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call the attention of the class to the similarity of this formula to the one previously learned. (See Art. 6). It may be mentioned that it consists of two factors and their product; that whenever a product is required, multiplication is the process by which it is obtained; and, whenever a factor is required, division is the process by which it is obtained.
Now, the teacher may point to the word “surface" on the black-board, and ask of the class, this question
To obtain surface, why is multiplication the process ?--and the answer, Because a product is required, should be obtained from the class, else the teacher must give it and impress it upon them. The explanation is as follows :
A length of 25 feet has a row of 25 square feet along the edge, and a width of 14 ft. has 14 such rows, or 14 times 25 square ft., which gives 350 square feet.
9. Next, take this example (or, one similar)—
Ex. 4 floor 25 feet long contains 350 square feet of surface; how wide is the floor? Again, we write on the board-
LENGTH X BREADTH = SURFACE, and ask the class which two of these three parts are to be found in this example; the answer, length and surface, being given, let there be written beneath the general formula the following :
25 X WHAT = or, to be exact,
25 SQ. FT. X WHAT= 350 SQ. FT. Then, continue the explanation, etc., as seen in Art. 7, to which this article is similar.
Next, take this example (or a similar one) Ex. A floor 14 feet wide contains 350 sq. feet of surface ; how wide is the floor ?
The explanation, etc., should be similar to that in Article 7. The work should appear as follows :
LENGTH X BREADTH = SURFACE.
WHAT X 14 = 350,
II. When three (or more) factors occur in the question or statement, the process of finding any one of them will be the same as has already been given. For example, in the statement
4 X 7 X 5 = 140, if the first factor, (4), is required we would have for the work (using ? instead of WHAT)
? X 7 X 5 = 140,
13. If the second factor (7) is required, we would have for the work
? 4 X? X 5= 140,
?= 140 = (4 X 5),
= 140 • 20,
? 7. 14. And, if the third factor (5) is required, we would have for the work- 4 X 7 X?= 140,
?= 140 + (4 X 7),
4 X 7 X 5 = ?
4 X 7 X 5 = 140. We see in the four preceding articles that when the factor is required, division is the process; and, when the product is required, multiplication is the process.
17. Illustrative examples involving three factors will now be given.
Ex. How many cubic yards of earth were removed in digging a cellar 18 ft. long, 13 ft. wide, and 8 ft. deep?
First, show by black-board illustration or by small cubes that there will be a row of 18 cubic feet along the length; that in a width of 13 feet, there will be 13 such rows, or 13 times 18 cu. ft. (234 cu. ft.) in a layer; and, in a hight (or depth) of 8 feet, there will be 8 such layers, or 8 times 234 cu. ft. (1872 cu. ft.) in the cellar.
In this way is developed the general practical formula
LENGTHX BREADTH XDEPTH (or hight)=CUBIC CONTENTS (or solidity).
18. The dimensions being of the same denomination, their product will give the number of cubic measures of the same denomination, contained in the cellar.
19. Writing after each part of the formula that which denotes it in the example, we have
18 X 13 X 8=?,
Hence, 1872 cu. ft. The explanation may be as follows:A length of 18 feet has a row of 18 cubic feet along the edge; a breadth of 13 feet has 13 such rows, or 13 times 18 cubic feet, which is 234 cubic feet in a layer; and a depth of 8 feet has 8 such layers, or 8 times 234 cubic feet, which is 1872 cubic feet, in the cellar.
It takes 27 cubic feet to make one cubic yard; therefore, there are as many cubic yards in 1872 cu. ft., as the number of times 27 is contained in 1872, or 6973 times; hence, 697/3 cu. yds.
Ex. In digging a cellar 18 feet long and 13 feet wide, 1872 cubic feet of earth were removed; how deep was the cellar ?
LENGTH X BREADTH X DEPTH = CUBIC CONTENTS. By the items in the example, and by Art. 18, we have
18 X 13 X ? 1872. Here, we see that one of the factors is required; hence, the product of all three of them must be divided by the two given factors, and the quotient will be the required factor. The work may be indicated thus:
P= 1872 + (18 X 13), which means that the number required equals the quotient obtained by dividing 1872 by the product of 18 by 13. The whole form of work may appear thus :
LXBXD= CUBIC CONTENTS.
?= 1872 + (18 X 13),
The different items of such an example must be of the same denomination before the actual work is begun.
23 Ex, In digging a cellur 6 yards long and 8 ft. deep, 6973 cubic yards of earth were removed; how many yds. wide is the cellar?
FORM OF WORK. 6 yards = 18 feet.
6973 cu. yds. = 1872 cu. ft.
P= 1872 + (18 X 8),
13; hence, B = 13 ft. = 47 yd. 24. Ex. In digging a cellar 4/3 yd. wide and 8 ft. deep, 1872 cubic feet of earth were removed; how many yd. long is the cellar?
FORM OF WORK.
?= 18; hence, L= 18 ft. = 6 yd. .
A DAY IN COL. PARKER'S NORMAL SCHOOL.
S. S. PARR, PRIN. DE PAUW NORMAL SCHOOL.
The writer recently enjoyed a day's visit to the Cook County (Illinois) Normal School, at Normal Park, a suburb of Chicago, of which Col. Francis W. Parker is principal. The pleasure of the visit was greatly enhanced by the courtesy and attention received from Col. Parker, who gave opportunity for one to see all that was going on, and kindly explained the meaning of the various processes of teaching and of management that was wit nessed.
A young Mr. Kellogg, son of Mr. Amos Kellogg, of the New York School Journal, is Col. Parker's clerk. He very kindly aided in explaining and showing one around, and thus contributed to the pleasure and profit of the visit.
The first exercise seen was that of the opening exercises for the teachers' class, held in the hall of the school building. Col. Parker read a few paragraphs from the Sermon on the Mount. There was singing. Earnestness was the characteristic of the whole exercise. The music was good—a statement seldom possible of opening-exercise music. Exery one entered into the spirit of what was done. After reading and singing, Col. Parker addressed a few words to the students on the subject of their purpose. The principal thought was that each one would find what she was looking for. If formal results, or immediate returns were looked for in their own and the children's minds, these things would be found. If growth, substantial development, on the other hand, were sought, it would be found.
Opening exercises over, visits were made to all the classes and rooms, for the sake of getting a general idea of the plan of the school and of the nature of the work. Interest and attention marked all the exercises. Teachers were at white heat. No listless pupils were noticed. Freedom of action presented itself as one of the marks of all the work. Col. Parker knows every chick and child about the premises, and was greeted with the smiles and the enthusiasm that belongs to the class of magnetic personalities of which he is one. Not only does he know each child's face and name, but its mental peculiarities, and as he passed around spoke to this one about a defect in pronunciation, which was being overcome, to another about some peculiarity of memory, etc.
The moral to all this is a fact entirely overlooked by many who have essayed to criticise favorably or unfavorably; viz., that Col. Parker is not merely a man with a theory, but one who has the closest kind of a mastery of details—a condition antecedent to all success.
One would of course fail to mention an important feature, if he did not say something of the learning to do by doing" that has had so much said about it by all visitors and critics. An effort, more or less successful, is made to carry it out in all the work done. Thus in geometry, in the high-school, the pupils develop the theorems without the demonstrations usually gjven before