A B C D 3 and ... are 5. 5 and ... are 8. 4 and ... are 5. 4 and ... are 8. 3 and ... are 9. 3 and ... are 6. 5 and ... are 6. 1 and ... are 7. 4 and ... are 7. 4 and ... are 9. 6 and ... are 9. 6 and ... are 7. 5 and ... are 7. 2 and ... = 6. 1 and ... are 8. 8 and ... are 9. 6 and ... are 8. 5 and ... = 9. 3 and ... are 7. 3 + ... are 4. 4 and ... are 6. 2 and ... = 7. 1 + ... are 3. 7 + ... are 8. 2 and ... are 5. 3 and ... = 8. 1 + ... are 5. 4 + ... are 9. 2 and ... = 8. 1 and ... = 4. 4 + ... are 8. 2 + ... are 3. 3 and ... = 6. 2 and ... = 4. 7 + ... are 9. 1 + ... are 9. 6 and ... = 9. 3 and ... = 8. 2 + ... = 4. 3 + ... = 6. 4 and ... = 6. 6 and ... = 7. 3 + ... = 8. 5 + ... = 9. 4 and ... = 7. 2 and ... = 5. 4 + ... = 5. 1 + ... = 3.
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:--
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
E For 5 cents you can buy 1 small loaf of bread. For 10 cents you can buy 2 small loaves of bread. For 25 cents you can buy .... small loaves of bread. For 45 cents you can buy .... small loaves of bread. For 35 cents you can buy .... small loaves of bread.