ty, 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.

These are the four principal modes of calculating which occur to me.
Pupils do not generally practice any one of them exclusively, but
occasionally resort to each, according to the circumstances of the
particular case."

The teacher here stopped to inquire how many of the class were
accustomed to add by calculating in either of these ways; or in any
simpler ways.

3. "There is one more mode which I shall describe: it is by _Memory_.
Before I explain this mode I wish to ask you some questions which I
should like to have you answer as quick as you can.

How much is four times five?--Four _and_ five?

How much is seven times nine?--Seven _and_ nine?

Eight times six?--Eight _and_ six?

Nine times seven?--Nine _and_ seven?"

After asking a few questions of this kind, it was perceived that the
pupils could tell much more readily what was the result when the numbers
were to be multiplied, then when they were to be added.

"The reason is," said the teacher, "because you committed the
multiplication table to memory, and have not committed the addition
table. Now many persons have committed the addition table, so that it is
perfectly familiar to them, and when they see any two numbers, the
amount which is produced when they are added together comes to mind in
an instant. Adding in this way is the last of the three modes I was to
describe.

Now of these three methods, the last is undoubtedly the best. If you
once commit the addition table thoroughly, you have it fixed for life;
whereas if you do not, you have to make the calculation over again every
time, and thus lose a vast amount of labor. I have no doubt that there
are some in this class who are in the habit of _counting_, who have
ascertained that seven and eight for instance, make fifteen; by counting
up from seven to fifteen, _hundreds of times_. Now how much better it
would be, to spend a little time in fixing the fact in the mind once for
all, and then when you come to the case, seven and eight are--say at
once "Fifteen,"--instead of mumbling over and over again, hundreds of
times, "Seven, eight, nine, ten, eleven, twelve, thirteen, fourteen,
fifteen."

The reason then, that some of the class add so slowly, is not probably
because they want skill a