NEW EDITION, REVISED AND ENLARGED. MENTAL ARITHMETIC, UPON THE INDUCTIVE PLAN. DESIGNED FOR PRIMARY AND INTERMEDIATE SCHOOLS. BY BENJAMIN GREENLEAF, A. M., BOSTON: PUBLISHED BY ROBERT S. DAVIS & CO. NEW YORK: D. APPLETON & Co., AND MASON BROTHERS. 1861. Educt 118.61.438 Entered according to Act of Congress, in the year 1845, by BENJAMIN GREENLEAF, In the Clerk's Office of the District Court of the District of Massachusetts. Entered according to Act of Congress, in the year 1851, by In the Clerk's Office of the District Court of the District of Massachusetts. MAR JUL 30 918 13. HellCambridge. GREENLEAF'S SERIES OF MATHEMATICS. 1. MENTAL ARITHMETIC, upon the Inductive Plan; designed for Primary and Intermediate Schools. Revised and enlarged edition, 144 pp. 2. INTRODUCTION TO THE NATIONAL ARITHMETIC; OR, COMMON SCHOOL ARITHMETIC. Improved stereotype edition. 324 pp. 3. THE NATIONAL ARITHMETIC, for advanced scholars in Common Schools and Academies. New improved electrotype edition. 444 pp. COMPLETE KEYS TO THE INTRODUCTION, AND NATIONAL ARITHMETIC, containing solutions and Explanations, for Teachers only. 4. PRACTICAL ALGEBRA, for Academies and High Schools, and for advanced Students in Common Schools. New edition, revised & stereotyped. 5. ELEMENTS OF GEOMETRY, for Academies and High Schools, and for advanced Students in Common Schools. 320 pp. Just published. PREFACE. THE design of the author, in revising and enlarging this work, has been, to present to the mind of the learner a more complete collection of intellectual exercises than was contained in former editions. The object of the work is to teach the pupil how to think, and to enable him, by an almost imperceptible gradation of thought, to advance from the simplest forms of reasoning to the more vigorous exercise of the mind. Hence, no arbitrary rules have been introduced, and only such hints and suggestions, with occasional formulæ of reasoning, as were considered necessary for the profitable study of the lessons. A scholar should not be satisfied with results merely; - he should know the conditions, upon which those results depend, and be able, from those conditions, to give a reason for the results. Copious practical exercises have been introduced, in connection with the abstract questions, particularly in connection with Fractions, that the pupil may see the application of numbers to the common business of life. A larger amount of matter, it is believed, will be found in connection with the tables of money, weights, and measures, than is contained in any other similar work. There are also frequent lessons for general exercise, to refresh the mind in the preceding principles, and test the proficiency that the pupil is making as he advances. Several pages of Written Arithmetic have been introduced, at the close of the work, which can be used while the pupil is advancing in the Mental department, or omitted until that is finished. In most schools, however, pupils commence Written Arithmetic before they finish the more difficult parts of the Mental department. But in no case should the pupil be allowed the use of the slate in the performance of intellectual exercises. It is the opinion of the author, that a thorough understanding of this work will fully prepare the mind for the profitable study of the second book of the series. Bradford Seminary, November, 1851. B. GREENLEAF. SUGGESTIONS TO TEACHERS. Ir is respectfully suggested, that, in using this work, the pupil should be taught, from the commencement, to give a clear Analysis of every question he performs. Many teachers permit their pupils to use their books in the class, by reading each question before solving it. Other teachers prefer to read the questions themselves to the whole class, and then call upon some one for a solution. By the former method of recitation, the class appears better, and makes a finer show to the spectator. By the latter mode, the attention of each member of the class is gained in every question, and more earnestness of thought elicited. The practice of permitting a class to answer in concert, whereby the palm of scholarship is carried off by the most boisterous, cannot be too highly censured. With very small children, however, the multiplication table may be repeated in concert, care being taken to avoid an unpleasant "sing-song" tone, in the exercise. A sufficient number of notes for the teacher, and explanations for the scholar, are introduced, to lead to a profitable use of the work. B. G. MENTAL ARITHMETIC. .1. ADDITION. LESSON I. I IF you wish to know how many fingers you have on your right hand, what must you do? ANSWER. should count them. 2. What, then, is counting? ANS. - Finding the number of things. 3. When you count, with what number do you always commence ? 4. Count the cups in each of the following rows. |