NEW

MENTAL

ARITHMETIC:

FOR

PRIMARY DEPARTMENTS

BY JAMES .B. THOMSON, LL. D.,

AUTHOR OF DAY & THOMSON'S ARITHMETICAL SERIES; EDITOR OF DAY'
SCHOOL ALGEBRA, LEGENDRE'S GEOMETRY, ETC.

NEW YORK:

CLARK & MAYNARD, PUBLISHERS,

5 BARCLAY STREET

1876.

T

#575 Edur 7118.76.530 78, Nov.16

Math 474.1.3/5/ Gift of

Educt Goi. 5. M. Higginson 6.4.15.41) 1872 THOMSON'S NEW GRADED SERIES.

of Cambridge

IN THREE BOOKS.

I. NEW MENTAL ARITHMETIC.
(For Primary Departments.)

II NEW RUDIMENTS OF ARITH-
METIC. (For Intermediate Departments.)

III. NEW PRACTICAL ARITHMETIC.
(For Grammar Departments.)

THOMSON'S SUPPLEMENTARY COURSE.
FOR HIGHER INSTITUTIONS. (In preparation.)

Entered according to Act of Congress, in the year 1872, by
JAMES B. THOMSON,

In the Office of the Librarian of Congress, at Washington, D. C.

Electrotyped by SMITH & MCDOUGAL, 82 Beekman Street, N. Y.

PREFACE.

THE New Mental Arithmetic now presented to the public, is the first of the three books which constitute the author's 66 'New Graded Series."

The work is designed for primary classes. It begins with Counting, and proceeds step by step through the simple combinations of whole numbers, the elementary operations in Fractions, and closes with a few practical exercises in Compound Numbers. The questions, at first, refer to sensible objects with which the pupil is familiar. As he becomes acquainted with the solution of concrete examples, he is gradually introduced to those containing abstract numbers and more difficult combinations.

From the outset, the learner is taught to illustrate for himself the increase and decrease of Numbers, the formation of the Tables, etc., by counters, the slate, and the black board. This method has been adopted from a conviction of its superiority as an educational force, over others in use.

I. All admit that the first lessons in counting and the combinations of numbers should be given in connection with sensible objects-objects addressed to the eye, or the touch, or to both. But counters can be both seen and handled by the pupil; therefore they have a decided advantage over pictures, which are presented to the eye only.

2. Next, the method by counters has the merit of flexibility and comprehensiveness. Instead of a few stereotyped objects on a printed page, selected for the occasion, and incapable of change to meet the different conditions of other questions, the slate, the blackboard, and surrounding portable objects present facilities for illustration as diversified as the varied conditions of problems, and as comprehensive as the operations and principles to be illustrated.