The Stone Arithmetic

THE

STONE ARITHMETIC

ADVANCED

JOHN C. STONE, A.M.

STATE NORMAL SCHOOL, MONTCLAIR, NEW JERSEY, AUTHOR OF THE
TEACHING OF ARITHMETIC, HOW TO TEACH PRIMARY NUMBER,

A CHILD'S BOOK OF NUMBER, AND JUNIOR HIGH SCHOOL
MATHEMATICS, AND CO-AUTHOR OF THE STONE-MILLIS
SERIES OF ELEMENTARY AND SECONDARY

615206

BY BENJ. H. SANBORN & CO.

PREFACE

A TEXTBOOK in arithmetic for seventh and eighth grades should do three distinct things: (1) It should furnish material that will develop a high degree of accuracy and reasonable speed in the necessary processes with whole numbers, fractions, and decimals. (2) It should give the pupil the accurate and practical knowledge that is necessary for the interpretation of references to those modern industrial and business terms and problems that are met in the common walks of life. And (3) it should furnish a means of developing the powers of "arithmetical reasoning" so that the pupil may successfully attack problems that he has not met before. In other words, it should furnish a means of developing a real mathematical type of thinking in quantitative relationships.

To meet the first of these requirements, each grade devotes one chapter to computation. These drill exercises are also diagnostic tests. They show the time limit usually allowed for each, and test the various fundamental abilities needed in building up the final finished processes. While grouped in one chapter for the conveniences of the pupil and the teacher, they should be used frequently throughout the year until satisfactory standards have been attained.

To meet the second requirement, chapters are devoted to graphs, to practical problems of measurement, to indirect measurement, and to those civic and business terms and problems met in modern. life. To make those civic and business topics concrete and vital, problems are introduced by some situation within the experience or comprehension of the pupil. For example, see the problems in discount and commission, and the introduction to stock corporations, to taxes, and to insurance.

The third purpose of this text is one that has been greatly neglected in recent texts and courses of study. This neglect is due

to the false notion that "practical arithmetic" means only the arithmetic met in our daily affairs, and that the problems should be solved largely through memory alone. But there is a quantitative side to most questions of human activity, quite outside of one's own personal problems met in buying or selling food, shelter, and clothing. Hence power to see and express quantitative relationships is indispensable to one's understanding of many phases of human interest. Such power is quite as "practical" to an intelligent and alert person as the mere utilitarian side of life.

With this concept of the purposes of arithmetic in mind, the author has devoted one chapter in each grade to a study of "method of attack" in solving a new problem and has given many problems to develop "arithmetical reasoning.' There are also many "reasoning tests" and "tests in quick thinking" throughout the two grades.

The text, then, not only meets the needs of the pupil who can get type problems only through memory, but the needs of those pupils who are capable of greater mathematical training. It thus furnishes the means by which each individual pupil may achieve all of which he is capable in skill in computation, knowledge of the practical affairs of life, and in the development of "arithmetical reasoning."

FEBRUARY, 1925

JOHN C. STONE

CHAPTER

CONTENTS

SEVENTH GRADE: FIRST SEMESTER

I. COMPARING NUMBERS

Topics: Comparing two numbers by division (1); Approxi-

mate relations of large numbers (5); Relations shown by graphs

(6); Constructing graphs (7); Using squared paper in construct-

ing graphs (8); Broken-line graphs (9); Finding data and con-
structing graphs.

II. REVIEWING THE FUNDAMENTAL PROCESSES

Topics: Exercises in addition (12); Checking addition (13);