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แผนการจัดกิจกรรมการเรียนรู้ที4 แผนการจัดกิจกรรมการเรียนรู้โดยเน้นการคิดแบบฮิวริสติกส์ หน่วยการเรียนรู้ที1 สมการเชิงเส้นตัวแปรเดียว เรื่องย่อย การแก้สมการเชิงเส้นตัวแปรเดียว แผนบูรณาการภายในกลุ่มสาระการเรียนรู้คณิตศาสตร์ เรื่องการแก้สมการเชิงเส้นตัวแปรเดียว และสมบัติของจานวนเต็ม
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คู่มือการใช้นวัตกรรม แผน4

Jul 23, 2015

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  • 4

    1

  • 143

    1.

    2.

    3.

    4.

    3 1 6 5

    1 (1 ) 2 (2 )

    3 (1 )

    4 (2 )

    5 (2 ) 6 (1 ) 7 (1 )

    8 (1 )

    9 (2 )

    10 (2 )

    ( TGT)

    ( Jigsaw II)

    3 .. 57 7 .. 57

    10 .. 57

    13 .. 57 14 .. 57 17 .. 57 21 .. 57 24 .. 57

    28 .. 57

    1 .. 57

    2 .. 57 8 .. 57

    9 .. 57

    15

    10 3 13

  • 144

    4 ()

    1 1 2 13 .. 57 14 ..57 --------------------------------------------------------------------------------------------------------------------- 1 1.2 1.4 4

    4.2 1.2 .1/1 1.4 .1/1

    4.2 1/2

    (Equation)

    =

  • 145

    1. 2. 3. 4.

    1.

    2. 3.

    / 1.

    2.

    1. 2. 3. 4.

    1. 1.1 - 1.2

    1.3 1.4 1.5

    2. 2.1 2.2 2.3 2.4 2.5

  • 146

    - -

    - - 0

    - = +

    - -

    -

  • 147

    - a b a + b = b + a

    - a b a b = b a - a , b c (a + b) + c = a + (b + c)

    - a , b c (a b) c = a (b c) - a , b c a (b + c) = (a b) + (a c)

    (Equation) =

    1. 2 2

    1. x = 3 3 = x 2. -3 + x = 1 1 = -3 + x 3. 2 p = -11 -11 = 2 p 4. s = t + 1 t + 1 = s 5. a + b = c c = a + b

    b=a a=b a b

  • 148

    2. 2

    1. 2 = x x = y 2 = y y = 2 2. = 2 2 = 64 = 64 3. c=b+a 6=c 6=b+a 4. r=qp 1+s2=r 1+s2=qp 5. y=x z=y z=x

    1. 2

    1. x = -5 x - 3 = -5 - 3 2. 4=22 ( ) 3+4=3+22 3. 5y + 4 = 7 (5y + 4) + (-4) = -7 + (-4) 4. q=p p + (-r) = q + (-r)

    b=a c=b c=a a , b c

    b=a c+b=c+a a , b c

    b=a a c = b - c a, b c

  • 149

    2

    1. 4

    1x3 4

    4

    143x)(

    2. 422 ( ) 34=322 3. yx y2x2

    4. nm n4

    1m

    4

    1

    n4

    1m

    4

    1

    5. zy

    x 0y yzx

    k

    1 k 0k

    k

    1 x 5 = 12 x 5 = 12 5 x 5 + 5 = 12 + 5 x = 17 x 17 x 5 = 12 17 5 = 12 17 x 5 = 12 17

    b=a cb=ca a , b c

    ba c

    b

    c

    a b,a c 0c

  • 150

    2 5

    7

    5

    1y

    5

    7

    5

    1y

    5

    1

    5

    1

    5

    7

    5

    1

    5

    1y

    5

    6y

    5

    17y

    y 5

    6

    5

    7

    5

    1y

    5

    7

    5

    1

    5

    6

    5

    7

    5

    7

    5

    6

    5

    7

    5

    1y

    5

    6

  • 151

    3 7x3

    1

    7x3

    1

    3

    73x3

    13

    21x

    x 21 7x3

    1

    7213

    1

    77

    21 7x3

    1

    21 4 12y4 12y4

    41

    4

    12

    4

    y4

    3y y 3 12y4 1234 1212

    3 12y4 3

  • 152

    5 532

    x

    532

    x

    3

    35332

    x

    82

    x

    2

    822

    x2

    16x

    x 16 532

    x

    532

    16

    538 55

    16 532

    x

    16 6 287x3 287x3 7 72877x3 21x3 3

    3

    21

    3

    x3

    7x

  • 153

    x 7 287x3 28773 28721

    2828 7 287x3

    7

    7 4

    3

    2

    1x3

    4

    3

    2

    1x3

    2

    1

    2

    1

    4

    3

    2

    1

    2

    1x3

    4

    1x3

    4

    23x3

    3

    34

    1

    3

    x3

    12

    1x

    3

    1

    4

    1x

    x 12

    1

    4

    3

    2

    1x3

    4

    3

    2

    1

    12

    13

    4

    3

    2

    1

    4

    1

  • 154

    4

    3

    4

    21

    4

    3

    4

    3

    12

    1

    4

    3

    2

    1x3

    12

    1

    7

    ... ...

    8 7 4

    3

    2

    1x3

    4

    3

    2

    1x3

    ... 2 4 4 ...

    4

    34

    2

    1x34

    32x12

    32

    14)x3(4

    2 2322x12 1x12 12

    12

    1

    12

    x12

    12

    1x

    12

    1

  • 155

    7 8

    () 1. (Relate)

    1.1

    - () - () -

    ( )

    - 2 2. (Investigate)

    2.1 4 2

    2.2 2

    2.3 1 2 2.4 2

    2.5 3 4 2.6

    2.7 5 , 6 7

    2.8 8 7

    7

  • 156

    2.9 4 1 3. (Evaluate and Communicate)

    3.1

    3.2 3.3

    - 4. (Create)

    4.1

    4.2 4-6

    1.

    2. 4 2 www.pookpikschool.wordpress.com www.pookpikschool.com

    - - 4

    - 4

    - www.pookpikschool.wordpress.com

    www.pookpikschool.com

  • 157

    1. 1.1 1.2

    - 4 - 4

    1.3 - - - -

    1.4 - -

    2. 2.1 2.2

    - 4 - 4

    2.3 - - - -

    2.4 - -

    3. 3.1

    90-100 4 80-89 3 70-79 2 70 1

  • 158

    3.2 80 4 70-79 3 60-69 2 60 1

    3.3

    3 2 1 0

    3.4

    3 2 1 0

    13 - 15 09 - 12 01 - 80 0

    - 4 2

    - -

    - www.pookpikschool.wordpress.com

    www.pookpikschool.com

  • 159

    -

    - /

    -

  • 160

  • 161

    70% 10%

    60% 50%

    50%

    www.pookpikschool.wordpress.com www.pookpikschool.com

    ................................................................ ............ ( )

  • 162

    4

    1. 4

    2. 4

    3. 4. 5. 6.

  • 163

    4

    1. 2 2

    1. x = 3 3 = x 2. -3 + x = 1 1 = -3 + x 3. 2 p = -11 -11 = 2 p 4. s = t + 1 t + 1 = s 5. a + b = c c = a + b

    2. 2

    1. 2 = x x = y 2 = y y = 2 2. = 2 2 = 64 = 64 3. c=b+a 6=c 6=b+a 4. r=qp 1+s2=r 1+s2=qp 5. y=x z=y z=x

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

    ba ab a b

    ba cb ca a , b c

  • 164

    1) x22

    1 x2 ...............

    2) qp 4q 4.............. 3) b1a2 ............b 4) t4s 7t 4s ................

    5) y

    8x 0y

    y

    8..............

    6) 1ab2 ............... ab2 7) 11xy 11z xy ............... 8) q5p q ..............

    9) n3m5

    2 .................. m

    5

    2

    10) yx2

    1 12y

    x2

    1 ................

    3. 2

    1. x = -5 x - 3 = -5 - 3 2. 4=22 ( ) 3+4=3+22 3. 5y + 4 = 7 (5y + 4) + (-4) = -7 + (-4) 4. q=p p + (-r) = q + (-r)

    ba cbca b,a c

    ba cbca b,a c

  • 165

    4. 2

    1. 4

    1x3 4

    4

    143x)(

    2. 422 ( ) 34=322 3. yx y2x2

    4. nm n4

    1m

    4

    1

    n

    4

    1m

    4

    1

    5. zy

    x 0y yzx

    k

    1 k 0k

    k

    1 125x 125x 5 51255x 17x x 17 125x 12517 17 125x 17

    ba cbca b,a c

    ba c

    b

    c

    a a ,b c 0c

  • 166

    2 5

    7

    5

    1y

    5

    7

    5

    1y

    5

    1

    5

    1

    5

    7

    5

    1

    5

    1y

    5

    6y

    5

    17y

    y 5

    6

    5

    7

    5

    1y

    5

    7

    5

    1

    5

    6

    5

    7

    5

    7

    5

    6

    5

    7

    5

    1y

    5

    6

    3 7x3

    1

    7x3

    1

    3

    73x3

    13

    21x

    x 21 7x3

    1

  • 167

    7213

    1

    77

    21 7x3

    1

    21 4 12y4 12y4

    41

    4

    12

    4

    y4

    3y y 3 12y4 1234 1212

    3 12y4 3

    5 532

    x

    532

    x

    3

    35332

    x

    82

    x

    2

    822

    x2

    16x

  • 168

    x 16 532

    x

    532

    16

    538 55

    16 532

    x

    16 6 287x3 287x3 7 72877x3 21x3 3

    3

    21

    3

    x3

    7x x 7 287x3 ( ) 28=7+73 28721

    2828 7 287x3

    7

    7 4

    3

    2

    1x3

    4

    3

    2

    1x3

    2

    1

    2

    1

    4

    3

    2

    1

    2

    1x3

  • 169

    4

    1x3

    4

    23x3

    3

    34

    1

    3

    x3

    12

    1x

    3

    1

    4

    1x

    x 12

    1

    4

    3

    2

    1x3

    4

    3

    2

    1

    12

    13

    4

    3

    2

    1

    4

    1

    4

    3

    4

    21

    4

    3

    4

    3

    12

    1

    4

    3

    2

    1x3

    12

    1

    7 ... ...

  • 170

    8 7 4

    3

    2

    1x3

    4

    3

    2

    1x3

    ... 2 4 4 ...

    4

    34

    2

    1x34

    32x12

    32

    14)x3(4

    2 2322x12 1x12 12

    12

    1

    12

    x12

    12

    1x

    12

    1

    7 8

  • 171

    4

    1.

    (1) nm ............... n3m (2) 15a7 a ...............

    (3) 45r 3

    r ...............

    (4) 63

    7p

    7p ................

    (5) 25x .............. 30 (6) 195y15 .............. 39 (7) y2x 9x ................

    (8) 3

    qp p3 .................

    (9) 6x

    8.1 0x x6 ..................

    (10) 52

    yx

    .................... 2)5(

    2. (1) 43x 43x 3 ........................ x x .............. .............................. ........................

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

    ..

  • 172

    (2) 2y5 2y5

    5 .......... ........................ y y .............. .............................. ........................

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

    ..

    (3) 112

    r

    112

    r

    ......... .......... ........................ r r .............. .............................. ........................

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

    ..

    (4) 7

    15p5

    7

    15p5

    ......... .......... ........................ p p .............. .............................. ........................

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

    ..

  • 173

    (5) x312 x312 .......... .............. ........................ x x .............. .............................. ........................

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

    ..

    (6) 1z3

    1

    1z3

    1

    .......... .............. ........................ z z .............. .............................. ........................

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

    ..

    (7) 54

    9

    2

    a

    54

    9

    2

    a

    .......... .............. ........................ a a .............. .............................. ........................

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

    ..

  • 174

    4 13-14 . . .. 2557

    -

    4 4 4 12

    1 4 4 3 11 2 4 3 4 11 3 3 3 4 10 4 4 4 3 11 5 3 4 3 10 6 4 3 3 10 7 4 3 3 10 8 4 4 3 11 9 4 3 4 11 10 3 4 3 10 11 3 3 4 10 12 3 3 3 9 13 2 3 3 8 14 3 3 3 9 15 3 2 2 8 16 3 3 3 9 17 4 4 4 12 18 4 3 3 10

  • 175

    -

    4 4 4 12

    19 3 2 4 9 20 2 3 3 8 21 3 3 3 9 22 3 3 3 9 23 3 4 3 10 24 4 3 3 10 25 4 3 3 10 26 3 4 3 10 27 4 4 3 11 28 4 2 3 9 29 3 4 2 9 30 3 3 2 8 31 4 3 3 10

    70 8 () ............................................... ( )

  • 176

    (Rubrics) 1

    4 3 2 1 1. 1.1

    1. 2.

    1. 2.

    1. 2.

    1. 2.

    1.2

    1. 2.

    1. 2.

    1. 2.

    1. 2.

    1.3

  • 177

    4 13-14 . . .. 2557

    -

    4

    4

    10 10 20

    1 8 9 17 2 9 9 18 3 9 9 18 4 9 9 18 5 9 9 18 6 8 8 18 7 8 8 16 8 9 8 17 9 8 8 16 10 9 7 16 11 9 9 18 12 9 9 18 13 9 9 18 14 8 8 16 15 8 7 15 16 9 9 18 17 9 9 18 18 9 10 19

  • 178

    -

    4

    4

    10 10 20

    19 8 8 18 20 8 8 16 21 9 8 17 22 8 8 16 23 9 7 16 24 9 8 17 25 8 8 16 26 9 7 16 27 8 8 18 28 7 7 14 29 9 8 17 30 8 8 16 31 9 7 16

    70 14 () ............................................... ( )

  • 179

    4 13-14 . . .. 2557

    -

    3 3 3 3 12

    1 3 3 2 3 11 2 3 2 2 2 9 3 3 3 3 2 11 4 3 3 2 3 11 5 3 3 3 3 12 6 3 3 2 3 11 7 3 2 2 2 9 8 2 3 3 2 10 9 3 3 2 3 11 10 3 3 3 3 12 11 3 3 2 3 11 12 3 2 2 2 9 13 3 3 3 2 11 14 2 3 2 3 10 15 3 2 2 2 9 16 3 3 3 2 11 17 3 3 3 3 12 18 3 3 3 3 12

  • 180

    -

    3 3 3 3 12

    19 3 3 2 3 11 20 3 2 2 2 9 21 3 3 3 2 11 22 3 3 2 3 11 23 3 3 3 3 12 24 3 3 2 3 11 25 3 2 2 2 9 26 2 3 3 2 10 27 3 3 2 3 11 28 3 2 2 3 10 29 3 3 2 3 11 30 3 2 2 2 9 31 3 3 3 3 12

    70 8 () ............................................... ( )

  • 181

    18

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

    ............................................................................... ....1... ...............

    3 2 1 0

    1.

    1.1 1.2 1.3

    2.

    2.1 2.2 2.3

    3.

    3.1 3.2 3.3

    4.

    4.1 4.2

    ..................................................... (.......................................................)

    ............. /................... /..............

  • 182

    - 3 - 2 - 1

    - 0

    - 2.5-3.0 3 - 1.5-2.4 2 - 0.5-1.4 1 - 0.0-0.4 0 -

  • 183

    4 13-14 . . .. 2557

    -

    15 15 30

    1 12 12 24 2 14 13 27 3 13 13 26 4 13 12 25 5 13 13 26 6 13 13 26 7 14 12 25 8 12 12 24 9 13 13 26 10 11 12 23 11 12 12 24 12 11 11 22 13 13 12 25 14 11 13 24 15 13 13 26 16 12 11 23 17 14 13 27 18 12 14 26

  • 184

    -

    15 15 30

    19 14 12 26 20 13 12 25 21 12 12 24 22 13 13 26 23 13 13 26 24 12 15 27 25 13 13 26 26 11 12 23 27 15 12 27 28 11 10 21 29 13 13 26 30 12 13 25 31 13 13 26

    70 21 () ............................................... ( )

  • 185

    ............................................................................... ....1... ...............

    :

    (3)

    (2)

    (1)

    (0)

    1.

    1.1 - 1.2

    1.3 1.4

    1.5

    3 2 1 0

    13 - 15 09 - 12 01 - 80 0

  • 186

    ............................................................................... ....1... ............... :

    (3)

    (2)

    (1)

    (0)

    2.

    2.1

    2.2

    2.3 2.4 2.5

    3 2 1 0

    13 - 15 09 - 12 01 - 80 0