A4-systemet
616
Talföljder på laborativt vis
Pesach Laksman
lärarutbildare vid Malmö högskola
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1
2
2
2
1
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3
2
1
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4
Potenser
1:
2
= 2: 2 = 2 :1
2
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5
Biennal 2008
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6
20
Hur mycket är
2
0
Elevernas vanliga svar är
0 eller 2.
Biennal 2008
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7
Antal vikningar
2
8
Antal delar
1
0
2
3
4
Mitt förslag kan vara 13.
Biennal 2008
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Antal vikningar
Biennal 2008
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9
Antal delar
Antal vikningar
10
Antal delar
1
2
1
2
2
4
2
4
3
8
3
8
4
16
4
16
17
?
Biennal 2008
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11
Biennal 2008
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12
Antal vikningar
Antal delar
1
2
2
4
3
8
4
16
4
2
?
3
8
5
17
32
?
?
n
Biennal 2008
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Biennal 2008
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13
Antal vikningar
2
n
14
Antal delar
0
20
1
21
2
22
3
23
17
217
n
2n
n
Biennal 2008
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15
Biennal 2008
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16
gör ovikt en gång
antal vikningar
1
2 =
2
0
2 =1
−1
antal delar
Biennal 2008
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17
Biennal 2008
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18
3
n
?
1
Biennal 2008
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19
3
1:
20
3
= 3: 3 = 3 :1
3
1
Biennal 2008
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3
3
2
1
Biennal 2008
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21
22
4
1
23
Biennal 2008
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24
1
Vändning av tal
½
2
Biennal 2008
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1
2
3
4
5
1
6
7
8
9
10
6
11
12
13
14
15
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18
19
20
Biennal 2008
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5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
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4
5
7
8
9
10
11
12
13
14
15
16
17
18
19
20
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3
1
29
26
28
3
5
7
8
9
10
11
12
13
14
15
16
17
18
19
20
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1
3
7
5
9
10
1
3
7
5
9
11
12
13
14
15
11
12
13
14
15
16
17
18
19
20
16
17
18
19
20
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1
3
7
11
16
17
5
14
15
11
18
19
20
16
7
17
18
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1
18
11
20
19
20
34
5
9
13
17
35
15
3
7
15
19
9
Biennal 2008
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9
13
5
13
33
5
32
3
7
13
3
11
1
9
Biennal 2008
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1
Biennal 2008
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31
15
19
Biennal 2008
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20
36
1
3
7
11
5
9
13
17
15
11
19
17
5
11
17
15
7
11
12
15
19
Biennal 2008
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40
1
15
19
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13
39
13
17
7
17
5
6
38
5
11
19
1
19
Biennal 2008
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15
1
9
13
9
13
37
1
7
5
7
Biennal 2008
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1
5
6
7
11
12
13
17
41
19
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1
5
6
7
11
12
13
17
18
7
11
12
13
17
18
5
1
6
7
8
6
11
12
13
11
17
18
19
6
7
11
16
17
5
6
13
11
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47
5
8
13
18
1
19
44
19
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18
7
45
4
19
4
17
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4
1
4
6
19
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1
1
7
46
4
5
19
20
8
13
17
18
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1
6
4
7
11
16
17
1
8
6
13
11
18
19
20
Biennal 2008
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1
6
7
17
6
13
15
11
20
16
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1
7
11
16
17
10
13
15
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19
53
19
20
50
4
7
17
8
10
13
15
18
19
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1
8
18
17
51
4
10
13
1
10
19
8
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8
18
7
49
4
11
16
16
4
52
4
7
8
10
11
12
13
15
16
17
18
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54
1
4
1
7
8
10
11
12
13
15
16
17
19
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1
8
12
16
17
13
12
16
17
8
10
13
15
19
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14
4
10
15
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12
16
17
12
13
17
14
11
19
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4
12
13
17
59
15
19
1
15
14
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4
13
10
11
56
10
19
1
11
55
4
11
4
9
10
14
15
19
Biennal 2008
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60
1
11
4
1
9
10
15
12
13
14
17
18
19
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1
4
9
11
12
13
14
17
18
19
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4
1
62
4
9
11
15
9
12
13
14
15
12
13
14
15
17
18
19
20
17
18
19
20
Biennal 2008
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1
Biennal 2008
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4
1
4
9
17
9
13
14
15
18
19
20
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17
65
18
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14
15
19
20
66
1
4
1
4
9
9
15
17
18
19
20
Biennal 2008
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1
17
1
17
18
19
20
16
18
1
Biennal 2008
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70
4
9
19
19
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4
16
68
9
Biennal 2008
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1
20
4
9
16
19
Biennal 2008
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4
18
9
20
16
71
20
Biennal 2008
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1
4
Vilka frågor kan man ställa till eleverna?
9
16
Biennal 2008
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Biennal 2008
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73
• Vilket tal skulle komma näst om vi hade
flera kort?
Biennal 2008
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Biennal 2008
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25, 36, …
Biennal 2008
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75
• Vilket tal skulle komma näst om vi hade
flera kort?
• Hur hittar vi nästa element?
77
74
1
9
4
+3
+5
76
25
16
+7
Biennal 2008
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+9
78
• Vilket tal skulle komma näst om vi hade
flera kort?
• Hur hittar vi nästa element?
• Hur hittar vi ett element om vi vill flytta
oss många steg framåt?
Biennal 2008
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I
II
III
IV
V
n
1
4
9
16 25
n
2
79
Biennal 2008
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81
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1=1
4=1+3
9=1+3+5
16=1+3+5+7
25=1+3+5+7+9
Biennal 2008
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18 (2, 3, 6, 9, 18)
16 (2, 4, 8, 16)
Varför blir just kvadrattal synliga
och inga andra?
Biennal 2008
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83
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1 18
2 9
3 6
1 16
2 8
4 4
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85
Låt oss undersöka ett tal exempelvis
149.
Liknande tankar kan användas då vi vill ta
reda på om ett visst tal är primtal.
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86
Talet 149 ligger mellan nedanstående
primtals kvadrater.
2
2
11 <149<13
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Talet 149 är varken delbart med
•
•
•
•
2
3
5
7
Detta innebär att 149 är ett primtal.
• eller 11
Biennal 2008
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89
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Sociala relationer…
Biennal 2008
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Antal personer
…inom en grupp
Biennal 2008
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91
Antal kramar
92
Antal personer
Antal kramar
1
1
0
2
2
1
3
3
4
4
5
5
6
6
7
7
8
8
9
9
10
10
11
11
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93
94
Antal personer
Antal kramar
Antal personer
Antal kramar
1
0
1
0
2
1
2
1
3
3
3
3
4
6
4
6
5
10
5
10
6
6
15
7
7
21
8
8
28
9
9
36
10
10
45
11
11
55
Biennal 2008
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95
Biennal 2008
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Hur många kramar blir det om
n personer träffas?
Biennal 2008
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97
Biennal 2008
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98
Sociala relationer mellan två grupper
0+1+2+3+4+5+….+(n – 1)=
n(n −1)
2
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99
Biennal 2008
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100
Hur många handskakningar blir det
mellan grupper på m och n personer?
mn
Biennal 2008
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101
Biennal 2008
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102
Vilka blir flest – handskakningar eller
kramar?
Biennal 2008
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Antal personer
Antal kramar
1
0
2
1
3
3
4
6
5
10
6
15
7
21
8
28
9
36
10
45
11
55
103
Biennal 2008
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104
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105
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106
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108
Antal personer
Antal kramar
1
0
2
1
3
3
4
6
5
10
6
15
7
21
8
28
9
36
10
45
11
55
Biennal 2008
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109
Biennal 2008
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110
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111
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112
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114
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115
