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. 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. HOLYOKE, September, 1897. WILBUR F. NICHOLS. INTRODUCTION TO BOOK V. THIS book contains a review of the work done in Book IV., the extension of the principles taught there to more difficult problems, and a few new topics. Notation and Numeration receive more attention. The work in fractions is extended to include multiplication and division, using only small denominators. The subject of bills is introduced under the head of decimal fractions. The subject of Compound Numbers is enlarged, and includes their addition. Examples in Percentage previously performed by using the common fraction representing the per cent, are now solved decimally. The work in measurements, believed to be a valuable feature of the previous grades, is here extended to area of circles, cylinders, and cones. Interest by an easy, short, and "business" method is taken up. The reason for introducing so many lessons of a miscellaneous character should not be overlooked. These lessons give a constant review, and are far more beneficial to a pupil than examples all classified and labeled for him. Lessons 1, 5, 10, 15, 20, 22, 25, 30, 32, 40, 42, 45, 50, 52, 55, 60, 62, 65, Lessons 9, 12, 14, 16, 24, 29, 33, 34, 39, 41, 46, 47, 48, 59, 61, 64, 66, 69, |