(a.) Counting by your fingers. ("Yes sir.") You take the first figure,—suppose it is seven, and the one above it, eight. Now you recollect that to add eight, you must count all the fingers of one hand, and all but two again. So you say seven—eight, nine, ten, eleven, twelve, thirteen, fourteen, fifteen."
"Yes sir," "Yes sir," said the scholars.
(b.) "The next mode of counting is to do it mentally, without using your fingers at all, but as it is necessary for you to have some plan to secure your adding the right number, you divide the units into sets of two each. Thus you remember that eight consists of four twos, and you accordingly say, when adding eight to seven, seven;—eight, nine;—ten, eleven;—twelve, thirteen;" &c.
(c.) "The third mode is, to add by three, in the same way. You recollect that eight consists of two threes and a two; so you say, seven;—eight, nine, ten;—eleven, twelve, thirteen;—fourteen, fifteen."
The teacher here stops to ascertain how many of the class are accustomed to add in either of these modes. It is a majority.
2. "The next general method is calculating. That is, you do not unite one number to another by the dull and tedious method of applying the units, one by one, as in the ways described under the preceding head, but you come to a result more rapidly by some mode of calculating. These modes are several.
(a.) Doubling a number, and then adding or subtracting as the case may require. For instance in the example already specified; in order to add seven and eight, you say, "Twice seven are fourteen and one are fifteen;" ("Yes sir," "Yes sir,") or "Twice eight are sixteen, and taking one off, leaves fifteen. ("Yes sir.")
(b.) Another way of calculating is to skip about the column, adding those numbers which you can do most easily, and then bringing in the rest as you best can. Thus, if you see three eights in one column, you say three times eight are twenty-four, and then you try to bring in the other numbers. Often in such cases, you forget what you have added and what you have not, and get confused, ("Yes sir,") or you omit something in your work, and consequently it is incorrect.
(c.) If nines occur, you sometimes add ten, and then take off one, for it is very easy to add ten.
(d.) Another method of calculating, which is, however, not very common, is this. To take our old case, adding eight to seven, you take as much from the eight to add to the seven as will be sufficient to make ten, and then it will be easy to add the rest. Thus, you think in a minute, that three from the eight will make the seven a ten, and then there will be five more to add, which will make fifteen. If the next number was seven, you would say five of it will make twenty, and then there will be two left, which will make twenty-two. This mode, though it may seem more intricate than any of the others, is in fact more rapid than any of them, when one is little accustomed to it.