The task for reasoning is only to try, one after another, numbers that seem promising and to select the right one when found. With a little stimulus and direction children can thus derive the subtractions up to those with 9 as the larger number. Let them then be taught to do the same with the printed forms:—
Subtract
| 9 | 7 | 8 | 5 | 8 | 6 | |
| 3 | 5 | 6 | 2 | 2 | 4 | etc. |
| — | — | — | — | — | — |
and 9 − 7 = ..., 9 − 5 = ..., 7 − 5 = ..., etc.
In the case of the divisions, suppose that the pupil has learned his first table and gained surety in such exercises as:—
| 4 5s = .... | 6 × 5 = .... | 9 nickels = .... cents. |
| 8 5s = .... | 4 × 5 = .... | 6 " = .... " |
| 3 5s = .... | 2 × 5 = .... | 5 " = .... " |
| 7 5s = .... | 9 × 5 = .... | 7 " = .... " |
If one ball costs 5 cents,
two balls cost .... cents,
three balls cost .... cents, etc.
He may then be set at once to work at the answers to exercises like the following:—
Write the answers and the missing numbers:—
| A | B | C | D |
| .... 5s = 15 | 40 = .... 5s | .... × 5 = 25 | 20 cents = .... nickels. |
| .... 5s = 20 | 20 = .... 5s | .... × 5 = 50 | 30 cents = .... nickels. |
| .... 5s = 40 | 15 = .... 5s | .... × 5 = 35 | 15 cents = .... nickels. |
| .... 5s = 25 | 45 = .... 5s | .... × 5 = 10 | 40 cents = .... nickels. |
| .... 5s = 30 | 50 = .... 5s | .... × 5 = 40 | |
| .... 5s = 35 | 25 = .... 5s | .... × 5 = 45 |