Numeracy is about handling numbers and the times tables is a
very useful window on
FIFTY NINE NUMBERS below 144, with thirty four under 50.
FIFTY NINE NUMBERS below 144, with thirty four under 50.
What are
these fifty nine numbers?
THE PERFECT SQUARES are the only numbers that appear
an odd number of times. That is twelve numbers. 36 appears five times, 4, 9 and 16
three appearances each and the rest just one.
All of the remaining 132 can be called 66 pairs –
commutative means the product
for 6 x 9 appears twice.
for 6 x 9 appears twice.
There are 5 prime numbers that appear twice
(2,3,5,7,11) but from 13 up, primes and their multiples are not products,
thereby excluding themselves.
Two numbers make 6 appearances – 12 and 24; ten make
4 appearances (the largest is 72)
Going up to 12 x 12 is a great introduction to three digit
competency. Only seven numbers meet the criteria; three of which end in “0”.
The times tables is about getting to know thirty four numbers
under 50 and fifty nine under 144. Barely enough of them to be able to reward speed
and perseverance, once they have been learned. By Grade 6, all learners should have passed a
torture test (150 written questions – yes include duplicates – in 7 minutes,
weekly till score beats 145. Allow them a couple of minutes to savour their accomplishment
and the feelings that go with it. Then start the trek through the next topic.
Rote? Repetition? Tell McDonalds it won’t work.
3 * 12 = 4 * 9 = 6 * 6 = 9 * 4 = 12 * 3 = 36
NUMBERS UP TO 144 – COLLECTIONS AND EXCLUSIONS
Inside the 12 Times Tables
|
Inside the 144
|
|
Used 6 times
|
Two: (12 and 24)
|
None
|
Used 5 times
|
One: Only 36
|
None
|
Used 4 times
|
Ten: (6, 8, 10, 18, 20, 30, 40, 48, 60, 72
|
None
|
Used an odd number of times
|
Twelve: all the
perfect squares
|
144
|
Prime Numbers
|
Five: 2,3,5,7,
11
|
Thirty Four:2, 3, 5, 7, 11, 13, 17, 19,23, 29, 31, 37, 41, 43, 47,
53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131,
137, 139
|
Numbers 100 and over
|
Seven:
100, 108, 110, 120, 121, 132, 144
|
Forty five:
100-144
|
THE TIMES TABLE GRID
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
11
|
12
|
|
1
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
11
|
12
|
2
|
2
|
4
|
6
|
8
|
10
|
12
|
14
|
16
|
18
|
20
|
22
|
24
|
3
|
3
|
6
|
9
|
12
|
15
|
18
|
21
|
24
|
27
|
30
|
33
|
36
|
4
|
4
|
8
|
12
|
16
|
20
|
24
|
28
|
32
|
36
|
40
|
44
|
48
|
5
|
5
|
10
|
15
|
20
|
25
|
30
|
35
|
40
|
45
|
50
|
55
|
60
|
6
|
6
|
12
|
18
|
24
|
30
|
36
|
42
|
48
|
54
|
60
|
66
|
72
|
7
|
7
|
14
|
21
|
28
|
35
|
42
|
49
|
56
|
63
|
70
|
77
|
84
|
8
|
8
|
16
|
24
|
32
|
40
|
48
|
56
|
64
|
72
|
80
|
88
|
96
|
9
|
9
|
18
|
27
|
36
|
45
|
54
|
63
|
72
|
81
|
90
|
99
|
108
|
10
|
10
|
20
|
30
|
40
|
50
|
60
|
70
|
80
|
90
|
100
|
110
|
120
|
11
|
11
|
22
|
33
|
44
|
55
|
66
|
77
|
88
|
99
|
110
|
121
|
132
|
12
|
12
|
24
|
36
|
48
|
60
|
72
|
84
|
96
|
108
|
120
|
132
|
144
|
ERATOSTHENES
SEIVE OF PRIME NUMBERS below 144
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
11
|
12
|
13
|
14
|
15
|
16
|
17
|
18
|
19
|
20
|
21
|
22
|
23
|
24
|
25
|
26
|
27
|
28
|
29
|
30
|
31
|
32
|
33
|
34
|
35
|
36
|
37
|
38
|
39
|
40
|
41
|
42
|
43
|
44
|
45
|
46
|
47
|
48
|
49
|
50
|
51
|
52
|
53
|
54
|
55
|
56
|
57
|
58
|
59
|
60
|
61
|
62
|
63
|
64
|
65
|
66
|
67
|
68
|
69
|
70
|
71
|
72
|
73
|
74
|
75
|
76
|
77
|
78
|
79
|
80
|
81
|
82
|
83
|
84
|
85
|
86
|
87
|
88
|
89
|
90
|
91
|
92
|
93
|
94
|
95
|
96
|
97
|
98
|
99
|
100
|
101
|
102
|
103
|
104
|
105
|
106
|
107
|
108
|
109
|
110
|
111
|
112
|
113
|
114
|
115
|
116
|
117
|
118
|
119
|
120
|
121
|
122
|
123
|
124
|
125
|
126
|
127
|
128
|
129
|
130
|
131
|
132
|
133
|
134
|
135
|
136
|
137
|
138
|
139
|
140
|
141
|
142
|
143
|
144
|
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