Charles Scribner's Sons EDITION FOR NEW YORK Prepared by DR. JAMES SULLIVAN of the High School of Commerce "OUR GOVERNMENT, Local, State and National' By James A. James of Northwestern University and LIST NO. 3793. GRADES 5A-8B. PRICE, 80 CENTS. So thoroughly does this book cover the work for Civics in the new Syllabus that it might well have been the basis of the requirements. THE EUGENE FIELD READER By ALICE LOUISE HARRIS, Supervisor of Primary Grades, Evansville, Ind., and 'FRANK W. COOLEY, Superintendent of Schools, Evansville, Ind. LIST NO. 3662. GRADES 1B-2A-2B. PRICE, 32 CENTS. Contains fifty excellent illustrations and well graded prose lessons based upon the most popular of Eugene Field's poems. LIST NO. 237. KING'S "ELEMENTARY GEOGRAPHY" By CHARLES F. KING, Author of "Methods PRICE, 52 CENTS. In writing this volume Mr. King has given in the subject matter precisely the same descriptions, explanations, plans and devices that the grade teacher would have to invent for herself in order to make the average elementary geography interesting and intelligible to the child. GORDY'S "A HISTORY OF THE UNITED STATES' By WILBUR FISK GORDY, Superintendent of Pre-eminently teachable books-in fact, the only United States Histories before the public to-day which were written by an author whose continual actual experience had been that of a grammar school master and teacher of history in the class room. REDWAY'S "COMMERCIAL GEOGRAPHY" LIST NO. 1646. By JACQUES W. REDWAY, F.R.G.S., for Grammar and High Schools. PRICE, $1.00. The plan is suggestive. First, the general principles of commerce as governed by topography and climate. Second, the principles of transportation. Third, the great products of the earth-where they go: why they go; how they go. Fourth, the various nations of the world-what the people do, and why they do so. CHARLES SCRIBNER'S SONS 153-157 FIFTH AVENUE NEW YORK CITY 681 PLANS AND DETAILS OF GRADE WORK MARCH 1906 Short Processes in Arithmetic for the Several Grades BY FLORENCE GILLILAND, State Normal Training School, Brockport, N. Y. This article is concerned with those short processes only which are of practical value in elementary arithmetic. There are several standard textbooks which contain treatments of short processes, but there are very few lists of such processes classified according to the grades in which they are presented. The belief that teachers will appreciate even a brief list of problems so graded has inspired this attempt. By way of preface it may be said that "short cuts" until recently were supposed to be the peculiar possession of the expert accountant or mathematician. The knowledge of such methods of calculation and facility in their use were regarded as high polish added as a final finish after the arithmetic of the school had been completed. But teachers and writers now agree that the practical short processes should be learned early, simultaneously with the long processes and practiced throughout the study of school arithmetic. If the habit of following out the full processes in all cases is thoroughly fixed before any attention is given to abridgment, it will be difficult to establish the use of the shorter forms. The most valuable training in calculation will be the development into a habit of that tendency of mind that seeks the easier and shorter plans of calculation. Most short processes of interest to the mathematician are applications of general formulas of algebra and geometry. The proof that the short method is always valid depends upon the analysis of the corresponding formula. Thus, to square 65. 6 X 7 42, annex 25; then 652 = 4,225. That is, drop the 5, multiply the result by 1 more than itself and annex the square of 5. The reason is found in the algebraic formula: (10a + 5)2 = 100 (a + 1) + 52. Short cuts, if unexplained, are apt to impress children as "jugglery," consequently it is best to introduce only those for which a good reason can be given. It is possible to explain all of the practical short processes, if presented at the proper time. = I. It is doubtful if any formal short processes may safely be given. before the fourth year of school work. The teacher, of course, will emphasize certain number facts which lead over the path of least resistance without setting them apart or labeling them as peculiar methods. For example, in teaching the elementary sums, suppose the first tables taught to be It is easy after counting objects to add 1 or 2 to any number from 1 to 8, but it is not so easy to learn the results of adding any number from 1 to 8 to 1 or to 2. Hence, the teacher introduces a short cut by teaching that 2+7 is the same as 7 + 2, 2 + 6 is the same as 6 + 2, 1 + 9 is the same as 91, and so on. This relation holds, of course, throughout addition. The same advantage is taken in the case of elementary products. We often say that from 1 X 1 to 10 X 10 there are 100 facts to learn, when in reality there are only 50. Furthermore, it is easier to teach that 9 fives are 45 than that 5 nines are 45. II. In the third year the process of multiplication takes the place of addition in the case of equal addends. For example, instead of Here we have introduced a short process, although it is one of the fundamental operations. Would not this be a good way to present the first formal multiplication? III. Another abbreviated form of work which is taught incidentally is the multiplication by 10 or by 100, and the division of numbers ending in one or two zeros by 10 or 100 respectively. The applications should be of this type: ORAL: 1. If an apple orchard contains 180 trees with 10 trees in a row, how many rows are there? 2. If 10 United States muslin flags can be bought for 80c., what will one flag cost? 3. A box containing 500 balls of twine is packed 10 balls deep; how many balls are there in one layer? 4. A plat of ground containing 100 square feet was sold for $300; what was the selling price per square foot? 5. At the end of a week 100 mill operatives, hired at the same rate, receive $700; what is each one paid? 6. The machines which they run cost $2,000; what was the price of one machine? 7. In a room containing 240 looms one man is able to run 10 looms; how many men are required to run them all? 8. A 10-cent spool of silk holds 100 yards; how many spools are needed to hold 5,000 yards? WRITTEN : 1. For Fourth of July decoration three merchants each bought 100 yards of bunting at 12c. a yard; what amount was paid by the three men? 2. A merchant sells 100 tops at 5c. apiece, 100 balls at 10c. each, and 1 10 kites at 25c. each; what was the amount received from each sale? From all the sales? 3. Mary bought 10 yards of linen at 75c., 100 skeins of silk at 3c. a skein, and 10 yards of ribbon at 36c. a yard; how much did she pay for each purchase? How much did she pay for all? 4. A fruit grower sells at wholesale a 5-pound basket of grapes for 12c.; what does a grocer pay for 10 baskets? 5. Each of 100 delegates to a political convention is to be supplied with a badge of ribbon 9 inches long; how many inches will be needed? How many yards? 6. On one evening 100 people each paid 25c. admission to an entertainment, and the following evening 150 people did the same; what were the receipts of both evenings? 7. A business man orders 10 pounds of white bond paper at 50c. a pound, 30 envelopes at 40c. per 100, and 500 business cards at 35c. per 100; what is his bill? 8. Eight feet of rope is needed to raise a window awning; how many feet of rope is necessary to furnish 100 windows of an office building with awnings? 9. A wheat farm of 100 acres produced one year 58 bushels to the acre, the next year 50 bushels to the acre, and the third year 49 bushels to the acre; what was the total crop for the three years? = IV. When a pupil is led to see that 50 is 1⁄2 of 100 just as 5 is 1⁄2 of 10, that 897 96 just as 97 16, that 4 fifties are 200 just as 4 fives are 20, and so on, he is learning the most useful short processes. The following are suggestive exercises: 1. Mr. Grant told his two sons that he would give each one 1⁄2 as much money as he could earn in a day. One boy earned 10c, the other earned $1. What amount did the father give to each? 2. Out of a bag containing 20 chestnuts 5 were bad; and out of a bag containing 100 walnuts 25 were bad; what part of each kind were poor? 3. Philip planted 9 hills of potatoes in his garden. His father planted 90 hills; if of the vines in each garden were blighted, how many did Philip lose? How many did his father lose? 4. When 1⁄2 the marshmallows from a box containing 20 are gone, and from a box containing 200; how many will be gone from each? The three following exercises in rapid work will teach most quickly the constant relation of the digits in addition: 8. Charles had 15 marbles and his brother gave him 8 more; how many had he then? George had 35 marbles, and his uncle gave him & more; how many had he? 9. Elsie gave away 7 roses from a bunch of 24; how many had she left? Blanche gave away 17 pansies from a bunch of 44; how many pansies were left? 10. A small boy picks 4 quarts of berries in an hour, and his older brother picks 8 quarts in the same time; how many quarts can each pick in 10 hours? 11. A dealer in toys bought 4 carts at $6 apiece. A dealer in wagons bought 4 buggies for $60 apiece. What did each pay for his purchase? 12. In one bookcase there are 20 books, in another 200 books; if the capacity of each were doubled, how many books would each one hold? FOURTH YEAR. In the tourth year it is safe for pupils to practice adding by tens in column work. Thus, in the example, the braces at the right show how the pupil may read the right hand column to see that the sum is 30. When the tens do not occur so regularly as in the case of the left column, more practice is required. But the plan of adding by tens is of great value in facilitating the process. I. The following exercises will illustrate: 43 (61) } 45 10 25 163 42 25 |