worth of cherries; how many cents how many cents must you have had he left? back? 19. Take eight and three from 26. A person rode twenty miles sixteen, what remains? in three hours; the first hour he 20. George has nine merits, and rode seven miles, the second six, John five and Charles two; how how many miles did he ride the many more has George than both third hour? the others? 27. A man owed another twenty 21. Sarah had nineteen plumbs five dollars of which he paid at one and gave five of them to Lucy and time nine dollars, and at another four to Mary; how many had she seven dollars, how much remains left? 22. Five and four from nineteen, what remains? due ? 28. Take nine and six from twenty and what remains? 29. A boy is thirteen years old 23. Eighteen persons are in a room, but only seven are sitting, and his sister is eighteen what is how many are standing? the difference of their ages? 21. A boy had twenty cents and 30. Twenty four pounds of sulost six of them, how many had begar are put into three boxes, one left? box contains seven pounds anoth25. If you buy a slate for twelve er nine, what does the other con cents and a sponge for six and give tain? 15. In twenty-five how many times five? 16. In twenty how many times 6. Divide twelve apples between two boys, how many will each ten? have?--between three boys ?-be- 17. If I have eight apples and tween four boys? give you half of them, how many 7. Fourteen cents were divided shall I give you? between two poor boys, how many 18. In thirty how many times ten?-how many times five? did each have? 8. If buy four books for sixteen how many three ? cents, how much do I give for one 19. In eighteen how many times book? nine-how many times six ?— 9. I sold nine quills for eighteen three ?-two? cents, how much is that a piece? 21. If a boy owes an another 10. If twenty men ride in two twenty-one cents and pays him coaches how many will be in each three cents every day, how many coach? days will it take to pay the debt? 22. In twelve how many times vided among nine girls, how many one? how many times two? how will each have? many times three ?-four?-six ? 19. In thirty-two how many 23. I bought five oranges for fif times eight? teen cents, how much was that a 30 In thirty how many times piece? five? how many times six? ten? 24. At twelve cents a dozen fifteen ? what will half a dozen apples cost? 81. In a garden are forty-nine 25. If twenty-eight cents be di-hills of corn planted in seven equal vided between four boys, how ma-rows, how many hills are there in ny will each have? a row? 26. If a quire of paper cost twen ty-four cents, how much is that sheet? 32. Divide thirty-nine chesnuts between three boys, how many will each have? 27 If twelve sheets of paper 33. Divide ninety-one cents becost twenty-four cent, how much tween seven children, how many is that a sheet? will each have? 28. If thirty-six cherries be di FRACTIONS. The following questions should be illustrated by dividing an apple before the pupils according to the conditions of each question. 12, 1. If an apple be divided apples will give two boys just one into two equal parts what are those pple a piece, and that one apple parts called? A. Halves. will give them half of an apple a 2. If an apple be divided into piece, so that three apples will give three equal parts what are those two boys one apple and a half each. parts called? A. Thirds. 12. Divide five apples between 3. I an apple be divided into four boys, how many will each four equal parts what are those have? parts called? A. Fourths, or quar 13. Divide ten cents between three boys, how many will each have. 14. Divide one apple and a half of an other between six boys, how much will each receive? 15. How many quarters in three 6. How many fourths in a whole apples? apple? 7. Which is most one half of an apple, or one third of an apple ?— one third or one fourth? 8. In two whole apples how many halves? how many thirds? how many fourths? 16 How many thirds in three apples? 17. To how many apples are eight quarters equal? 18. To how many apples are twelve halves equal? 19. How many apples will ten 9. Eight quarters of a dollar are thirds make? how many whole dollars? 20. How many apples will fifteen 10. Seven halves of a dollar arc quarters make? how many whole dollars? 21. Divide eleven apples be 11. If three apples be dividedtween four boys; how many will between two boys how many will each receive? each have? 22. How many quarters are one The pupil will observe that two half and one quarter ? 12. 1. If a pear is worth two dollars, and it be cut into two ecents, what is one half of it worth? qual parts, what are each of these A. One cent; because, if two cents parts worth? be divided into two equal parts, 8. If a yard of cloth is worth one of the parts is our cent. four dollars, what is half a yard 2. If a lemon is worth three worth ?-one quarter of a yard ?cents, what is one third of it worth three quarters ? two thirds of it? 9. If one pound of tea is worth 3. If three shillings will buy a one dollar, what is half a pound bushel of rye, what part of a bush-worth? a quarter of a pound?el will one shilling buy?-will two one third of a pound?—two thirds? shillings buy? 10. If one quarter of an orange 4. If you can buy a barrel of ci-is worth one cent, what is a whole der for two dollars how much can orange worth?-what is an orange you buy for three dollars? for one and a half worth? dollar? for half a dollar? 11. Two apples are what part of 5. What is meant by one half three apples? A. Two times one of a thing?* third, or two thirds of three apples. 12. Two apples are what part of four apples? 6. What is meant by one third of a thing? what by two thirds what by one for th by two fourths? by three fourths? 7. If a yard of cloth cost two 13. Three apples are what part of four apples. SECTION III. 13 The pupils having by this time learned to form and decompose numbers with considerable facility, may now be taught the method of expressing numbers by characters. For this purpose they should be furnished with slates, upon which they should be required to form the characters at the same time they are learning them By this exercise they will learn the characters, and the method of expressing numbers by them, much faster than by any other means, and will at the same time be learning to write. The method of writing the numbers from one to one hundred is as follows: * *Questions of this kind should be frequently repeated, that the pupil may have a clear idea of the meaning of the different expressions used. As the pupils advance, these exercises should be extended beyond the numbers contained in the foregoing table, and repeated till they become familiar with the laws of notation. 14. When numbers are applied to any particular things, as men, dollars, &c. they are called concrete numbers; but when numbers are used without refering them to any particular things, they are called abstract numbers. Hitherto the numbers employed have mostly been concrete. The following tables are made up of abstract numbers and upon these the pupils should be exercised repeatedly until they are made perfectly familiar with them and have the various results all treasured up in their memories. In exercising the pupils, the teacher should put the table into an interrogative form; thus, 0 and 1 are how many? A. one, &c. After the pupils can answer all the questions in the order in which they arise they should be proposed promiscuously from all parts of the table until they can all be answered without hesitation. 15. The following table must also be put into the interrogative form by the teacher, when exercising the learner; thus one taken from one, of one from one, what remains? A. Nothing. One from two, what remains? A. One. Or thus; one lessened one, or one less one are how many? A. Nothing. Two less one are how many? A. One. If the latter method be used, the pupil should be made to understand clearly that two less one means the same thing as one taken from or out of two SUBTRACTION TABLE. 1 from 1 remains 0 2 from 2 remains 0 | 3 from 3 remains 1 from 2 remains 1 from 3 remains 1 fron 4 remains 1 from 5 remains 1 from 6 remains 1 from 7 remains 1 from 8 remains 1 2 from 3 remains 3 from 4 remains 1 3 2 from 5 remains 7 8 remains 72 from 9 remains 1 from 9 remains 3 from 12 06 from 6 remains U 16 from 7 remains 1 26 from 8 remains 2 36 from 9 remains 3 46 from 10 remains 4 56 from 11 remains 5 remains 66 from 12 remains 6 10 from 12 remains 210 from 16 remains 6 10 from 19 remains 9 10 from 13 remains 3 |