INTRODUCTION. THAT frequent exercise in mental computations have a happy influence upon the mind, by inducing habits of attention, by strengthening the memory, and by producing a promptness of recollection, is, at present, universally admitted. And, that exercises of this nature should be more extensively introduced into our primary schools, is acknowledged and even urged by many of our most experienced and successful instructers. The success, which has, in most cases, attended the introduction of Mental Arithmetick, would doubtless appear incredible to those unaccustomed to it. But experience has shown, that children may, in this way, be made acquainted with the first principles of Arithmetick, at as early an age as they can be taught the Alphabet and its most simple combinations. Classes of children under nine years of age, by the force of memory and the aid of a few plain rules, without the assistance of pen or pencil, have been taught to multiply seven or eight figures by an equal number, enumerate and announce accurately the product, amounting to quintillions; and then extract the square root of this large product, and state the root and remainder, without varying a figure from the truth. In the ordinary course of instruction, Arithmetick has been studied only by the boys; and it has usually been deferred by them to the last portion of their attendance at school. The consequence has been, that few have become familiar with its first principles, before they have been obliged to quit school, and enter upon the business of life. Commencing the study of Arithmetick at this advanced period, the scholar is sensible he has but little time to devote to it, but, being determined to cipher through his book, he applies himself with diligence, yet he hurries on from rule to rule with such rapidity, that he learns nothing as he ought. He may indeed reach the end, and thus accomplish his principal purpose; but, of what he has gone over, scarcely a trace remains upon his mind. He has not even made himself thoroughly acquainted with any of the elements of the science; nor has he made himself so familiar with the rules, as to derive from them any considerable practical advantage. It is asserted with confidence, that children, after having learned to talk, cannot too soon be made acquainted with numbers, and exercised in mental computations. But care should be taken, that these exercises be adapted to the age and capacity of the child -that the questions proposed, be such as the child can fully comprehend. And as very young children are scarcely capable of the exercise of abstraction, the instructer will derive much advantage from the employment of sensible objects. The child will find no difficulty in conceiving sensible objects, that are before Lim, to represent such as are absent, even at an age when they could form no conception of abstract numbers. After making the child acquainted with the nature of the several operations by means of these objects, he should be directed to perform the same by the force of memory, and he will, in this way, soon become familiar with fundamental principles of Arithmetic, and his judgment, as it becomes matured by age, will direct him in the application of these principles to practical purposes. He will at the same time be acquiring habits of attention, and a promptness of computation, which will be of inestimable value to him in after life. All this may be done as an amusement, and a relaxation to the young mind, without interrupting, in the least, its other pursuits; and thus may every boy and girl, of ordinary capacity, be made more thoroughly acquainted with the elements of Arithmetick, before they arrive at the age of ten years, than most of our scholars are on leaving school, after having plodded through the whole Arithmetick in the ordinary way. A knowledge of Arithmetick, at the present day, is scarcely less necessary to the female sex than to our own, and if the course be adopted, which is here recommended, it is believed, they will not be found less capable of proficiency in this science It is hoped that our teachers, both male and female, will take this subject into consideration, and use their exertions to bring about a reformation so desirable in the course of arithmetical instruction. ADDITION. 1. I have two cents in one hand, I how much do I give for the cow and and one in the other; how many have I in both? 2. How many fingers have you on one hand? 3. How many on both? 4. If you count your thumbs with your fingers; how many will it make? 5. George has three apples in one pocket and two in the other; how many has he in both? 6. How many are three and two? 7. Henry has four cents and Geo. two; how many have both? 8. David gave three cents for a lemon and five for an orange; how many did he give for both? 9. Three and five are how many? 10. Peter had six cherries, and Dick gave him four more; how many had he then? 11. John had seven nuts and Peter gave him two more; how many had be then? 12. A man bought a barrel of flour for seven dollars, and a barrel of soap for four dollars; how much did they both cost? 13. A man has six cows at one barn, and eight at another; how many has he at both? 14. Eight and six are how many? 15. A person bought a hundred weight of sugar for ten dollars, and a barrel of flour for seven dollars; how much did he give for both ? 16. A man travelled four miles the ûrst hour, three the next, and two the next; how far did he travel in the three hours ? 17. If I give nine dollars for three sheep, and ten dollars for a cow, sheep? 18. Eight and four are how many? 19. Nine and five are how many? 20. Seven and seven are how many? 21. Seven & eight are how many? 22. Nine & eight are how many? 23. Nine & ten are how many? 24. Nine & nine are how many? 25. Eleven & nine are how many? 26. Twelve & nine are how many? 27. A boy gave to another boy six peaches, to another four, and had three left; how many had he at first? 28. A boy bought a slate for 22cts. a pencil for three, and a sponge for six; how much did they all cost? 29. A man gave seven dollars for a sleigh, gave six dollars for ironing it, and four dollars for painting it; what did the whole cost? 30. A drover bought twenty-three sheep of one man, seven of another, and five of another; how many did he buy of the three ? 31. A lady bought some pins for eleven cents, a comb for twenty-five, and some tape for eight cents; what did they all cost? 32. Nine and eight and six are how many? 33. Five and three and eleven are how many? 34. Seven and four and twelve are how many? 35. Thirty-five and six and four are how many? 36. Forty-seven and three and seven are how many? 37. A man bought a cow for seventeen dollars, a hog for five dollars, and three sheep for six dollars; what did they all cost? 40. How many are nineteen, and nine, and twenty-nine? 38. From Burlington to Montpelier it is thirty-eight miles, and from Montpelier to Woodstock it is forty41. A boy paid ten cents for a seven miles; how far is it from Bur-card of gingerbread, six cents for a lington to Woodstock? pint of plumbs, lost twenty-eight 39. A man bought a horse forcents at play, and had eleven cents. forty eight dollars, a yoke of steers for twenty-three dollars and a half, and a cow for fourteen dollars and a left; how many had he at first? SUBTRACTION. 1. David had six plums, and gave two of them to George; how many had he left? 2. A boy had eight cents and lost three of them; how many had he left? 3. A man bought a barrel of flour for eight dollars, and sold it again for twelve dollars; how much did he gain by the trade? 4. A person bought nineteen lbs. of rice, and having lost a part of it, found he had nine pounds left; how much did he lose? 17. Twenty-seven less eleven are how many? 18. A man owed seventy-five dollars, of which he paid at one time fifteen, and at another twenty-five dollars; how much remains to be paid? 19. Twenty-five less eight and six. are how many? 20. A person bought a horse for sixty dollars, a saddle for twenty dollars, and a bridle for two dollars and a half, and sold them all together for eighty-six dollars; did he gain or lose? and how much? 5. A boy having twenty cents, bought one quart of plums for six cents, and a pound of figs for ten cents; how many cents had he left? 6. A man bought a cow for sixteen dollars, and sold it again for twelve | and twenty-five are how many? dollars; how much did he lose? 7. Seven less three are how many? 8. Eight less three are how many? 9. Eleven less four are how many? 10. Twenty-one less four are how many? 11. Thirty less six are how many? 12. Six and ten less four are how many? 13 Nine and fifteen less eight are how many? 14. A lady bought a comb for thirty-three cents, some tape for eight cents, and some needles for six cts. She gave fifty cents; how much change must she receive? 15 Peter had twelve cents, and John gave him ten more, with which he bought eleven cents worth of cake; how many cents had he left? 16 Twenty-one less nine are how many? 21. Twenty-one and eight and seven less seventeen are how many? 22. Thirty and forty less twenty 23. A lady bought two yards of calico for sixty-two cents, a yard of ribbon for twenty-one cents, and two skeins of silk for eight cents, and gave a dollar bill; how much should she receive back? 24. A barrel containing thirtytwo gallons of cider, sprung a leak, and nine gallons run out; how much was there left? 25. A man sold a drover seven sheep for twelve dollars, a yoke of oxen for sixty-eight dollars, two cows for twenty-six dollars, and received in payment one hundred dollars; how much remains his due? 26. If I buy a horse for seventydollars, and a saddle for nineteen dollars, and sell them both for ninety-five dollars, do I lose or gain, and how much? MULTIPLICATION. 1. What cost two apples at one *cent a piece? 2. What cost two lemons at two cents a piece? 3. What cost four yards of tape at two cents a yard? 4. What cost three barrels of cider at three dollars a barrel? 5. At four cents a piece what will three oranges cost? 6. At four cents a yard what will four yards of ribbon cost? 7. If a man travel three miles an Two times two? Two times six ? Two times seven? Two times eight? Two times ten ? hour, how far will he travel in six hours? 8. What will eight yards of cloth cost at four dollars a yard? 9. What will six pounds of raisins cost at nine cents a pound? 10. What will seven yards of shirting cost at three shillings a yard? 11. What will sixteen yards of shirting cost at ten cents a yard? 12. If four bushels of wheat make a barrel of flour; how many bushels will it take to make eight barrels ? Multiplication Table. How many are Four times five? 13. What will twelve pounds of butter cost, at twelve and a half cents a pound? 14. If a person earn five dollars a week, how much does he earn in twelve weeks ? 15. If a person earn seven shillings a day, how much does he earn in nine days? 16. At twelve cents a pound, what will eleven pounds of sugar cost? 17. Peter has fifteen cents, and John has three times as many; how many has John? Six times twelve ? Seven times eleven ? Ten times eleven ? 18. A certain room has four windows, each containing eighteen panes of glass; how many panes are there in the whole? 19. A ream of paper contains twenty quires, of twenty-four sheets each; how many sheets in a ream? 20. What will nineteen bushels of potatoes cost, at eighteen cents a bushel? 21. What will twenty-one barrels of cider cost, at seventy-five cents a barrel? 22. What will fifty sheep cost, at one dollar twenty cents a piece? DIVISION. 1. If two apples cost four cents, how much is that a piece? 2. If three lemons cost nine cents, how much is that a piece? 3. A lad had twelve plums, which he divided equally among six boys; how many did each have? 4. If you divide twenty dollars equally among four men; how much will each have? 5. In fifteen how many times five? 6. In twenty-one how many times seven? 7. In sixteen how many times four? 8. In thirty how many times five? 9. In twenty-four how many times eight? two? 10. In eighteen how many times 11. If a quire of paper cost twelve cents, how much is that a sheet? 12. If five lemons cost thirty cents, * how much is that a piece? 13. If fifty-four cherries be divided among six girls, how many will they have a piece ? 18. A certain cornfield contains three hundred and twenty hills, and the rows are forty hills long; how many rows are there? 19. In five hundred, how many times twenty ? 20. If a bushel of wheat cost eighty cents, how much is that a quart; there being four pecks in a bushel, and eight quarts in a peck? 21. In two dozen and a half, how many half dozen? 22. In a certain village are two hundred and eighty-five persons, and the average number in each family is five; how many families are there? |