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 gives me pleasure to acknowledge my obligations to D. W. Fish, of Rochester, N. Y., a thorough, practical teacher, and who has, by my request, prepared this little book, which, it is confidently believed, will, by its progressive and systematic arrangement, its simplicity and adaptation to the juvenile mind, insure for it abundant success.

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.

LESSON I.

1. What is the first thing to be taught and learned in Arithmetic? 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? ANs. Ten. 8. Name them.

ANS. Naught, One, Two, Three, Four, Five, Six, Seven, Eight, Nine. 1, 2, 3, 4, 5, 6, 7, 8, 9.

1

2

3

4

One.

Two.

Three.

Four.

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

Nine.

Ten.

LESSON II.

1. What is Notation? Ans. Writing numbers.

2. What is Numeration? Ans. Reading numbers.

3. How many letters are used to express numbers? Ans. Seven.

4. What are they? Ans. I, V, X, L, C, D, and M.

5. What is this method called? Ans. The Roman method.

6. Why is it so called? Ans. Because it was first used by the Romans.

7. How many figures or characters are used to express numbers? Ans. Ten.

8. What are they? Ans. 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

9. What is this method called? Ans. The Arabic method.

10. Why is it so called? Ans. Because it was first used by the Arabs.

11. What may the ten figures used in expressing numbers be called? Ans. The Arithmetical Alphabet.

12. Can all numbers be expressed by these ten figures? Ans. They can, by repeating

and combining them.

LESSON III.

REMARK. This lesson presents the printed and written figures, and the Roman letters, by which numbers are commonly expressed. It should be carefully studied by children, until they can read the figures with facility when written on the black-board, or when they meet with them in books.