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its general plan, leaving the many other differences (which, doubtlessly, will be considered of much importance) to be found by those who study the book.
CHAPTER FIRST, SECOND, THIRD, and Fourth, treats respectively of Addition, Subtraction, Mulplitication, and Division of simple numbers; each of which is rendered familiar by an extensive collection of practical examples. The last Lesson in Chapter Second, consists of practical questions, which combine Addition and Subtraction. The last Lesson in Chapter Third, consists of practical questions combining Addition, Subtraction and Multiplication. Thus, an intimate connection between Lessons and even Chapters is kept up through the whole work, with the exception of Chapter Fifth, which contains a few of the most important tables of Weights and Measures; each of which is illustrated with appropriate examples. The table of Sterling Money, being foreign to our currency, has been omitted."
CHAPTER SIXTH is devoted to the subject of Fractions, and contains twenty lessons, in which many original combinations and concise solutions
CHAPTER SEVENTH consists of practical and intricate questions of various kinds, which require for their solution a thorough knowledge of the preceding Chapters. This Chapter (the greater part of which is believed to be found in no similar work) when thoroughly understood, will be of incalculable benefit to those who are studying, or intend to study Algebra.
CHAPTER EIGHTH includes Interest, Discount,
and per cent. of every description, in all their various modifications. The method of treating these subjects is original; and renders the rules in Written Arithmetic, under these heads (which are usually so incomprehensible to pupils) perfectly intelligible by reducing the whole to one continued train of reasoning.
It is believed that this Chapter, if thoroughly taught, cannot fail to quicken, strengthen, and develope the reasoning powers; bringing into exercise, as it does, nearly every principle taught in the twenty lessons of Chapter Sixth, and also the greater part of Chapter Seventh, it must of necessity cause the pupil to acquire the habit of systematically classifying his knowledge, that he may, at any time, be able to call to his aid, such portions of it as will assist in illustrating or demonstrating the subject under consideration;—a habit, of infinite importance to a person in every condition of life.
The mind is composed of a variety of faculties which require for their development appropriate and constant exercise. That Intellectual Arithmetic, properly taught, is better calculated, than any other study, to invigorate and develope these faculties, to produce accurate and close discrimination, and, to enable the pupil to acquire a knowledge of the Higher Mathematics with greater ease, cannot for a moment admit of a doubt.
J. F. STODDARD.
LIBERTY, JAN. 1849.
SUGGESTIONS TO TEACHERS.
To those whose experience is limited, the Author would beg leave to present the following suggestions in regard to the most approved methods of teaching this important branch of study.
First. The lessons should be assigned previous to recitation, to afford the pupil an opportunity for its examination: the use of the book, during class exercise, should be entirely prohibited.
Secondly.-To concentrate the attention of the whole class, questions should be assigned promiscuously, and not in rotation as is too frequently done.
Thirdly. No question should be read more than once, if done slowly and distinctly; the student should be required to reproduce and solve it without interruption, unless it be to make a necessary criticism or correction. Care should be taken that the language of the pupil be rigidly accurate, as to construction and articulation.
Fourthly. It is respectfully suggested that, the particular forms given for the solution of questions be carefully adhered to, unless, better ones should be devised by the teacher.
J. F. S.
1. 2 and 1 are how many ? 2. 2 and 2 are how many 3. 2 and 3 are how many ? 4. 2 and 4 are how many ? 5. 2 and 5 are how many ? 6. 2 and 6 are how many ? 7. 2 and 7 are how many ? 8. 2 and 8 are how many ? 9. 2 and 9 are how many ? 10. 3 and 2 are how many ? 11. 3 and 3 are how many ? 12. 3 and 4 are how many ? 13. 3 and 5 are how many ? 14. 3 and 6 are how many ? 15. 3 and 7 are how many ? 16. 3 and 8 are how many ? 17. 3 and 9 are how many? 18. 4 and 3 are how many ? 19. 4 and 4 are how many ? 20. 4 and 5 are how many ? 21. 4 and 6 are how many? 22. 4 and 7 are how many ? 23. 4 and 8 are how many? 24. 4 and 9 are how many?
25. James killed 2 birds and John 1 ; how many did they both kill?
26. Gave 2 cents to Henry, and 2 cents to Harvey; how many cents did they both receive?
27. Hiram had 2 cents, and his brother gave him 3 more; how many had he then ?
28. George gave me 2 apples, and Mary gave me 4; how many did they both give me?
29. A man had 2 cows, and he purchased 5 more; how many cows did he then have?
30. John's father gave him 2 oranges, and his mother gave him 6; how many did he receive in all ? 31. Philo bought 2 peaches, and his brother gave him 7 more; how many has he in all?
32. Philip gave me 2 plums, and Myron gave me 8; how many did they both give me?
33. A farmer had 2 horses, and bought 9 more; how many had he then?
34. William had 3 candies, and Moses gave him 2 more; how many did he then have ?
35. John had 3 apples, and I gave him 3 more; how many had he then?
36. Philip gave 3 cents for some nuts, and 4 cents for some candies; what did he pay for both?
37. I paid 3 cents for some wafers, and 5 cents for a stamp; what did they both cost me?
38. A merchant bought 3 barrels of sugar, and 6 barrels of molasses; how many barrels did he then have?
39. Ralph is 3 years old, and Edward is 7; what is the sum of their ages ?
40. A lemon cost 3 cents, and a pine-apple cost 8; what was the cost of both ?
41. James solved 3 questions in arithmetic, and Oliver 9; how many did they both solve?
42. If it take 4 yards of cloth for a coat, and a pair of pants, how many yards will it take for both?