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Entered, according to act of Congress, in the year 1832, by FREDERICK EMERSON, in the Clerk's Office of the District Court of Massachusetts.

IL A Key to this work, containing solutions and answers, (for teachers only,) is published in a separate volume.



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This book is intended for the use of scholars who have been taught in ́ · Part First,' or by some other means have learned to add, subtract, and multiply numbers as high as 10, mentally.

The whole Course of Exercises, of which this is the Second Part, has been divided into three parts, more for the sake of economy and convenience, than on account of any natural division of the subject. The work is not intended to be a record of the science,

--such as might befit the pages of an encyclopedia,-but, a system of induction, through which the scholar may be led to the discovery of arithmetical truth, and the proper application of arithmetical operations. Rules, and the technical language necessary to their composition, are avoided in the early part of the

they are not introduced until the learner is supposed prepared, by intellectual improvement from previous lessons, to meet them understandingly.

In the arrangement of the exercises in this volume, I have been governed by the natural order of the science; believing, that any deviation from that order, with a view of rendering the work more immediately practical, would render it in reality less practical, as it would necessarily lead the scholar into a habit of performing operations, without comprehending the principles which justify them. The first six chapters consist of oral exercises, and the last six of correspondent written exercises. The work may therefore be viewed as two entire systems of arithmetic-Oral and Written.

Although Part Second does not complete the series of books, entitled • The North American Arithmetic,' still it contains the essential principles, and the common application of the science. Scholars, therefore, who shall be properly conducted through this volume, will have acquired a knowledge of Arithmetic, adequate to all the purposes of common business. Part Third is designed for those, whose continuance at school shall afford opportunity for prosecuting a more extended course of study.

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The mode of teaching arithmetic, and the text-books, used for the purpose, in a great portion of our country, are radically defective. Much of arithmetic is practised at school, but little is learned. The scholar is put to ciphering without adequate mental preparation, and is referred to the direction of rules, whose phraseology and principles are to a learner equally obscure. By a tedious course of practice, perhaps he acquires a certain mechanical dexterity in performing operations; but no sooner does he enter upon the business of life, than he abandons the rules of his book, and, in his own way, learns so much of arithmetic as his occupation requires.

Whether the following treatise is calculated to afford any remedy for the defects I have alluded to, others will decide. I shall spare myself the task of a prefatory detail of what the author conceives” to be its advantages, and will only add, that the design and execution of the work, have cost me much time and labor.

F. EMERSON. Boston, January, 1832,

NOTE TO TEACHERS. It will be most advantageous for young scholars, to go through with all the Oral Arithmetic before they enter upon the Written Arithinetic. Older scholare, however, after performing the exercises in the first chapter of Oral Arithmetic, may pass immediately to the exercises in the first chapter of Written Arithme. tic: and after concluding this chapter, may take up the two second chapters in the same order; and thus proceed through the book.

Much time has been wasted in some of our schools, by the practice of teaching individually, instead of teaching in classes. If this practice has been owing in any degree to the arrangement of text-books, it is hoped the present arrangement will afford a remedy. There can be no more objection to a distinct classification of a school for the purpose of teaching arithmetic, than there is to a like classification for the purpose of teaching orthography: and the advantages of class-instruction in the former branch, are as great as those in the latter.

The examples contained in the first six chapters, do not require the use of the slate. The answers, with the process of obtaining them, and the reasons which justify the process, are to be given orally. For example, the following question inay be supposed to give rise to the subjoined exercise.

Example. A trader purchased 9 barrels of flour, at 7 dollars a barrel, and sold the whole for 68 dollars. What did he gain in the trade? Pupil. He gained five dollars.' Teacher. "How do you perceive it?' Pupil. If one barrel cost seven dollars, nine barrels must have cost nine times seven dolars, which is sixty-three dollars. He must have gained the difference between sixty-three dollars and sixty-eight dollars. 63 from 68 leaves 5.'

Learners should not be confined to any form of expression in solutionstheir reasoning should be their own. By a little practice, they will acquire an astonishing acuteness of apprehension, and facility of expression,




Section 1. When we have a large number of articles to count, such as quills, nuts, cents, &c., we may, if we please, count them by tens. Let us suppose we have a quantity of cents before us, and proceed to count them as follows.

We first count out ten cents, and lay them in a pile. We then count out ten more, and lay them in another pile; then ten more for another pile; and thus we continue to count out ten at a time, until we have counted ten piles. We put these ten piles together, and they make a large pile containing One Hundred cents.

Again we count out ten cents at a time, until we have counted ten small piles, as before. We

We put these together, and they make a large pile containing one hundred, like the hundred we first counted. We have now counted two hundred cents, and they lie in two large piles.

Having learned what is meant by two hundreds, we proceed to count out one hundred cents more; and after placing them by the side of the two hundreds, the three piles make three hundreds. Four large piles will be four hundreds; five piles will be five hundreds; six piles will be six hundreds; seven piles will be seven hundreds; eight piles will be eight hundreds; nine piles will be nine hundreds; and when we have counted out ten of these piles, we put the whole together. They make a pile still larger, and the number of cents contained in it is One Thousand,

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