ELEMENTARY ARITHMETIC BY M. A. BAILEY, A.M. PROFESSOR OF MATHEMATICS IN THE KANSAS STATE NORMAL NEW YORK: CINCINNATI .:. CHICAGO WARVARD COLLEGE LISA 4 GIFT OF GEORGE ARTHUR PLIMPTON COPYRIGHT, 1898, BY M. A. BAILEY. AM. ELE. ARITH. E-P 1 PREFACE THIS book is intended to cover the first five years' work in arithmetic; it is the first of a two-book series, of which the second is the "American Comprehensive Arithmetic." It is divided into two parts: Part First, for primary classes; Part Second, for the three succeeding grades. The work is based upon the psychology of number. The need or demand which gives rise to each cumulative step in mental activity has been considered, and exercises have been prepared to develop this activity in harmony with the laws of the mind. Thus, after the pupil has learned how to find the value of 6+6 +6 +6 by addition, his attention is called to the need of a shorter process, and he is introduced to multiplication by a method founded upon this demand. Psychology requires also that the relations of "what is given" and "what is required" shall be clearly ascertained as a basis for deciding upon the plan of procedure. These relations are not confined in this book to ratio alone; i.e., to how many times one quantity contains another, but are extended more broadly to how much one quantity exceeds another. It is now recognized that suitable apparatus is as necessary to the teacher of primary arithmetic as to the teacher of the physical sciences. The apparatus called for in this book consists of paper, pasteboard, etc., and of toy money, blocks, and splints, which may be prepared by the teacher, or obtained of any dealer in kindergarten materials. Attention is called to the educative value of the illustrations. The attempt has been made to present every subject twice: first, 3 |