MATHEMATICS FOR COMMON SCHOOLS PART II GRAMMAR-SCHOOL ARITHMETIC INCLUDING EASY ALGEBRAIC EQUATIONS AND SIMPLE GEOMETRICAL PROBLEMS BY JOHN H. WALSH ASSOCIATE SUPERINTENDENT OF PUBLIC INSTRUCTION, BROOKLYN, N.Y. BOSTON, U.S.A. D. C. HEATH & CO., PUBLISHERS MARYARD COLLEGE LIBRARY GRADUATE SCHOD OF EDUCATION COPYRIGHT, 1895, BY JOHN H. WALSH. Norwood Press : J. S. Cushing & Co. - Berwick & Smith. PREFACE. THE PRIMARY ARITHMETIC, Part I., of the two-part edition of MATHEMATICS FOR COMMON SCHOOLS is designed to cover the work of the first four years, and contains those portions of the subject needed by all pupils of the common schools: addition, subtraction, multiplication, and division of whole numbers; simple fractions; and the most commonly used denominations of compound numbers. Part II., the GRAMMAR SCHOOL ARITHMETIC, completes the ordinary grammar-school course in this subject, and contains, besides, two chapters on algebraic equations and one on elementary constructive geometry, with applications. The first algebra chapter should be taken up with the seventh year's work in percentage and interest. The remaining one, Chapter XV., may be profitably studied where there is time to continue this subject. Although placed at the end of the book, it is intended that suitable portions of the geometry work of Chapter XVI. be taught from time to time during the last two years of the grammar school. The special features of the work are its division of the arithmetical portion into half-yearly chapters, instead of the ordinary arrangement by topics; the omission, as far as possible, of rules and definitions; the very great number and variety of the examples; the use of the equation in the solution of arithmetical problems, especially in those of percentage and interest; and the introduction of the elements of algebra and geometry. Believing that there is some foundation for the complaints frequently made by business men and high-school teachers that grammar-school graduates are too often slow and inaccurate in ordinary computations, the author has furnished throughout the entire work systematic drills and reviews in the addition, subtraction, multiplication, and division of ordinary numbers and of fractions. In this endeavor to enrich the grammar-school course in mathematics, the attempt has not been made to shorten it so much as some may desire. The intelligent teacher can and should do the remainder for himself, by rigorously omitting all such topics as he finds unnecessary. BROOKLYN, N. Y., January, 1895. J. H. W. |