............................................................................................................................................. ...............................

.............................................................................................................................................. .................................................................

.............................................................................................................................................. ...................................................................................................

..............................................................................................................................................

แบบฝกทักษะการแกโจทยปญหา

........................................................................................................................................... ........................................ ........................................ ............................................... ........................................................ ................................................................ ........................................................................ ................................................................ .............................................................................................................................

............................................................................................................................................ ........................................ ........................................ ................................................. .......................................................... ..................................................... ............................................................................ .............................................................................................................................

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

3 ก

...........................................................................................................

.................................................................................................................................................................................................................................................

.......................................................................................................................

...........................................................................................................................................

...........................................................................................................................................

...........................................................................................................................................

...........................................................................................................................................

.............................................................................................................................

4

.............................................................................................................

......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................

43

โดย เพลินพิศ ปฏิเตนัง

........................................................................................................... ...................................................................................................

........................................................................................... ..................................................................................

........................................................................... ...............................................

........................................................... ...........................................................................

...........................................................................................................................................

............................................................................................................. ...........................

........................................................................................... .........................................................

......................................................................... ................................................................

....................................................... ............................................................................................................................................

แบบฝกทักษะการแกโจทยปญหา

กก

1) ...............................2) ก

..........................................

........................................................................................................................................... .......................................... .......................................... ................................................. ........................................................ ............................................................. ...................................................................... ............................................................................. .................................................................................... ...........................................................................................

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

2

กก 20 % 3,000 ก

1

........................................................................................................... ........................................................................................................

...............................................................................................................

2 ก

.........................................................................................................

...........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................

.................................................................................................................................................................................................................................................

.................................................................................................................................

42

โดย เพลินพิศ ปฏิเตนัง

ก

.......................................................... ...........................................................

....................................................................................................

......................................................................................................... .........................

......................................................................................... ...................................................

........................................................................... ....................................................................

............................................................. ......................................................

............................................... ........................................

แบบฝกทักษะการแกโจทยปญหา

ก ก .................................................................................................................

............................................................................................................................. ..................................................................................................................... ............................................................................................................................. ............................................................................................. ............................................................................................................................. ..................................................................... ............................................................................................................................. ............................................. ............................................................................................................................. ........................................................................................................................

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

3 ก

....................... = .............................. ....................... = .............................. ....................... = .............................. = ..............................

ก ............................ .................................................................................................................

4

.............................................................................................................................

..........................................................................................................................................

.............................................................................................................................

..........................................................................................................................................

.............................................................................................................................

..........................................................................................................................................

.............................................................................................................................

..........................................................................................................................................

........................................................................................................................................................................................................................................

41

โดย เพลินพิศ ปฏิเตนัง

.................................................................................................................

......................................................................................................................................... .....................

.......................................................................................................................................... .............................................

.......................................................................................................................................... .....................................................................

.......................................................................................................................................... .............................................................................................

.......................................................................................................................................... ...........................................................................................................

แบบฝกทักษะการแกโจทยปญหา

..............................................................

ก ก

ก ก

ก ก ก

1) .......2) ก

..............................................................................................................................................

ก ก ก ก

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

แบบฝกทักษะ 2.3 ก ก (b =

%)

.............................................................. ............ ก

ก ก

1

ก ก 2 28 ก ก ก

1

............................................................................................................ ........................................................................................................

...........................................................................................................................

2 ก

ก ก 2 ............ ก .............. ....................... ............................

ก ก 2 ................ ก .................. ........................ .....................

=

.............................................

...........................................

40

โดย เพลินพิศ ปฏิเตนัง

ก 2

14

................................................................................ .............................................................................

...........................................................................................................................

.............. ............................

.................. ...........................

แบบฝกทักษะการแกโจทยปญหา

ก

68, 68,750 × 8

100

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

3 ก

5,500m = 8

100 5,500 × 100 = 8 × m m = 5,500 × 100

8 = 68,750

68,750 68,750

4

,750 8% = 5,500 ( ก )

68,750

39

โดย เพลินพิศ ปฏิเตนัง

แบบฝกทักษะการแกโจทยปญหา

1) 2) ก

ก 8

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

ตัวอยางท่ี 2

8% 5,500

1

8% 5,500

2 ก

5,500 m 5,500 : m 5,500

m8 100

8 : 100 8100

m

5,500

100

8 =

38

โดย เพลินพิศ ปฏิเตนัง

5,500

500

แบบฝกทักษะการแกโจทยปญหา

ก

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

3 ก

36,000y = 20

100

36,000 × 100 = 20 × y y = 36,000 × 100

20 = 180,000

180,000 180,000

4

180,000 36,000

36,000 × 100180,000 = 20 ( ก

180,000

37

โดย เพลินพิศ ปฏิเตนัง

ก )

แบบฝกทักษะการแกโจทยปญหา

1) 2) ก 20 %

ก

20

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

บัตรตัวอยาง 2.3

ก ก (b = %

)

ตัวอยางท่ี 1

36,000 20 %

1

36,000

2 ก

36,000 y 36,000 : y 36,000

y 100

20 : 100 20100

y

36,000

100

20 =

36

โดย เพลินพิศ ปฏิเตนัง

000

000

แบบฝกทักษะการแกโจทยปญหา

............................................................. ..................................................................... ............................................................................. ..................................................................................... ................................................................................... ..................................................................................................... ..................................................... ..................................................................................................................... .............................................................................................................................. .............................................................................................................................

..................................................... ............................................................... ......................................................................... ....................................... ............................................................................................. ....................................................................................................... ................................................................................................................ .........................................................................................................................

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

3 ก

.............................................................................................................................................

.............................................................................................................................................

.............................................................................................................................................

.............................................................................................................................................

.............................................................................................................................................

.............................................................................................................................................

.............................................................................................................................................

......................................................................................................................................................................................................................................

.............................................................................................................................

4

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

...............................................................................................................................................

.....................................................................................................................................................................................................................................................................

.........................................................................................................................

.........................................................................................................................

35

โดย เพลินพิศ ปฏิเตนัง

........................................................................ ................................................................

............................ ................................................

........................................ ................................

........................

......................... .......................................................................................................................

..............................................................................................................................................

................................................................................ ......................................................................

............................................................ ..................................................

......................................... ...............................

............................ ...............................................................................................................................................

แบบฝกทักษะการแกโจทยปญหา

ก ก ก ก ก ก

ก 6 : 4 ก ก ก

1) .................

.............................................................................................................................................2) ก

..............................................

............................................................................................................................. ......................................................................................................................... ............................................................................................................................. ........................................................................................................... ............................................................................................................................. ............................................................................................. ............................................................................................................................. ............................................................................... ............................................................................................................................. .......................................... ............................................................................................................................. ............................................................................................................................. .........................................................................................................................

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

4

ก ก ก ก ก กก ก ก

1

..........................................................................................................................................................................................................................

.................................................................................................................................................................................................................

2 ก

.............................................................................................................................

.........................................................................................................................

.............................................................................................................................

.....................................................................................................................................

.............................................................................................................................

.....................................................................................................................................

.............................................................................................................................

.....................................................................................................................................

.............................................................................................................................

.......................................... ...........................................................................................

.............................................................................................................................

.............................................................................................................................

.........................................................................................................................

34

โดย เพลินพิศ ปฏิเตนัง

ก ก ก ก ก ก ก ก ก

................................................................... ................................................................................................................

............................................................. ..............................................................................................

.....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... ..........................

..................................................................................................................................... ........................................

..................................................................................................................................... ......................................................

..................................................................................................................................... .....................................................................

.....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

แบบฝกทักษะการแกโจทยปญหา

ก ก ก ...............................................................................................................

............................................................................................................................. ...................................................................................................................... ............................................................................................................................. .............................................................................................. ............................................................................................................................. ...................................................................... ............................................................................................................................. .............................................. ............................................................................................................................. ........................................................................................................................

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

3 ก

.......................... = ............................

.......................... = ............................ .......................... = ............................ = ............................

ก ก .............................. ...............................................................................................................

4

.............................................................................................................................

..........................................................................................................................................

.............................................................................................................................

..........................................................................................................................................

.............................................................................................................................

..........................................................................................................................................

.............................................................................................................................

..........................................................................................................................................

.....................................................................................................................................................................................................................................................

33

โดย เพลินพิศ ปฏิเตนัง

............................

............................

............................

............................

...............................................................................................................

........................................................................................................................................ ....................

.......................................................................................................................................... ............................................

.......................................................................................................................................... ....................................................................

.......................................................................................................................................... ............................................................................................

.......................................................................................................................................... ........................................................................................................................

แบบฝกทักษะการแกโจทยปญหา

ก ก 5

ก

1) .............

...........................................2) ก

...........................................

ก ก ก ก ............................................... ก ก ....................

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

3

5 ก 3 ก ก ก

1

......................................................................................................................................................................................................................

...............................................................................................................................................................................................................

2 ก

ก ก ................ ก ............... .......................... ............................

............................................... .................... ก ....................... .......................... ............................

=

ก

ก

32

โดย เพลินพิศ ปฏิเตนัง

ก ก ก

...................................................................... ................................................................................................

.................................................................. ...............................................................................................

แบบฝกทักษะการแกโจทยปญหา

.............................................................................................................................

.......................................................................................................................... ............................................................................................................................. .......................................................................................................... ............................................................................................................................. ............................................................................................ ............................................................................................................................. ............................................................................ .............................................................................................................................

.......................................................................................................................................................................................................................................................

............................................................................................................................. ............................................................................................................................. ......................................................................................................................... ............................................................................................................................. .......................................................................................................... .............................................................................................................................

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

3 ก

.............................................................................................................................

..........................................................................................................................

.............................................................................................................................

....................................................................................................................................

.............................................................................................................................

.....................................................................................................................................

.............................................................................................................................

....................................................................................................................................

.............................................................................................................................

4

.............................................................................................................................

..........................................................................................................................

.............................................................................................................................

.............................................................................................................................

.........................................................................................................................

.............................................................................................................................

.....................................................................................................................................

.............................................................................................................................

31

โดย เพลินพิศ ปฏิเตนัง

....................................................................................................................................

.....................................................................................................................................

..................................................................................................................................... ..........................

.................................................................................................................................... .........................................

..................................................................................................................................... ........................................................

....................................................................................................................................

....................................................................................................................................

.....................................................................................................................................

.....................................................................................................................................

....................................................................................................................................

....................................................................................................................................

..................................................................................................................................... ...........................

....................................................................................................................................

แบบฝกทักษะการแกโจทยปญหา

ก

ก

1) ...............

............................................................................................................................2) ก

.................................................

............................................................................................................................. ........................................................................................................................ ............................................................................................................................. ............ ............................................................................................ ............................................................................................................................. ......................................................................................... .............................................................................................................................

............................ ...............................................

............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ......................................................................................................................... ............................................................................................................................. .......................................................................................................... .............................................................................................................................

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

2

ก 870 ก 1,000 ก

1

...........................................................................................................................................................................................................

......................................................................................................................................................................................................................

2 ก

.............................................................................................................................

........................................................................................................................

.....................................................................................................................................................................................................................................................

.............................................................................................................................

.....................................................................................................................................

.....................................................................................................................................................................................................................................

.............................................................................................................................

.............................................................................................................................

.............................................................................................................................

.........................................................................................................................

.............................................................................................................................

.....................................................................................................................................

.............................................................................................................................

30

โดย เพลินพิศ ปฏิเตนัง

.................................................................. ..................................................................................................................

......................................................................... ..............................................................................................

.....................................................................................................................................

.....................................................................................................................................

.................................................................................................................................... ............................

..................................................................................................................................... ............................................

.................................................................................................................................... .........................................................

.....................................................................................................................................

.....................................................................................................................................

....................................................................................................................................

....................................................................................................................................

..................................................................................................................................... ...........................

....................................................................................................................................

แบบฝกทักษะการแกโจทยปญหา

ก ก ...................................................................................................................

............................................................................................................................. .................................................................................................................... ............................................................................................................................. ............................................................................................ ............................................................................................................................. .................................................................... ............................................................................................................................. ....................................

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

3 ก

.......................... = ............................ .......................... = ............................ .......................... = ............................ = ............................

ก.....................................................................................................................................................................

4

.............................................................................................................................

..........................................................................................................................................

.............................................................................................................................

..........................................................................................................................................

.............................................................................................................................

..........................................................................................................................................

.....................................................................................................................................................................................................................................................

29

โดย เพลินพิศ ปฏิเตนัง

............................

............................

............................

............................ ...........................................

...................................................................................................................

.......................................................................................................................................... ......................

.......................................................................................................................................... ..............................................

.......................................................................................................................................... ......................................................................

.......................................................................................................................................... ....................................................................................

แบบฝกทักษะการแกโจทยปญหา

..........................

ก ก

300 ก ก ก ก ก ก

1)

...........................................................................................................................................2) ก

............................................................................................................................................

...................

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

แบบฝกทักษะ 2.2 ก ก (c % = )

............................................................... ............. ก

ก ก

1

ก ก ก ก 225 ก ก กก ก

1

.....................................................................................................................................................................................................................................

............................................................................................................................................................................................................

2 ก

..................ก ก ............... .......................... ............................

...................ก ก ................ก ก .......................... ............................

=

.

28

โดย เพลินพิศ ปฏิเตนัง

ก 2

ก ก ก

.............................................................. ...........................................................................................................................

.............................................................. .................................................................................................................

...............ก ก ............................

ก ก ............................

แบบฝกทักษะการแกโจทยปญหา

ก

1, 1,800 × 72.22

100

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

3 ก

h100 = 1,300

1,800

h × 1,800 = 1,300 × 100 h = 1,300 × 100

1,800

= 72.22 72.22 % 72.22 %

4

,800 ก 72.22% 22 = 1,300 ( ก )

72.22 %

27

โดย เพลินพิศ ปฏิเตนัง

แบบฝกทักษะการแกโจทยปญหา

1,800 ก

ก

1) 2) ก ก 1,300

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

ตัวอยางท่ี 3

ก 1,300

1

ก 1,800

2 ก

h 100

h : 100 h100

1,300 1,800 1,300 : 1,800 1,300

1,800

100

h

1,800

1,300 =

26

โดย เพลินพิศ ปฏิเตนัง

300800

แบบฝกทักษะการแกโจทยปญหา

ก

5 5 × 60

100

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

3 ก

z100 = 35

z × 5 = 3 × 100 z = 3 × 100

5 = 60

60 % 60 %

4

5 60% ก = 3 ( ก )

60 %

25

โดย เพลินพิศ ปฏิเตนัง

แบบฝกทักษะการแกโจทยปญหา

1) 2) ก

ก 2 + 3

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

ตัวอยางท่ี 2

2 : 3 ก

1

ก

2 ก

z 100 z : 100 z

100 + 3 = 5 5

3 : 5 35

100

z

5

3 =

24

โดย เพลินพิศ ปฏิเตนัง

ก

2 : 3

แบบฝกทักษะการแกโจทยปญหา

ก 36

6% ก 600

100 36

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

3 ก

m

100 = 36600

m × 600 = 36 × 100 m = 36 × 100

600 = 6

6 % ก 36 6 % ก

4

ก 600 600 × 6

100 = 36 ( ก ) 6 % ก

23

โดย เพลินพิศ ปฏิเตนัง

แบบฝกทักษะการแกโจทยปญหา

36 ก

1) 2) ก

ก 36 ก

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

บัตรตัวอยาง 2.2

ก ก (c % = )

ตัวอยางท่ี 1

ก 600 ก ก

1

ก ก 36 ก 600

2 ก

m ก 100 m : 100 m

100 ก 600

36 : 600 36600

100

m =

600

36

22

โดย เพลินพิศ ปฏิเตนัง

ก ก

ก ก 600

แบบฝกทักษะการแกโจทยปญหา

1. ก ............................................................................................................................. .......................................................................................................................................... ............................................................................................................................. ............................................................................................................................. ............................................................................................................. ............................................................................................................................. .............................................................................................................................

2. ............................................................................................................................. ................................................................................................................... ............................................................................................................................. ......................................................................................... ............................................................................................................................. ............................................................... ......................................................................................................................... ...........................................................................................................................

............................................................................................................................. .................................................................................................................... ............................................................................................................................. ............................................................................................ ............................................................................................................................. ............................................................................................................................. ...........................................................................................................

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

3 ก

ก 30% .............................................................................................................................

....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................

50% ก .....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................

......................................................................................................................... ................................................................................................

...........................................................................................................................

4

.............................................................................................................................

..........................................................................................................................................

.............................................................................................................................

..........................................................................................................................................

.............................................................................................................................

.............................................................................................................................................................................................................................................................

21

โดย เพลินพิศ ปฏิเตนัง

.......................................................................................................................................... ......................................................................................................................

..........................................................................................................................................

.......................................................................................................................................... .............................

..........................................................................................................................................

..........................................................................................................................................

.......................................................................................................................................... .......................

.......................................................................................................................................... .................................................

.......................................................................................................................................... ...........................................................................

......................................................................................................................... ....................................................................

...........................................................................................................................

.......................................................................................................................................... ......................

.......................................................................................................................................... ..............................................

..........................................................................................................................................

.......................................................................................................................................... .....................

แบบฝกทักษะการแกโจทยปญหา

1,200 ก ก

1) 2) ก

...

ก ............................................................................................................................. ............................................................................................................................. ................................................................................................................... ............................................................................................................................. ......................................................................................... ............................................................................................................................. ............................................................................................................................. .............. ............................................................................................................................. ...................................................................................... ............................................................................................................................. ............................................................ ............................................................................................................................. .......................................................................................................................................... .............................................................................................................................

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

4

ก 30% ก ก ก

1

... . .

...

2 ก

ก ................ .....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................

.................... .............. ก................

.............................................................................................................................

..........................................................................................................................................

.............................................................................................................................

..........................................................................................................................................

.....................................................................................................................................................................................................................................

.............................................................................................................................

20

โดย เพลินพิศ ปฏิเตนัง

ก 50%

... . .

...

..........................................................................................................................................

.......................................................................................................................................... .......................

.......................................................................................................................................... .................................................

..........................................................................................................................................

..........................................................................................................................................

..........................................................................................................................................

.................................................... ..........................................................................................................................................

.............................................................................. ..........................................................................................................................................

........................................................................................................ ..........................................................................................................................................

แบบฝกทักษะการแกโจทยปญหา

.............................................. ............................................................................................................................. ............................................................................................................................. ............................................................................................................................. ................................................................................................................... ............................................................................................................................. ......................................................................................... ............................................................................................................................. ............................................................... ............................................................................................................................. ..................................... ............................................................................................................................. ........................................................................................................................................ .............................................................................................................................

............................................................................................................................. ............................................................................................................................. ................................................................................................................... ............................................................................................................................. ......................................................................................... ............................................................................................................................. ............................................................... .............................................................................................................................

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

3 ก

...................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................

..........................................................................................................................................................................................................................................................

4

.............................................................................................................................

.............................................................................................................................

..........................................................................................................................................

.............................................................................................................................

..........................................................................................................................................

.............................................................................................................................

..........................................................................................................................................

.............................................................................................................................

19

โดย เพลินพิศ ปฏิเตนัง

............................................................................ .......................................................................................................................................... .......................................................................................................................................... ..........................................................................................................................................

....................... ..........................................................................................................................................

................................................. ..........................................................................................................................................

........................................................................... ..........................................................................................................................................

..................................................................................................... ..........................................................................................................................................

............................................................................................................................... ..........................................................................................................................................

..........................................................................................................................................

.......................................................................................................................................... .......................

.......................................................................................................................................... .................................................

.......................................................................................................................................... ...........................................................................

..........................................................................................................................................

แบบฝกทักษะการแกโจทยปญหา

ก 5

1) ...................................................... 2) ก

............................................................................................................................. ............................................................................................................................. ................................................................................................................... ............................................................................................................................. ......................................................................................... ............................................................................................................................. ............................................................... ............................................................................................................................. ..................................... ............................................................................................................................. ........................................................................................................................................ ............................................................................................................................. .............................................................................................................................

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

3

1,200 ก

1

..................................................................................................................... ...............................................................................................................

2 ก

.............................................................................................................................

.............................................................................................................................

..........................................................................................................................................

.............................................................................................................................

..........................................................................................................................................

.............................................................................................................................

..........................................................................................................................................

.............................................................................................................................

..........................................................................................................................................

..........................................................................................................................................................................................................................................................

.............................................................................................................................

.............................................................................................................................

18

โดย เพลินพิศ ปฏิเตนัง

ก

.................................... ...................................................................

..........................................................................................................................................

.......................................................................................................................................... .......................

.......................................................................................................................................... .................................................

.......................................................................................................................................... ...........................................................................

.......................................................................................................................................... .....................................................................................................

.......................................................................................................................................... ...............................................................................................................................

..........................................................................................................................................

..........................................................................................................................................

แบบฝกทักษะการแกโจทยปญหา

............................................................................................................................. ................................................................................................................... ............................................................................................................................. ......................................................................................... ............................................................................................................................. ............................................................... ............................................................................................................................. ..................................... ............................................................................................................................. ........................................................................................................................................ .............................................................................................................................

............................................................................................................................. ............................................................................................................................. .................................................................................................................... ............................................................................................................................. ............................................................................................................................. .................................................................................................................... ............................................................................................................................. ............................................................................................ .............................................................................................................................

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

3 ก

.........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................

..........................................................................................................................................................................................................................................................

4

.............................................................................................................................

.............................................................................................................................

..........................................................................................................................................

.............................................................................................................................

.............................................................................................................................

..........................................................................................................................................

.............................................................................................................................

..........................................................................................................................................

.............................................................................................................................

17

โดย เพลินพิศ ปฏิเตนัง

.................................................................................................................................... .......................

.......................................................................................................................................... .................................................

.......................................................................................................................................... ...........................................................................

.......................................................................................................................................... .....................................................................................................

.......................................................................................................................................... ...............................................................................................................................

..........................................................................................................................................

..........................................................................................................................................

.......................................................................................................................................... ......................

..........................................................................................................................................

.......................................................................................................................................... ......................

.......................................................................................................................................... ..............................................

..........................................................................................................................................

แบบฝกทักษะการแกโจทยปญหา

ก

1) ....................................... 2) ก

.................................................................................................................................................

............................................................................................................................. ............................................................................................................................. ................................................................................................................... ............................................................................................................................. ......................................................................................... ............................................................................................................................. ............................................................................................................................. ................................................................................................................... ............................................................................................................................. ......................................................................................... .............................................................................................................................

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

2

ก 450 20% ก

1

.................................................................................................................... ..............................................................................................................

.............................................................................................................................

2 ก

.............................................................................................................................

.............................................................................................................................

..........................................................................................................................................

.............................................................................................................................

..........................................................................................................................................

.............................................................................................................................

.............................................................................................................................

..........................................................................................................................................

.............................................................................................................................

..........................................................................................................................................

.............................................................................................................................

16

โดย เพลินพิศ ปฏิเตนัง

ก

........................................... ..............................................................................

...................................................................................................................................

..........................................................................................................................................

.......................................................................................................................................... .......................

.......................................................................................................................................... .................................................

..........................................................................................................................................

.......................................................................................................................................... .......................

.......................................................................................................................................... .................................................

..........................................................................................................................................

แบบฝกทักษะการแกโจทยปญหา

ก ก ....................................................................................................................

............................................................................................................................. .................................................................................................................... ............................................................................................................................. ............................................................................................ ............................................................................................................................. .................................................................... ............................................................................................................................. ............................................ ............................................................................................................................. ก

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

3 ก

............................ = ............................ ............................ = ............................ ............................ = ............................ = ............................

ก ............................ ....................................................................................................................

4

.............................................................................................................................

..........................................................................................................................................

.............................................................................................................................

..........................................................................................................................................

.............................................................................................................................

..........................................................................................................................................

.............................................................................................................................

..........................................................................................................................................

......................................................................................................................................................

15

โดย เพลินพิศ ปฏิเตนัง

............................

............................

............................

............................

....................................................................................................................

.......................................................................................................................................... ......................

.......................................................................................................................................... ..............................................

.......................................................................................................................................... ......................................................................

.......................................................................................................................................... ..............................................................................................

..........................................................................................................................................

แบบฝกทักษะการแกโจทยปญหา

..........................................................

ก ก

ก 200 ก

1) ................................ 2) ก

.................................................................................................................................................

ก ........................ ก .........................

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

แบบฝกทักษะ 2.1 ก ก (a = c % b)

.......................................................... ................... ก

ก ก

1

60 กก ก

1

..................................................................................................................... ........................................................................................

.............................................................................................................................

2 ก

........................ ....................... ........................... ................................

......................... ....................... ........................... ................................

=

...............................................

................................................

14

โดย เพลินพิศ ปฏิเตนัง

ก 2

ก

.......................................................... .....................................

...................................................................................................................................

....................... ................................

................................

แบบฝกทักษะการแกโจทยปญหา

ก

p × 100

ก

q × 100

35,000

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

3 ก

15%

p35,000 = 15

100

p × 100 = 15 × 35,000

p = 15 × 35,000

100 = 5,250

5,250 2%

5,250 p = 5,250 q

p = 2100

q5,250 = 2

100

× 100 = 2 × 5,250 q = 2 × 5,250

100 = 105

105 5,250 + 105 = 5,355

35,000 - 5,355 = 29,645 29,645

4

000 5,250 5,250 × 100

35,000 = 15 ( ก

105 5,250 105 × 100

5,250 = 2 ( ก

5,250 + 105 = 5,355 29,645 5,355 + 29,645 = 35,000

29,645

13

โดย เพลินพิศ ปฏิเตนัง

5,250

355 645

ก )

ก )

645

แบบฝกทักษะการแกโจทยปญหา

15%

1) 2) ก

2%

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

ตัวอยางท่ี 3

% 2% 35,000 ก

1

ก 15%

35,000

2 ก

p p 35,000

15 100

q q

2 100

35,000

p

100

15 =

p

q

100

2 =

12

โดย เพลินพิศ ปฏิเตนัง

ก

000

p 100

แบบฝกทักษะการแกโจทยปญหา

1) ก

ก

2) ก

ก

ก ก

ก ก

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

3 ก

ก ก y

250 = 74100

y × 100 = 74 × 250 y = 74 × 250

100 = 185 ก ก

ก 185 ก ก ก

ก z250 = 26

100 z × 100 = 26 × 250

z = 26 × 250

100

= 65 ก ก

ก 65 ก ก ก 250 ก ก

ก 185 ก ก ก 65 ก ก

4

ก 250 ก ก ก 185 ก ก

185 × 100

250 = 74 ( ก )ก 250 ก ก ก 65 ก ก

65 × 100

250 = 26 ( ก

ก 250 ก ก ก 185 ก ก ก 65 ก ก

11

โดย เพลินพิศ ปฏิเตนัง

ก ก

ก ก

ก ก

)

ก )

ก ก

แบบฝกทักษะการแกโจทยปญหา

ก ก 74 ก ก กก ก

1) ก กก ก 2) ก

ก ก ก

ก ก ก

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

ตัวอยางท่ี 2

74 % ก 26 % ก ก ก กก ก

1

ก 250 ก ก กก กก ก

ก ก 74 % ก 26

2 ก

ก y ก ก ก y ก ก 250 ก ก

74 ก ก 100 ก ก

ก z ก ก ก z ก ก 250 ก ก

26 ก ก 100 ก ก

250

y

100

74 =

ก ก

ก

150

z

100

26 =

ก ก

ก

10

โดย เพลินพิศ ปฏิเตนัง

ก 250 ก ก

ก ก ก

26 %

แบบฝกทักษะการแกโจทยปญหา

ก

120 × 100

150

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

3 ก

x

150 = 80100

x × 100 = 80 × 150

x = 80 × 150

100 = 120

120 150 120

4

150 120

= 80 ( ก ) 120

9

โดย เพลินพิศ ปฏิเตนัง

แบบฝกทักษะการแกโจทยปญหา

80

1) 2) ก

ก

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

บัตรตัวอยาง 2.1

ก ก (a = c % b)

ตัวอยางท่ี 1

80 150 ก

1

150 ก 80

2 ก

x ก 150 x : 150 x

150 80 ก 100 80 : 100 80

100

150

x

100

80 =

8

โดย เพลินพิศ ปฏิเตนัง

ก

100

แบบฝกทักษะการแกโจทยปญหา

การแกโจทยปญหารอยละ

ก ก ก ก ก ก ก

1 1) 2) ก

2 ก1) ก ก2) ก3)

ก

3 ก ก ก ก 4

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

การแกโจทยปญหารอยละ

ก ก ก ก ก ก ก 4

ก

ก ก ก

ก

ก ก ก ก

( ก ก )

( ก ก )

7

โดย เพลินพิศ ปฏิเตนัง

ก ก ก

แบบฝกทักษะการแกโจทยปญหา

ก 3

ก = ก

b = ×

a c% c

8 25% 8

ึ

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

a b ก

× 100 b = %

a c c 100 a ก

25 100 8 25 % a

=

b = × b = 32

ึ ...

6

โดย เพลินพิศ ปฏิเตนัง

ก

8 ก

แบบฝกทักษะการแกโจทยปญหา

ก ก ก

ก 1

ก = ก

a = × b

c % b ก c

25 % 60 ก a

ก 2

ก = ก

c = × 100

a ก a

9 ก 9 c %

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

ใบความรูที่ 2

ก ก ก 3 ก

a b ก

b a = c % b

ก c b ก 100 ก b

ก 25 100 ก 60

=

a = × a = 15

a b ก

100 c % =

b a b a b ก 100

ก 45 9 45 ก c % 45

=

c = × c = 20

5

โดย เพลินพิศ ปฏิเตนัง

100

ก

ก

ก 60

ก

ก 100

แบบฝกทักษะการแกโจทยปญหา

ก ก

1 2 ก 1 ก ก 0 ก ก

2 ก 2 ก ก ก ก ก 1 ก ก ก ก ก 0 ก ก ก ก ก

3 ก 2 ก ก ก ก ก 1 ก ก ก 0 ก ก ก

4 2 ก ก ก 1 ก ก ก 0 ก ก

เกณฑการใหคะแนน

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

ก ก ก ก ก

2 ก ก

2 ก

ก ก ก ก

ก 2

ก ก ก ก ก กก ก ก ก ก

ก ก ก ก ก

ก 2

ก ก ก ก กก ก ก กก ก ก ก

2

ก ก กก ก กก ก ก

เกณฑการใหคะแนน

4

โดย เพลินพิศ ปฏิเตนัง

ก ก ก

ก ก ก ก ก ก

ก ก ก ก ก ก

ก ก ก ก ก ก

ก

แบบฝกทักษะการแกโจทยปญหา

1. 2. ก

ก / ก ก1. ก2. ก ก3. ก

ก 1. ก2. ก3. ก

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

ก

ก

ก ก ก ก ก ก

ก ก กก ก

ก ก

ก

3

โดย เพลินพิศ ปฏิเตนัง

ก ก ก ก

แบบฝกทักษะการแกโจทยปญหา

1 ก ก

1.1 ก ก ก .2/4 ก ก ก ก

6 ก ก ก

6.1 ก ก ก ก .1-3/1 ก ก ก .1-3/2 ก ก .1-3/3 ก ก .1-3/4 ก ก ก ก ก .1-3/5 กก ก ก ก .1-3/6

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

ก

ก ก

ก ก กก ก ก ก

ก ก ก

ก ก ก ก ก ก

ก

ก ก ก ก ก ก ก

ก ก ก ก

ก ก ก ก ก

กก ก กก

2

โดย เพลินพิศ ปฏิเตนัง

ก ก ก ก ก ก ก

ก ก ก ก ก

ก

ก ก ก ก

ก ก ก ก ก

กก ก ก

แบบฝกทักษะการแกโจทยปญหา

1. ก กก ก 1

2. ก ก ก ก

3. ก ก 4.

ก ก 5.

6. ก ก ก

ก ก 7. ก ก ก

ก ก8. ก ก ก ก ก

ก9. ก ก ก

การแกโจทยปญหาคณิตศาสตร โดย เพลินพิศ ปฏิเตนัง

ก ก 2 ก ก ก ก

3 ก ก ก ก

ก ก

ก ก

ก ก ก 70

ก ก ก ก ก

ก ก ก ก ก ก ก กก

ก ก ก

1

โดย เพลินพิศ ปฏิเตนัง

ก ก

ก ก ก ก

ก

70

ก ก ก

ก ก ก