| Multipliers | Multiplicands |
|---|
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Totals |
|---|
| 1 | 299 | 534 | 472 | 271 | 310 | 293 | 261 | 178 | 195 | 99 | 2912 |
| 2 | 350 | 644 | 668 | 480 | 458 | 377 | 332 | 238 | 239 | 155 | 3941 |
| 3 | 280 | 487 | 509 | 388 | 318 | 302 | 247 | 199 | 227 | 152 | 3109 |
| 4 | 186 | 375 | 398 | 242 | 203 | 265 | 197 | 163 | 159 | 93 | 2281 |
| 5 | 268 | 359 | 393 | 234 | 263 | 243 | 217 | 192 | 197 | 114 | 2480 |
| 6 | 180 | 284 | 265 | 199 | 196 | 191 | 168 | 169 | 165 | 106 | 1923 |
| 7 | 135 | 283 | 277 | 176 | 187 | 158 | 155 | 121 | 145 | 118 | 1755 |
| 8 | 137 | 272 | 292 | 175 | 192 | 164 | 158 | 157 | 126 | 126 | 1799 |
| 9 | 71 | 173 | 140 | 122 | 97 | 102 | 101 | 100 | 82 | 110 | 1098 |
| | | | | | | | | | | | |
| Totals | 1906 | 3411 | 3414 | 2287 | 2224 | 2095 | 1836 | 1517 | 1535 | 1073 | |
TABLE 7
Amount Of Practice: Divisions Without Remainder In Textbook B, Parts I And II
| Dividends | Divisors |
|---|
| 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | Totals |
|---|
Integral multiples of 2 to 9
in sequence; i.e.,
4 ÷ 2 occurred 397 times,
6 ÷ 2 occurred 256 times,
6 ÷ 3, 224 times,
9 ÷ 3, 124 times. | 397 | 224 | 250 | 130 | 93 | 44 | 98 | 23 | 1259 |
| 256 | 124 | 152 | 79 | 28 | 43 | 61 | 25 | 768 |
| 318 | 123 | 130 | 65 | 50 | 19 | 39 | 19 | 763 |
| 258 | 98 | 86 | 105 | 25 | 24 | 34 | 20 | 650 |
| 198 | 49 | 76 | 27 | 22 | 30 | 33 | 16 | 451 |
77
180
69 | 54
91
46 | 36
50
37 | 31
38
24 | 28
17
12 | 27
13
17 | 16
22
16 | 9
16
15 | 278
427
236 |
| Totals | 1753 | 809 | 817 | 499 | 275 | 217 | 319 | 142 | |
TABLE 8
Division Bonds, With And Without Remainders. Book B
All work through grade 6, except estimates of quotient figures in long division.
| Dividend | 2 | 3 | 4 | 5 |
| Divisor | 1 | 2 | 1 | 2 | 3 | 1 | 2 | 3 | 4 | 1 | 2 | 3 | 4 | 5 |
Number of
Occurrences | 41 | 386 | 27 | 189 | 240 | 26 | 397 | 66 | 185 | 23 | 136 | 43 | 53 | 135 |
| |
| Dividend | 6 | 7 |
| Divisor | 1 | 2 | 3 | 4 | 5 | 6 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
Number of
Occurrences | 21 | 256 | 224 | 68 | 43 | 83 | 23 | 72 | 55 | 38 | 46 | 32 | 54 |
| |
| Dividend | 8 | 9 |
| Divisor | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
Number of
Occurrences | 17 | 318 | 30 | 250 | 22 | 28 | 39 | 91 | 19 | 50 | 124 | 49 | 25 | 15 | 18 | 30 | 38 |
| |
| Dividend | 10 | 11 |
| Divisor | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
Number of
Occurrences | 258 | 38 | 46 | 120 | 19 | 9 | 24 | 24 | 32 | 21 | 16 | 3 | 7 | 11 | 14 | 3 |
| |
| Dividend | 12 | 13 |
| Divisor | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
Number of
Occurrences | 198 | 123 | 152 | 29 | 93 | 9 | 16 | 7 | 45 | 16 | 15 | 11 | 7 | 4 | 5 | 3 |
| |
| Dividend | 14 | 15 |
| Divisor | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
Number of
Occurrences | 77 | 20 | 13 | 5 | 8 | 44 | 8 | 6 | 69 | 98 | 16 | 79 | 8 | 8 | 4 | 6 |
| |
| Dividend | 16 | 17 |
| Divisor | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
Number of
Occurrences | 180 | 19 | 130 | 14 | 6 | 9 | 98 | 3 | 61 | 9 | 15 | 14 | 6 | 6 | 12 | 3 |
| |
| Dividend | 18 | 19 |
| Divisor | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
Number of
Occurrences | 69 | 49 | 13 | 6 | 28 | 7 | 7 | 23 | 21 | 6 | 10 | 5 | 3 | 4 | 10 | 4 |
| |
| Dividend | 20 | 21 |
| Divisor | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
Number of
Occurrences | 24 | 86 | 65 | 11 | 3 | 23 | 5 | 54 | 12 | 8 | 5 | 43 | 10 | 5 |
| |
| Dividend | 22 | 23 |
| Divisor | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
Number of
Occurrences | 17 | 16 | 15 | 8 | 13 | 6 | 15 | 7 | 8 | 11 | 8 | 6 | 3 | 2 |
| |
| Dividend | 24 | 25 |
| Divisor | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
Number of
Occurrences | 91 | 76 | 18 | 50 | 5 | 61 | 1 | 11 | 13 | 105 | 5 | 6 | 5 | 3 |
| |
| Dividend | 26 | 27 |
| Divisor | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
Number of
Occurrences | 5 | 6 | 3 | 3 | 4 | 6 | 3 | 46 | 8 | 10 | 4 | 2 | 6 | 25 |
| |
| Dividend | 28 | 29 |
| Divisor | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
Number of
Occurrences | 4 | 36 | 8 | 3 | 19 | 3 | 7 | 6 | 8 | 0 | 5 | 11 | 2 | 3 |
| |
| Dividend | 30 | 31 |
| Divisor | 4 | 5 | 6 | 7 | 8 | 9 | 4 | 5 | 6 | 7 | 8 | 9 |
Number of
Occurrences | 21 | 27 | 25 | 6 | 7 | 13 | 4 | 3 | 1 | 1 | 4 | 2 |
| |
| Dividend | 32 | 33 |
| Divisor | 4 | 5 | 6 | 7 | 8 | 9 | 4 | 5 | 6 | 7 | 8 | 9 |
Number of
Occurrences | 50 | 11 | 3 | 6 | 39 | 5 | 8 | 7 | 7 | 2 | 6 | 1 |
| |
| Dividend | 34 | 35 |
| Divisor | 4 | 5 | 6 | 7 | 8 | 9 | 4 | 5 | 6 | 7 | 8 | 9 |
Number of
Occurrences | 8 | 3 | 5 | 2 | 1 | 1 | 10 | 31 | 5 | 24 | 5 | 3 |
| |
| Dividend | 36 | 37 |
| Divisor | 4 | 5 | 6 | 7 | 8 | 9 | 4 | 5 | 6 | 7 | 8 | 9 |
Number of
Occurrences | 37 | 16 | 22 | 2 | 6 | 19 | 12 | 8 | 7 | 5 | 3 | 9 |
| |
| Dividend | 38 | 39 |
| Divisor | 4 | 5 | 6 | 7 | 8 | 9 | 4 | 5 | 6 | 7 | 8 | 9 |
Number of
Occurrences | 7 | 8 | 7 | 1 | 1 | 5 | 4 | 3 | 7 | 4 | 3 | 1 |
| |
| Dividend | 40 | 41 | 42 |
| Divisor | 5 | 6 | 7 | 8 | 9 | 5 | 6 | 7 | 8 | 9 | 5 | 6 | 7 | 8 | 9 |
Number of
Occurrences | 38 | 9 | 2 | 34 | 2 | 6 | 6 | 3 | 7 | 5 | 7 | 28 | 30 | 10 | 3 |
| |
| Dividend | 43 | 44 | 45 |
| Divisor | 5 | 6 | 7 | 8 | 9 | 5 | 6 | 7 | 8 | 9 | 5 | 6 | 7 | 8 | 9 |
Number of
Occurrences | 7 | 5 | 10 | 3 | 2 | 7 | 6 | 4 | 5 | 0 | 24 | 6 | 7 | 10 | 20 |
| |
| Dividend | 46 | 47 | 48 |
| Divisor | 5 | 6 | 7 | 8 | 9 | 5 | 6 | 7 | 8 | 9 | 5 | 6 | 7 | 8 | 9 |
Number of
Occurrences | 3 | 3 | 2 | 2 | 2 | 6 | 2 | 2 | 0 | 3 | 7 | 17 | 4 | 33 | 2 |
| |
| Dividend | 49 | 50 | 51 | 52 |
| Divisor | 5 | 6 | 7 | 8 | 9 | 6 | 7 | 8 | 9 | 6 | 7 | 8 | 9 | 6 | 7 | 8 | 9 |
Number of
Occurrences | 4 | 7 | 27 | 9 | 2 | 4 | 6 | 3 | 8 | 2 | 3 | 1 | 2 | 5 | 5 | 5 | 3 |
| |
| Dividend | 53 | 54 | 55 | 56 |
| Divisor | 6 | 7 | 8 | 9 | 6 | 7 | 8 | 9 | 6 | 7 | 8 | 9 | 6 | 7 | 8 | 9 |
Number of
Occurrences | 4 | 3 | 2 | 2 | 12 | 5 | 1 | 16 | 5 | 3 | 4 | 2 | 0 | 13 | 16 | 8 |
| |
| Dividend | 57 | 58 | 59 | 60 | 61 |
| Divisor | 6 | 7 | 8 | 9 | 6 | 7 | 8 | 9 | 6 | 7 | 8 | 9 | 7 | 8 | 9 | 7 | 8 | 9 |
Number of
Occurrences | 0 | 3 | 1 | 3 | 2 | 2 | 3 | 1 | 2 | 3 | 0 | 3 | 3 | 9 | 1 | 1 | 2 | 5 |
| |
| Dividend | 62 | 63 | 64 | 65 | 66 | 67 |
| Divisor | 7 | 8 | 9 | 7 | 8 | 9 | 7 | 8 | 9 | 7 | 8 | 9 | 7 | 8 | 9 | 7 | 8 | 9 |
Number of
Occurrences | 4 | 6 | 1 | 17 | 5 | 9 | 5 | 22 | 0 | 1 | 10 | 1 | 2 | 1 | 4 | 0 | 1 | 1 |
| |
| Dividend | 68 | 69 | 70 | 71 | 72 | 73 | 74 | 75 |
| Divisor | 7 | 8 | 9 | 7 | 8 | 9 | 8 | 9 | 8 | 9 | 8 | 9 | 8 | 9 | 8 | 9 | 8 | 9 |
Number of
Occurrences | 1 | 3 | 2 | 0 | 6 | 1 | 6 | 2 | 1 | 0 | 16 | 10 | 7 | 5 | 3 | 3 | 5 | 3 |
| |
| Dividend | 76 | 77 | 78 | 79 | 80 | 81 | 82 | 83 | 84 | 85 | 86 | 87 | 88 | 89 |
| Divisor | 8 | 9 | 8 | 9 | 8 | 9 | 8 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 | 9 |
Number of
Occurrences | 3 | 2 | 3 | 0 | 4 | 1 | 0 | 2 | 4 | 15 | 2 | 4 | 1 | 2 | 0 | 3 | 2 | 7 |
Tables 3 to 8 show that even gifted authors make instruments for instruction in arithmetic which contain much less practice on certain elementary facts than teachers suppose; and which contain relatively much more practice on the more easily learned facts than on those which are harder to learn.