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PREFACE

This book covers the work in arithmetic that is usually assigned to the fifth and sixth school years. In Grade V there is usually a review of the fundamental operations with integers and United States money, a thorough study of the fractions of ordinary business, and a study of the denominate numbers used in practical life. The central feature of the year's work, in substantially all schools, is common fractions.

In Grade VI the central feature is usually decimal fractions, the other topics being practical measurements, a study of the best ways of solving problems, and an introduction to percentage. These are the topics discussed in the second half of this book, thus adapting it to the work of the sixth school year in all parts of the country.

Having always advocated the elimination of obsolete matter from arithmetic, as well as from other branches of mathematics, and having repeatedly urged the reduction of the number of separate topics and the avoidance of subjects in which the child has no immediate or remote interest, the authors take pleasure in presenting a series of books containing only those essentials of arithmetic which are needed in common life. More complete courses are offered in other books, but the teacher who sympathizes with the modern trend in education will find in this series all of arithmetic that the pupil must thoroughly know.

The arrangement of the book is topical, so that a pupil stays long enough with a subject at one time to acquire that feeling of mastery which is his right and privilege. Along with this sequence of topics, however, are two new features which are noteworthy : One is the Little Examinations, a brief series of tests covering each chapter in turn; the other is the Review and Drill section, also

placed near the end of each chapter, and furnishing a cumulative review of all preceding work. By the aid of these features a teacher may be assured that the pupil is kept refreshed upon those essentials of computation without which he cannot hope to succeed.

In the theory of the work the authors have no more sympathy with the idea that a pupil should be told to do a thing in a certain way, with no knowledge of why this way is the right one, than they have with the notion that he must explain every operation with all the care that a textbook writer would show. They believe that every process should be learned as a reasonable one, with an appeal to the pupil's understanding, and that thereafter it should become entirely mechanical; and in this way each operation has been presented in this book.

As to the applications, the effort has been to select the problems with reference to the life and interests of our people to-day. Groups of related problems are frequently given, and the isolated problems are, in general, typical of those which the pupil will need in the ordinary walks of life. The applications are more numerous than is usually the case in textbooks, but these applications are not permitted to exclude the abstract drill work without which no pupil has ever become a good computer. To balance adequately the abstract and the concrete, the drill work and the applied problem, the review work and the new material, has been one of the earnest endeavors of the authors in the preparation of this series.

When a pupil reaches this stage, certain features needed in the primary grades become unnecessary. He is now quite as interested in the process itself as he would be if a fictitious concrete dress were given to it, and he is quite prepared to abandon the use of objects, except in such cases as the introduction to percentage and the theory of fractions.

The authors hope that their effort to prepare a perfectly usable textbook for Grades V and VI, free from all eccentricities, will prove to be helpful to teachers and to pupils alike.

GEORGE WENTWORTH
DAVID EUGENE SMITH

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