REMARKS,

TO TEACHERS ON THE METHOD OF USING THIS BOOK.

BY omitting the recital of the rules and all the exercises that follow them as far as Interest; a course of study may be formed, peculiarly adapted to the capacities of beginners, and it is accordingly recommended to the consideration of teachers as forming a complete system of mental arithmetic.

In the review or second course, it will be well for the pupil to omit nothing. And it is thought to be of very great importance, that he should not be directed to commit the rule, until he has first performed a practical example on his slate, agreeable to the directions involved in the questions respecting the work, which are given in the book; diligently comparing this process with the rule. After having done this he will be prepared to learn his rule understandingly the recital of which should immediately follow.

It will be recollected that all the examples which precede those denominated "Exercises for the Slate," are designed to be performed mentally. This includes some examples preceding the rule and some following it. The latter are not designed for the above course of mental arithmetic, but are to be performed in the mind subsequently to the recital of the rule.

In the review it will be well for the pupil occasionally to perform the examples for mental exercise on the slate at recitation, for it often happens that the learner will solve questions in his mind which he could not with the slate.

The following course is designed for those who have not time or opportunity to devote to the whole contents of the work, and may be pursued independently of the other parts, as no embarrassment will arise from their omission, and it is thought sufficient for ordinary business transactions, viz. the whole, with the exception of the Compound Rules and Currencies, as far as Equation of Payments.

The above mentioned method is what the Author himself, has adopted; it may not perhaps be productive of the greatest good to the pupils for others to pursue the same course. Every intelligent teacher has a method of his own, which although not best in fact, still may be on the whole, the best for him. It is therefore left to his decision.

PART I.

FAMILIAR QUESTIONS,*

To be answered mentally without the slate,

IN FOUR SECTIONS.

SECTION I. Illustrates the principles and use of Addition, and

the Table.

II. Illustrates the principles and use of Subtraction, and the Table.

III. Illustrates the principles and use of Multiplication, and the Table.

IV. Illustrates the principles and use of Division, and the Table.

SECTION I.

1. How many little fingers have you on your right hand? How many on your left? How many on both? 2. How many eyes have you?

3. If you have two apples in one hand, and one in the other; how many have you in both? How many are two and one then, put together?

4. How many do your ears and eyes make, counted together?

5. If you have two nuts in one hand, and two in the other; how many have you in both? How many do two and two make, put together?

6. If you have three pins in one hand, and James puts another in; how many will you have in your hand? How many are three and one then?

7. If you have three pins in one hand, and James puts two more in; how many will you have in your hand? How many are three and two then?

8. If you have four apples in one pocket, and two in the other; how many will you have in both? How many are four and two then?

*The Questions in Sec. I. and II. are intended for very young children. Older pupils may omit these. But the two remaining sections and the four tables will claim an attentive perusal.

9. Thomas has four cents, and William has three; how many have they both together? How many are four and three then?

10. You have five pins in one hand, and three in the other; how many have you in both? How many are five and three then?

11. You have four nuts in one hand, and four in the other; how many have you in both? How many are four and four then?

12. If you count the fingers and thumb on one hand, and only the fingers on the other; how many will they make? How many are five and four then?

13. How many fingers and thumbs have you, on both hands?

14. James has five marbles and Thomas five; how many have they both? How many are five and five then?

15. How many cents would it take, to buy two whistles, if one cost six cents, and the other four? How many are six and four then?

16. If you have eight pins on one sleeve, and two on the other; how many will you have on both? How many are eight and two then?

17. How many legs have two cats, and a bird?

18. If I should give you six cents, and you should find five; how many would you have then? How many are six and five then?

19. If you count all your fingers, thumbs, and nose; how many will they make ?

20. If you buy a picture book for ten cents, and a pear for two cents; how many cents will pay for both? How many are ten and two then?

21. How much money would you have, if your father should give you seven cents, and your brother six? How many are seven and six then?

22. If you have seven pins in one hand, and seven in the other; how many will you have in both? How many are seven and seven then?

23. A man bought a chair for three dollars, and a looking glass for twelve; how much did he give for both? How many are three and twelve then?

24. You give thirteen cents for a spelling book, and three for an inkstand; how much do they come to? How many are thirteen and three?

Note. The pupil is to recite the above, with the written numbers covered over. The answers to the following questions, are to be given by writing them down' on the slate at recitation, to test the pupil's knowledge of numbers, from one to one hundred.

Seven. Eight.

26. Write down in proper figures, Four. Twelve. Eighteen. Twenty two. Thirty two. Forty five. Forty nine. Fifty six. Fifty nine. Sixty three. Seventy five. Eighty seven. Ninety two. Ninety seven. Ninety nine. 27. James has seventy eight cents, and Rufus eighty seven cents; which has the most?

28. Thomas has fifty nine dollars, and William sixty nine; which has the most? Which is the most, eighty nine, or ninety nine? Forty seven, or seventy four?

29. Repeat the Addition Table.

2 and 1 are 3

3 and 1 are 4

4 and 1 are

3 and 2 are 5

4 and 2 are

3 and

3 are 6

4 and 3 are

2 and

4 are 6

3 and

5 are

4 and 4 are

4 and 5 are

567890

4 and 6 are 10 4 and 7 are 11 4 and 8 are 12 4 and 9 are 13 4 and 10 are 14 4 and 11 are 15 4 and 12 are 16

30. How many are 2 and 5? 2 and 7? 2 and 10? 2 and 12? 3 and 3? 3 and 9? 3 and 12? 4 and 2? 4 and 6? 4 and 8? 4 and 10? 4 and 12? 5 and 3? 5 and 5? 5 and 9? 5 and 11? 6 and 4? 6 and 7? 6 and 10? 6 and 12? 7 and 2? 7 and 4? 7 and 7? 7 and 9? 7 and 12? 8 and 2? 8 and 5? 8 and 7? 8 and 9? 8 and 10? 8 and 12? 9 and 6? 9 and 9? 9 and 12? 10 and 3? 10 and 4? 10 and 6? 10 and 8? 10 and 11? 10 and 12? 11 and 3? 11 and 5? 11 and 6? 11 and 9? 11 and 12? 12 and 3? 12 and 6? 12 and 9? 12 and 12?