PRACTICAL TEACHING.

WHAT

AT shall be said for the teacher who fears to omit certain problems which are not utilitarian and whose culture value is counterbalanced by the fact that they give a false notion of business, or to omit those traditional puzzles which depend for their difficulty upon their ambiguity of statement? Many a teacher, especially in our country schools, will confess to such a fear of omitting problems, lest he be accused of an inability to solve them.

It would be well for all teachers to assist in creating a sentiment in favor of omitting the unquestionably superfluous or dangerous, and thus to avoid this weak criticism. It should also be understood by timid teachers that it is no disgrace to be unable to solve every puzzle that may be sent in, or even every legitimate problem.

DAVID EUGENE SMITH,

in Teachers' Professional Library.

THE COMMON SIGNS.

This sign is read and or plus.

When a pupil is first taught how many two apples and two apples are, we say "2 apples and 2 apples are 4 apples." When we write it this way:

2 apples

+2 apples, the sign+before the last figure indicates that we are to combine the numbers by adding them.

Teach the child to know that wherever he sees the sign it means that the numbers with which it is used are to be added.

These two short straight lines are read equals or are. They show that the numbers joined or connected by the sign = are equal, as, 4+2=6; 4+2=3+3. In the first case 4+2 are 6, so we write it 4+2=6. In the second case 4+2 are 6 and 3+3 are 6. We can show that they are equal by writing it thus:

4+2=3+3.

The number or numbers on the left of the sign equal those on the right of it.

This sign is read minus, less, or from, and is the sign of difference or subtraction. Whenever it is used it means that the number after it is to be taken away from the number before it. 42 means that we are to take 2 from 4, or subtract 2 from 4.

We may read it 4 less 2, 4 minus 2, or 2 from 4. The meaning is the same in all three. The ex

pression 4 minus 2 is the best one. When the child needs it teach it in that way.

X This sign means multiplied by. by. 6×3 should be read, 6 multiplied by 3. It may be read 6 times 3. The sign shows that the number before it is to be taken as many times as there are units in the number after the sign.

In 63 it means that 6 is to be taken 3 times. When the number after the sign has a name, as, 3 $5; 46 cows, etc., read the sign times always. 3 $5 is read 3 times $5. To say 3 multiplied by $5 is not right.

NOTE. This sign is sometimes used in certain kinds of business so that it is read by. A pane of glass 10 inches wide and 14 inches long is indicated in this way: 10 × 14 and is read "10 by 14."

The size of timbers is also shown in that way, as, a stick 4× 5 means a stick 4 inches by 5 inches in diameter.

TALK:

Don't try to tell the children all these meanings of the sign at once. Tell them only when they begin to need them, and illustrate by examples. They will not need to know the last use of the sign until they have been in school some years.

This sign is read divided by. It has two meanings. Teach the pupil only the first one given below. The last one is too difficult for young children. It is not needed in their early work, and when they get older they will understand it readily.

Teach this:-The sign means divided by, and it shows that we are to find how many times the number after the sign is contained in the number before the sign.

Use very small numbers to teach the use of the sign, as, 4+ 2; 62; 63; etc.

The sign may mean to find one of the equal parts of a number, as, $82 may mean to find

of $8. Do not try to teach this meaning at first. Leave it till a later time.

This is an ordinary comma and is put between numbers to show that they are to be called separately, as, 1, 2, 3, 7, 9, which means that the numbers one, two, three, seven, nine, are to be read as if written in words, each by itself.

The comma is also used to make the reading of large numbers easy. To read the number 2719346 would be slow if commas were not used to show the hundreds, thousands, etc. If written in this way2,719,346-you see at a glance that the 2 is millions, the 719 is thousands, etc.

This sign is made like an ordinary period, but is called a decimal point. It is of no practical value to know why, but anyone who wishes to know may ask any teacher to explain it.

The most common use of this mark is in writing dollars and cents. The decimal point is always put directly after the dollars' figures, or just before the cents' figures, as in $45.05, which is read, "Forty-five dollars and five cents."

The decimal point is always read AND.

These three dots arranged as shown are read therefore. They may be read hence. This sign is often used in the last sentence of a solution.

() The parenthesis indicates that all the numbers contained therein are to be considered together, as 4 (6−3+2+4)

means that all of that part within the parenthesis are to be treated together; in this case multiplied by 4.