IN ARITHMETIC GRADE III. BY WILBUR F. NICHOLS, A.M. 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 niany 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 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 short 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. WILBUR F. NICHOLS. HOLYOKE, September, 1897. INTRODUCTION TO GRADE III. The work of this book is designed for pupils of the third school year. It contains : 1, a review of the preceding book; 2, a continuation and extension of the work in the fundamental processes and in fractions ; 3, the introduction of several new principles in their simplest form, as Percentage. The exercises are divided into lessons for convenience. But this is not intended to indicate the amount which should be given for a single lesson. See general introduction. Better results will follow if the order indicated here is quite closely followed; for it combines new principles, and review of old principles, in such a way as to make the advance more uniform and thorough. V |