IN ARITHMETIC GRADE VI. BY WILBUR F. NICHOLS, A.M. PRINCIPAL HAMILTON STREET SCHOOL, HOLYOKE, MASS. THOMPSON, BROWN & CO. 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 iv GENERAL INTRODUCTION. connection with all the other topics previously learned. This constant review will be found very beneficial. 6. Few teachers will find the need of supplementary work, as so large a number of problems are given. On 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. The author desires to express his acknowledgments for many valuable suggestions to Mr. C. H. Morss, Superintendent of Schools of Medford, Mass. HOLYOKE, September, 1897. WILBUR F. NICHOLS. INTRODUCTION TO GRADE VI. THE plan of development pursued in the previous books of this series is continued. The topics in Grade V. are reviewed in this book. Some topics, as Fractions, are completed, as special subjects; and others, like Percentage, enlarged. Compound Numbers are completed, and Ratio introduced. The latter subject will be found helpful in much of the higher work in Percentage, and it has been introduced a little earlier than usual. Two or three topics are placed at the end of the book so that they may be more easily omitted unless the course of study demands that they shall be taught. A thorough mastery of any subject comes only from repetition; hence many review exercises are given so that the pupil may be able to rely upon himself and learn to work absolutely without assistance. Principles are taught, and not rules; and the work is made practical, so that the pupil can be prepared for the affairs of every-day life. V |