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IVISON, BLAKEMAN, TAYLOR & CO.,

PUBLISHERS,

NEW YORK AND CHICAGO.

1880.

Mathematical Series.

Graded to the wants of Primary, Intermediate, Grammar,

Normal, and High Schools, Academies, and Colleges.

Progressive Table Book.
Progressive Primary Arithmetic.
Progressive Intellectual Arithmetic.
Radiments of Written Arithmetic.
JUNIOR-CLASS ARITHMETIC, Oral and written. NEW..
Progressive Practical Arithmetic.
Key to Practical Arithmetic,
Progressive Highor Arithmetic.
Key to Higher Arithmetic.
New Elementary Algebra.
Key to New Elementary Algebra.
New University Algebra.
Key to New University Algebra.
New Geometry and Trigonometry. In one vol.
Geometry, Plane and Solid. In separate vol.
Trigonometry, Plane and Spherical. In separate vol
New Analytical Geometry and Conic Sectio
New Surveying and Navigation.
New Differential and Integral Calculus.
University Astronomy-Descriptive and Physical,
Key to Geometry and Trigonometry, Analytical Geometry and Conio Soce

tions, Surveying and Navigation,

Entered, according to Act of Congress, in the year 1858, and again in the year 1863, by

DANIEL W. FISH, A.M., In the Clerk's Office of the District Court of the United States, for the Northern

District of New York,

PREFACE.

This primary work is designed for small children, and as an easy introduction to the “ Progressive Intellectual Arithmetic,” for advanced classes.

Its object is to lead the young pupil, by brief and simple processes, applied to practical examples of easy gradation, to acquire habits of thought and of reasoning, in their simplest forms, and to draw out and strengthen the mind by a progressive and almost imperceptible gradation of thought and expression.

The operations of Adding and Subtracting, of Multiplying and Dividing, are first shown by pictorial objects; portions of the elementary tables are introduced at the commencement of each lesson, and applied to short examples concerning familiar objects; promiscuous reviews of the elementary tables, and the more simple and easy Denominate tables have been introduced. Fractions have been treated as far as was thought practicable in a work of this kind.

It is confidently believed that the progressive and systematic arrangement, the simplicity and adaptation to the juvenile mind, the typography and general attractiveness of this little book, will insure for it abundant

success.

THE AUTHOR.

(3)

SUGGESTIONS TO TEACHERS.

1. A TEACHER should have a particular time allotted to every exercise, and regular lessons should be assigned, to be recited each day at a specified hour.

2. Sufficient time being given the pupils to learn their lessons, they should not be allowed the use of the book at the time of recitation.

3. The teacher should first ascertain that the table is thoroughly learned by every pupil in the class.

4. Each question should be slowly and distinctly read, and the pupils be called upon promiscuously; the pupil called upon should stand erect, repeat the question, and then give the solution. This will require close attention.

5. A correct and uniform analysis of each question should be required from every pupil.

6. The class should be encouraged to detect and correct errors in the statement and solution of questions, to be signified by raising the hand.

7. The teacher can extend the questions in each lesson at pleasure, either by repeating those given, or making additional ones.

(4) FARVARD UNIVERSITY

LIBRARY

LESSON I.

1. What is the first thing to be taught and learned in Arith

metic? Ans. Counting. 2. What is counting? Ans. Expressing numbers by words. 3. What is a number: Ans. A unit, or a collection of units. 4. What is a unit: Ans. A single thing. 5. How may numbers be expressed ? Ans. By words, letters,

and figures. 6. Which is the most common method? Ans. By figures. 7. How many figures are used to express numbers ? ĂNS. Ten. 8. Name them. Ans. Naught, One, Two, Three, Four, Five, Six, Seven, Eight, Nine.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

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9. Count the bells on each of the above rows.

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