Q. What do you call this figure?-Arthur. A triangle. 6 in. 9 in. Q. And still what is the relation of this figure to the rectangle?-Edith. It is one-half of it. Q. If the rectangle is 9 inches long and 6 inches wide, by folding it that way I still have the length 9 inches and the width 6 inches; but you tell me the area is 27 square inches. Now, from that fact, how may the area of a triangle be found?—Lottie. Multiply the length by the breadth and divide by two. Q. Instead of calling the names length and breadth of the rectangle, the 9 inches may be called the base of the triangle, and the breadth of the rectangle, 6 inches, now becomes the altitude of the triangle. Now, using other terms, how may we find the area of the triangle?-Roy. Multiply the base by one-half of the altitude. Q. If the base is 9 inches and the altitude 6 inches, what is the area?-Roy. The area is 27 square inches. 9 times three square inchies are twenty-seven square inches. Practical problems by the same class, given by Assistant Superintendent: Q. What will 7 bushels 3 pecks 4 quarts of cherries cost, at $4.25 a bushel?-Chester. First reduce the 7 bushels 3 peeks 4 quarts to quarts, which are 252 quarts. Since there are 32 quarts in one bushel, in 252 quarts there would be as many bushels as 32 is contained times in 252, which are 73 times, or 7 bushels. 7 bushels would cost 73 times $4.25, which are $33.467. Q. How many square rods in 3 of an acre?-Mamie. 106 square rods. There are 160 square rods in one acre. In two-thirds of an acre there are two-thirds of 160 square rods. Q. Two persons observed an eclipse of the moon, one seeing it at 9 p. m. and the other at 11.30 p.m. What was the difference in their longitude? (Pupils were ready with an answer in less than one-half minute.)-Herman. 372 30'. Q. If 15 equal bars of silver weigh 24 pounds 8 ounces 16 pennyweights, what is the weight of each bar? (Several had answers in one minute.)—A. 1 pound 7 ounces 15 pennyweights 173 grains. Q. What part of a rod are 3 feet, 4 inches? (Three-fourths of the pupils had an answer in one minute.)-A. 33. Q. Reduce 0.096 of a bushel to a decimal of a pint. (One-half of the class had an answer in one minute.)-A 6.144. WHITTIER SCHOOL-MISS SIMMONS, TEACHER. [April 1, 1895-Class A, grade sixth.] Q. If you wish to carpet this room, in what direction shall the strips run?-Roy. Lengthwise. room. Teacher. You may find the length of the room [Roy measures the length of the room with a yard measure].-Roy. The room is thirty feet long. Q. How do you buy carpet?-Frank. By the yard. Q. How many yards are required for one strip?-Walter. Ten yards. Q. What is the next question to ask yourself concerning the room?- Phil. How wide is the room? Q. Why do you wish to find the width of the room?-Earl. To find how many strips are required. Teacher. Find the width of the room [Earl measures the width of the room with a yard measure].— Earl. The room is 22 feet wide. Q. How wide is carpet?-Clifford. One yard wide. Q. Is all carpet one yard wide?- Clifford. Some carpet is three-fourths of a yard wide. Q. We will suppose the carpet that we will use to be one yard wide. How many yards will be required for the width of this room?-Mildred. 7} yards. Q. If the carpet is one yard wide, how many strips are required?- Willie. 7 strips. Q. Could you buy of a strip?- Willie. No, ma'am. Q. How many strips, then, are required?-Harrell. Eight strips. Q. How many yards are required for one strip?-Roy. Ten yards. Q. How many strips altogether?-Roy. Eight strips. Q. How many yards are required for this room?-Anna. Eighty yards. Q. Is your carpet a perfectly plain surface?-Phil. No; the carpet is figured and should be matched. Q. How many yards would be required if there were no figures to be matched?-Walter. Eighty yards. Q. We will suppose that there are figures to be matched. Now, if we were laying the carpet, how many strips would we lay simply for the length required?-Clara. One strip. Teacher. Yes, there would be just one strip cut off the required length. What would occur on the second, third, fourth strips, and so on?-Clara. There would be a certain number of inches cut off or turned under. Q. What would you call that quantity cut off on account of matching of figures?-Delbert. Waste or loss. Q. I will say that there are eight inches loss in matching the figures; what will you do with the eight inches?-Harrell. We will reduce them to parts of a foot. Q. What would that equal?-Harrell. Two-thirds of a foot. Q. Who would have to stand this loss of foot?-Phil. The buyer. Q. How long is each strip?-Mattic. 30 feet long. Q. How many feet would you have to buy for the second, third, fourth strips, and so on? - Delbert. 30 feet. Q. How many yards would that equal? Theo. Ten yards. Mattie. Ten and two-ninths yards. Q. How many strips ten and two-ninths yards long would you require?-Roy. Seven strips. Q. Why did you say seven strips?-Roy. The first strip was only ten yards long, the remaining seven strips would be 103 yards long. Q. How long are those seven strips?--Clara. Ten and two-ninths yards long. Q. How many strips of that length do you require?- Walter. Seven strips, each 103 yards long. Q. What does that equal?-Class. 713 yards. Q. What is the length of the first strip?-Willie. Ten yards. Q. Making a total of, how many yards?-Mattie. 815 yards. Teacher. You may draw on your slates the illustration of the floor of a room, marking the dimen sions. Give the dimensions of yours. Mattie. Twenty-five feet long and twenty-two feet wide. Theo. Thirty feet long, twenty feet wide. Q. We will soive Theo's problem. In the last problem we took carpet one yard wide. Suppose we take for this problem carpet yard wide, the strips running lengthwise. How many yards wide is the room?-Emma. Six and two-thirds yards. 30 ft. 20 ft. yds. Q. Instead of reducing it to 6 yards, what may yon call it more conveniently?-Essie. Seven strips. Q. No; I did not ask for the number of strips.-Roy. Twenty-thirds yards. Q. Suppose the carpet is three-fourths of a yard wide; how many strips are required for a room 3 yards wide?--Earl. 83 strips; no, 9 strips. Q. Why did you not say 8 strips instead of 9 strips?-Earl. Because you can not buy of a strip. You must buy one whole strip, which makes 9 strips. Q. How many yards in length is the room?-Clifford. Ten yards. Q. Supposing there is a loss of nine inches in matching figures, on how many of the nine strips would there be a waste of nine inches?-Harrel. On eight strips. Q. How much would that nine inches loss on each of eight strips equal in yards?-Mattie. Onefourth of a yard on each strip. Q. How many yards long, then, would each of those eight strips be?-Anna. Ten and one-fourth yards. Q. How many yards would it require for eight strips ten and one-fourth yards long?-Anna. Eightytwo yards. Q. How many yards would the first strip require?-Willie. Ten yards. Q. Why did we not allow for loss on that first strip?-Fred. The first strip would be cut off just the length of the room. Q. How many yards shall we buy for that room?-Roy. Ninety-two yards. Assistant Superintendent. Miss Simmons, we shall not wait for the pupils to finish their problems and analyze them. This will be sufficient to show your plan of developing the subject. MORSE SCHOOL-MRS. MARSHALL, TEACHER. [April 1, 1895,-Class B, grade seventh.] Assistant Superintendent. I would like to have you take up some work, so that we may get an idea of how you teach the applications of percentage in profit and loss and in commission and brokerage; a short lesson in cach one. You have passed beyond this subject, have you not?-Mrs. Marshall. Yes, sir. Q. A drover bought cattle at $65 a head, and sold them for $84.50 a head. cent? (Frank repeats question.) Q. What is the first step that we take?-Olga. Find the gain in dollars. Fred. Divide the gain by the cost, and that will give the rate. (21 pupils out of 41 had an answer in one-half minute.) (Frank. 30 per cent.) What is the gain per Alfred. If a drover bought cattle at $65 a head, and sold them for $84.50 a head, he gained the dif ference between $84.50 and $65, which is $19.50. Q. What do you say next?-Ethel. The gain is as many per cent as $65 is contained times in $19.50, which is 30 hundredths times or 30 per cent. Q. In the subject of percentage the $84.50 would be called what?-Una. Amount. Q. To what would the $65 be equivalent in percentage?-Maggie. Base. Q. What would you be required to find in percentage?-Karl. The rate per cent. Q. What do you always do to find the rate per cent of gain or loss? Julia. Divide the gain or loss by the cost, and the amount expressed in hundredths is the gain or loss per cent. Jessie. Divide the gain or loss in dollars by the cost. Q. A man sold a watch for $180, and lost 163 per cent. What was the cost? working the problem?-Alfred M. 100 per cent minus 163 per cent is 833 per cent. Q. Why do you take 168 per cent from 100 per cent? Julia. Because $180 is only 834 per cent of the cost. (Four pupils only did not have an answer in of a minute.) Una. $216. Give the first step in Q. Give a full analysis of the problem.-Florence. The cost of the watch is 100 per cent of itself, and he lost 163 per cent. The difference is 834 per cent, or $180. Q. How do you find the cost when you have that? Florence. $180 is 83 per cent of the cost of the watch, or of the cost; one-sixth of the cost of the watch equals one-fifth of $180, which is $36, and six-sixths, or the cost of the watch, are six times $36, which are $216. Myrtle. 100 per cent, the cost of the watch, less 163 per cent equals 833 per cent, or $180. 1 per cent would equal one eighty-three and one-third of $180, or $2.16; 100 per cent would equal 100 times $2.16, or $216. Q. A house and lot were sold for $7,762.50, at a gain of 15 per cent. What was the cost? What is the first step in working this problem?-Ethel. 100 per cent of the cost of the house and lot plus 15 per cent gain is 115 per cent of the cost, or $7,762.50. Q. What is the next step? Ernst Z. The cost would be as many times $1 as 115 per cent is contained times in $7,762.50. (Seven pupils did not have an answer at the expiration of 45 seconds) Nana. $6.750. Q. Explain it.-Maggie K. The cost of the house and lot is 100 per cent, and if he gained 100 per cent Teacher. I do not agree with you.-Leslie. 100 per cent, or the cost, plus 15 per cent, the gain, is 115 per cent of the cost, or $7,762.50; and the cost would be as many times $1 as 115 per cent is contained times in $7,762.50, or 6,750 times, or $6,750. Teacher. Correct his mistake.-Hugh. The cost would be as many times $1 as 1.15 is contained times in $7,762.50, or 6,750 times, or $6,750. Q. In percentage what would you call that $6,750?-Ernest B. The base. Q. What would you call that $7,762.50?--Maggie S. The amount. Q. A man sold two horses for $150 each; on one he gained 25 per cent, and on the other he lost 25 per cent. Did he gain or lose by the transaction, and how much? What do we first do in this problem?-Daisy. Find the cost of the first horse. Q. What next?-Julia. Find the cost of the second horse. Q. And then what?-Ethel. Find the gain or loss on each. Q. What else could you do rather than that?--Fred. Add the costs and selling prices, and subtract. (One-half of the pupils had the problem solved in one minute; all had finished in 13 minutes.) Q. What was the question? May. Did he gain or lose by the transaction, and how much? Alfred. He lost $20. Hugh. He gained $20. Jessie. He neither gained nor lost. Frank G. He gained $38.50. Q. Explain.-Florence. The cost was four-fourths. If he gained 25 per cent on one, or 1, $150 was the sum of and, or . If of the cost equal $150, one fourth of the cost was one fifth of $150, or $30, and four-fourths, or the cost, was four times $30, or $120, which is the cost of the horse on which he gained 25 per cent. If on the other horse he lost 25 per cent, or one-fourth of the cost, then the ED 94- -38 difference between four-fourths of the cost and one-fourth of the cost is three-fourths of the cost, or $150. If $150 is three-fourths of the cost, one-fourth of the cost is one-third of $150, which is $50. Four-fourths, or the cost, would be four times $50, which are $200. If the second horse cost him $200, and the other horse cost him $120, the entire cost is the sum of $120 and $200, which is $320. The entire selling prices of the two horses is the sum of $150 and $150, which is $300. He would lose the difference between $320 and $300, which is $20. (Nine pupils had wrong answers.) Q. An agent furnished a schoolhouse for $45, and received $5.40 commission. commission? What is the first step in the problem?—Una. Find the rate. Q. In percentage what would the $45 be called?-Una. It would be the base. Q. What would the $5.40 be?-Saul. It would be the percentage. Q. What would be required to find? Class. The rate. (Every pupil had an answer in one minute; two pupils had wrong answers.) Willie. $1.80. Q. What pupil will tell me why Willie can not be right? What was the rate of Ernst Z. Because the answer is to be the rate per cent, and he gave his answer in dollars. Fred. 12 per cent. Alfred. 10 per cent. Teacher. 12 per cent is correct. Q. An agent received 5 per cent for buying wool, and his commission was $208.30; how much wool did he buy? What do we want to find in this problem?-Ethel. How much wool he bought. Q. What would that be in percentage!-Ethel. Base. Q. What would be the rate in this problem?-Frank G. The 5 per cent. Q. What would you call the $208.50? - Mary. Percentage. Q. How do we always find the base when we have the rate and percentage given? Olga. Divide the percentage by the rate to find the base. Ernst Z. He bought $4,170 worth of wool. If he received 5 per cent commission for buying wool, and received $208.50, he would buy as many dollars' worth of wool as 5 cents are contained times in $208.50, which are 4,170 times or $4,170. Q. A Boston merchant sent his broker in Cincinnati $3,529.20 to be invested in bacon, after deducting his commission of 2 per cent. How much bacon did he buy? What do we first want to find?—Alfred. We want to find how much money he invested in bacon. Q. What is the first step? --Tom. Add 100 per cent and 2 per cent. Q. Why? Tom. Because every dollar's worth of bacon the broker bought would cost the merchant $1.02—one dollar and the 2 cents commission, which makes $1.02. Ernst. For every dollar's worth of bacon the broker buys he received two cents for commission, and altogether, the one dollar for the bacon and his commission would be $1.02, and the entire bill would be the sum of what he received for bacon and his commission, or $3,529.20. Julia. If one dollar's worth of bacon cost $1.02, for $3,529.20 he could buy as many dollars' worth of bacon as $1.02 is contained times in $3,529.20, which are 3,460 times, or $3,400. (Six pupils did not have an answer at the expiration of one minute.) Q. What was the man's commission-Florence. $69.20. Assistant Superintendent. I have a watch charm here. A friend of mine gave it to me. It cost my friend $10. If I should sell this watch charm for $12, what would be my gain per cent?--Ernst. You did not gain any per cent. Q. Why do you think I did not gain any per cent?-Tom. You did not gain any per cent because you did not buy it. Q. What has that to do with it? Somebody bought it. If I sold it, is that not all that is necessary-Maurice. It did not cost you anything so you are just that much ahead. Q. Why can you not get a rate per cent on that?-Maurice. You did not buy it, so you could not gain any per cent. Q. What is the base in this problem?- Frank. There is no base. Q. Can you have a gain per cent when there is no base? Frank. No, sir. Ernst. The base is your friend's action in giving it to you, and if you did not have any money in your pocket, you are just that much ahead. WEBSTER SCHOOL-MRS. WHITELEY, TEACHER. [ April 2, 1895-Class A, grade seventn.] SUBJECT: Case forms of nouns and pronouns. Q. What is the subject of the lesson?-Katie. Case forms of nouns and pronouns. Q. What are we studying in regard to cases of nouns and pronouns?-Ada. Construction of the case forms of nouns and pronouns. Q. What do we understand by the construction of case forms?-Ada. The arrangement of the words in regard to case. Q. To what parts of speech has your lesson reference?-Lula. Pronouns. Q. Why has it especial reference to pronouns?-Roy. There are no nouns given in the lesson. Q. Why is it that in this lesson you find no nouns that are incorrectly used as regards case '--(No answer.) What shall I ask you to do Q. What parts of speech have special forms in regard to case?-Stella. Pronouns. Q. You mean by this that only pronouns have special forms for cases. if I speak about giving the cases of nouns?-Anna.. Give the declension. Q. You may decline any noun you wish.-Kitty. Singular: Nominative, man; possessive, man's; objective, man. Plural: Nominative, men; possessive, men's; objective, men. Q. Do we find three different forms for the three cases?-Eva. We find only two forms. Q. Where do we find these two different forms?-Ray. The nominative and objective are alike, and the possessive is different. Q. Nouns being alike in the nominative and objective, and different in the possessive, let us see how it is with pronouns. Decline I.-Eva. Singular: Nominative, I; possessive, my or mine; objective, me. Plural: Nominative, we; possessive, our or ours; objective, us. Q. How many forms do we find for the different cases?---Lula. Three different forms. Q. Decline another pronoun that has three different forms for the cases.-Nellie. Singular: Nominative, he; possessive, his; objective, him. Plural: Nominative, they; possessive, their or theirs; objective, them. Q. Do we not know that pronouns change in form for the cases, and that nouns do not? Our lesson has special reference to what part of speech?-George. To pronouns. Q. To what modification of pronouns ?-George. Case. Q. What is the cantion in to-day s lesson?-Ada. The pronouns, I, we, thou, ye, he, she, they, and who are nominative forms, and must not be used in the objective. Me, us, thee, him, her, them, and whom are objective forms, and must not be used in the nominative. Q. What do the sentences given you illustrate?-Wallace. They illustrato errors in use of case. These sentences in our lesson are not correct. (Pupils repeat the incorrect sentences, then correct them, and state the reasons.) Anna. It is not me you are in love with. Correct: It is not I you are in love with. I is the attribute complement, and should be in the nominative case. Tom. He was neither better bred nor wiser than you or me. Correct: He was neither better bred nor wiser than you or I. The nominative I should be used instead of the objective me, because it is the subject of the verb understood. Q. Why did you not change the case of the word you?-Tom. Because in form, it may be either the nominative or objective. Q. Where do we make our errors in the use of case?-Wallace. In using the nominative for the objective, and the objective for the nominative. Q. In which case do we not make this kind of mistake?-Wallace. In the possessive. Q. What error do we generally make in the use of the possessive? Stella. An error in spelling. Anna. Who will go? Me. Correct: Who will go? L The nominative I should be used instead of the objective me, because it is the subject of the verb will go, understood. Daisy. Him being a stranger, they easily misled him. Correct: He being a stranger, they easily misled him. The objective him should not be used for the nominative he, because it is used independ ently with the participle. Q. Now, you may think of what you have done, and recall the instances in which we need to use the nominative case. Jessie. We need to use the nominate case when the word is used as the subject, as the attribute complement, and when it is used independently. Ray. And when it is used as explanatory modifier. Q. This, so far, has not been shown. Give an illustration of a pronoun used as explanatory modifier, selecting from the list of sentences in this lesson.-Carrie. It was Joseph, he whom Pharaoh promoted. Q. In what case is the word he?-Maggie. In the nominative case. Q. Why is it in the nominative case?-Osmar. Because the word it explains is in the nominative case. Q. Are all explanatory modifiers in the nominative case?---Wallace. No'm; the explanatory modifier is always in the same case as the word it explains. Q. In what other instance do we need the nominative case besides those mentioned?- (No answer.) Assignment of lesson. Now, in preparation for to-morrow's lesson, you may select from this list of sentences all those in which the error of using the objective for the nominative has been made, and correct all such errors, being very careful to think of the reason for such corrections. You will then be able to answer my last question. |