een, 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 twen