་་་UU་ Cuirmitee of the City of B GRADED LESSONS IN ARITHMETIC BOOK VIII. BY WILBUR F. NICHOLS, A.M. PRINCIPAL HAMILTON STREET SCHOOL, HOLYOKE, MASS. BOSTON Educ T 119.08.612 HARVARD COLLEGE LIBRARY GIFT OF BOSTON SCHOOL COMMITTEE LIBRARY COPYRIGHT, 1899, 1905, BY WILBUR F. NICHOLS. GENERAL INTRODUCTION. 1. THESE lessons have been prepared in the belief that it is a mistake to assume that one topic is to be finished before another is begun. The elements of many topics are here given in lower grades in explanations, illustrations, and examples easily understood by the younger pupils; and then the work in each topic is made more and more difficult through the various grades until it is finished. These examples have stood the test of the school-room, and in no case have they been found too difficult. 2. The arrangement of the topics is such that pupils in passing into a new grade find but few new topics, and many pupils are prepared for promotion from grade to grade at various times during the year, and are not obliged to wait for the annual promotions. 3. Such practical subjects as Percentage and Interest are introduced in the lower grades, where many pupils are found who are obliged to leave school before they reach the more advanced grades. 4. Clear conceptions of geometric forms and mensuration are introduced at an early period, that principles thus developed may be applied to many practical problems. 5. One or more lessons are given to the developing of a new topic; then the following lessons are so arranged as to give the pupils practice in applying the new topic in iii connection with all the other topics previously learned. This constant review will be found very beneficial. On 6. Few teachers will find the need of supplementary work, as so large a number of problems are given. the other hand, few pupils should be required to solve all the problems. It is a good way to assign for required work for all the class that number of examples which even the slowest child can do, and then allow any child to work the remaining examples of the lesson as optional work. 7. The large amount of oral or mental examples will be appreciated by those who believe that ten minutes each day should be given to work of this kind. These are not mental gymnastics, but plain, practical, every-day questions. 8. The introduction of Algebra and Geometry in the higher grades will be found beneficial. 9. The methods here advocated are the shorter methods found in daily use among bankers, mechanics, and merchants. 10. Commencing in Book IV., and continuing through the series, we have frequently given only statements of certain problems. This tends to develop thought power, for the pupils must determine first what can be found, and then how to find it. The author desires to express his acknowledgments for many valuable suggestions to Mr. C. H. Morss, Superintendent of Schools, of Medford, Mass. WILBUR F. NICHOLS. INTRODUCTION TO BOOK VIII. THIS book completes the ordinary grammar school course in arithmetic, and covers all the work not included in the preceding books of this series. It is suggested, however, that, in places where there are nine grades, some topics should be omitted from the eighth grade and presented in the ninth. The number and variety of problems in each new subject furnish sufficient practice for the complete mastery of that subject. The same system of frequent reviews pursued in the lower books has been followed in this, with many examples in fractions and percentage, in order that the pupils may acquire facility and accuracy in ordinary business computations. The aim has been to furnish material sufficient to meet the demands of any school. Any teacher using this series of books should omit any topic or example which seems to him unnecessary. The work in algebra has been continued to include a knowledge of the fundamental principles and of the equation. The constructive and inventional work in geometry is continued, and a little demonstrative work introduced. |