THE

UNIV. OF
CALIFORNIA

NATURAL ARITHMETIC

BOOK III

BY

ISAAC O. WINSLOW, M.A.

PRINCIPAL OF THAYER STREET GRAMMAR SCHOOL

PROVIDENCE, R.I.

NEW YORK.:. CINCINNATI .:. CHICAGO
AMERICAN BOOK COMPANY

PURPOSES AND DISTINCTIVE FEATURES

THE purposes of this series of Arithmetics are: 1. To present the subjects in a spiral order.

Instead of presenting the general subjects of addition, subtraction, multiplication, division, fractions, etc., as complete wholes in regular succession, each subject is divided into parts with reference to the difficulty of the principles involved. The easier principles of various subjects are treated together, while the more difficult principles are reserved until the child has gained the power to apprehend them easily.

2. To make the work easy.

In the belief that it is better to keep mathematical work a little behind the child's mental grasp than to advance it beyond that limit, the work designed for the different grades has been made somewhat easier than that usually found in text-books. The pupil is kept busy with a varied application of the principles that he has already mastered instead of being too rapidly crowded forward into greater difficulties.

3. To give the subject variety and interest.

The problems are based upon facts and principles gathered from the different branches of study, as history, geography, nature study, astronomy, and physics, as well as on the customary commercial transactions, thus correlating arithmetic with other studies and adding distinctly to its vividness and interest.

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4. To develop genuine mathematical thought.

There is a large amount of mental work interspersed with the written work. Each new subject is first developed with numbers that are not too large for mental solution. After the principle has been well established, written practice with larger numbers is introduced. Originality is also promoted by exercises requiring the pupils to make problems for themselves from given data.

5. To give prominence to the idea of magnitude.

The psychological fact that all mathematical knowledge is a system of relations, or ratios, has been recognized throughout the series. For the purpose of suggesting to the pupils the application of number to magnitude, the simple geometric forms have been gradually introduced.

In Book III the treatment of the several branches of the subject is completed, and, as a means of bringing together the parts of each subject in a general review, a summary is given of all the processes involved in common fractions, decimal fractions, and percentage.

A simple treatment of algebraic methods with a development of the algebraic equation is made a special feature of the book. In order to correlate arithmetic and algebra, problems are frequently introduced which admit of either. an arithmetical or an algebraic solution.

To relieve the lack of interest which a prolonged continuance of drill in abstract processes is liable to produce, many of the problems are based upon interesting facts in ature and life.

INDEX

The numbers refer to pages.

Addition of common fractions, 155. | Common fractions, summary of pro-

Algebraic multiplication, 130, 131, Construction, 87, 109, 147, 187,

Algebraic problems, 31, 32, 33, 75, Cube root, 198.

Astronomy, problems from, 41, 57, Discount, 196.
178, 249.