twelfths twelfths. Story-William had a piece of wire f of a foot long; he cut from it a piece f of a foot long; what remained was twelfths of a foot long. 3. of a bushel multiplied by 7, means, take 7 times three fourthbushels; 7 times 3 fourth-bushels fourth-bushels, or and bushels. Story-A farmer fed to his horses } bu. of oats each day for a week; in all he fed and bushels. 4. 4 divided by $, means, find how many times 1 third is contained in 4. I can change 4 to thirds. 4 is 12 thirds. 1 third is contained in 12 thirds times. Story—The teacher divided 4 oranges among some boys, giving to each § of an orange; there were boys. 5. } of a bushel divided by 4, means, find 1 fourth of of a bushel. 1 fourth of j of a bushel = of a bushel. Story--A boy divided f of a bushel of oats equally among 4 ponies; each pony received of a bushel. 6. 64 plus 53, means, 62 and 53. 64 and 5} = and Story-In one jar there were 61 lb. of butter; in another there were 5} lb.; in both there were and pounds. 7. 64 minus 5}, means, 67 less 5). 64 less 5} and Story- A grocer had 6 lb. cheese, from which he sold 5} lb.; there remained and pounds. 8. 124 multiplied by , means, take { of 124. 3 fourths of 124 = cents. Story-At 124 a pound, i of a pound of meat costs cents. 9. j divided by ł, means, find how many times 1 sixth is contained in 2 thirds. I can change thirds to sixths; 2 thirds sixths; 1 sixth is contained in 4 sixths times. Story – Mrs. Smith divided j of a pie among some boys, giving to each of a pie; there boys. 10. 63 yd. divided by 2, means, find 1 half of 61 yards. 1 half of 64 yards = and yards. Story-A salesman cut 61 yd. of ribbon into 2 equal pieces; there were and yards in each piece. 11. 2 bu, 3 pk. plus 2 bu. 2 pk., means, 2 bu. 3 pk. and 2 bu. 2 pk. 2 bu. 3 pk. and 2 bu. 2 pk. bu. pk. Story - A dealer put 2 bu. 3 pk. of oats into one bag and 2 bu. 2 pk. into another bag; in both there were bushels peck. 12. 5 bu. 1 pk. minus 1 bu. 3 pk., means, 5 bu. 1 pk. less 1 bu. 3 pk. 5 bu. 1 pk. less 1 bu. 3 pk. = bu. pk. Story-Mr. Bean had 5 bu. 1 pk. of oats, from which he fed 1 bu. 3 pk.; there remained bushels pecks. 13. $f multiplied by ), means, take 1 half of 3 fifths of a dollar. 1 half of 3 fifths of a dollar = of a dollar. Story-At of a dollar ( yard, 1 half of a yard of ribbon is worth of a dollar. were 14. 71 divided by 21, means, find how many times 24 is contained in 71. I can change 21 and 7; to halves; 2) halves; 7) = halves. halves are contained in halves times. Story-A farmer put 7} bushels of oats into bags, putting 2} bushels in each bag; there were bags. 15. 54 tons divided by 2, means, find 1 half of 54 tons. 1 half of 54 tons = and tons. Story-54 tons of coal were divided equally between two families; each family received and tons. 16. 124 multiplied by 24, means, take 2 times 12€ plus 3 fourths of 124 (24 times 124). 2 times 124 plus 3 fourths of 12€ = — cents. Story-At 124 a pound 23 lb. of cheese cost cents. 17. 46 ft. divided by 2 ft., means, find how many times 2 ft. are contained in 46 ft. 2 ft. are contained in 46 ft. times. StoryA mechanic cut 46 ft. of moulding into pieces, each piece being 2 ft. long; there were pieces. 18. 46 ft. divided by 2, means, find 1 half of 46 ft. 1 half of 46 ft. ft. Story-Henry divided 46 ft. of wire into 2 equal parts; each part was feet long. 19. 12multiplied by 3, means, take 3 times 12; (3 times ], plus 3 times 12). 3 times 12) Story-One side of a triangle having equal sides is 121 ft.; the perimeter of the triangle is and feet. 20. 15 feet divided by 23 feet, means, find how many times 21 feet are contained in 15 feet. I can nge 15 ft. and 21 ft. to half-feet; 15 ft. = half-feet; 2; feet = half-feet; half-feet are contained in half-feet times. Story-A mechanic had 15 feet of moulding which he cut into pieces, each piece being 2ft. long; there were pieces. 21. 271 feet divided by 3, means, find i third of 27} feet. 1 third of 271 feet = and feet. Story—The perimeter of a triangle having equal sides is 271 feet; each side is and feet. 22. 121 multiplied by 23, means, take 2 times 12), plus of 121. 2 times 123, plus 1 of 123 and Story-At $12) per ton, 2} tons of hay cost and dollars. 23. 13} bu. divided by 21 bu., means, find how many times 2ų bu are contained in 13j bu. I can change 24 and 134 to fourths. 21 fourths. 131 fourths. fourths are contained in fourths times. Story-A farmer had 13} bu. of oats which he put into bags, putting 24 bu. in each bag. There were bags. .2 = * .05 = .6+ 2 = * 176.4 .6 .64 (2) 276.4 .6 x 2 = .12 x 9 = (3) 20 X 2 = (8) 20 X 3.2 = (13) .1 X.1= (16) .3 X.2 = (10) .6 : .2 = * .08 - .02 = (4) 8=.4 = (9) 4.05 = (14) 2.5 = .05 = (17) $.5) $24.5 (20) .6 ; 2= 5)$24.5 (18) 1. .24 plus .05, means, 24 hundredths and 5 hundredths. .24 and hundredths. Story-William had $.24; he earned $.05; he then had .05 = 2. .64 minus .05, means, 64 hundredths less 5 hundredths. .64 less .05 hundredths. Story--Martha had $.64; she spent $.05; she then had --- .12 = 3. .12 multiplied by 9, means, take 9 times 12 hundredths. 9 times hundredths, or and hundredths. 4. .08 divided by .02, means, find how many times 2 hundredths are contained in 8 hundredths. .O2 are contained in .08 times. Story-I paid $.08 for oranges at $.02 each; I bought oranges. 5. $.08 divided by 2, means, find 1 half of 8 hundredths of a dollar. One half of $.08 = Story-I paid $.08 for 2 lemons; one lemon cost 6. .24 plus .5, means, 24 hundredths and 5 tenths. 5 tenths 50 hundredths. .24 and .50 = hundredths. Story-John had $.24; Alfred had $.5; together they had 7. .64 minus .5, means, 64 hundredths less 5• tenths. 5 tenths 50 hundredths. .64 less .50 hundredths. Story-Sarah had $.64; Mary had $.5; Sarah had $ more than Mary. .* See Elementary Arithmetic, pp. 153 and 155. 20 = 8. 20 multiplied by .2, means, find 2 tenths of 20. One tenth of -; 2 tenths of 20 Story-At $20 an acre, .2 of an acre of land would cost dollars. 9. 8 divided by .4, means, find how many times 4 tenths are contained in 8. 8 = 80 tenths. 4 tenths are contained in 80 tenths times. Story-I paid $8 for potatoes at $.4 (4 dimes) a shel; I bought bushels. 10. $6.36 divided by 3, means, find 1 third of $6.36. One third of $6.36 = Story-I paid $6.36 for 3 barrels of apples; 1 barrel cost 11. The sum of 176.4 and 148.75 is 13. 20 multiplied 3.2, means, take 5 times 20, plus 2 tenths of 20. 3 times 20 2 tenths of 20 3 times 20, plus 2 tenths of 20 = Story-At $20 an acre, 3.2 acres of land are worth dollars. 14. 4 divided by .05, means, find how many times 5 hundredths are contained in 4. 4 = 400 hundredths. 5 hundredths are contained in 400 hundredths times. Story-I paid $4 for tablets at $.05 (54) each; I bought tablets. 15. 5.6 tons divided by 4, means, find 1 fourth of 5.6 tons. One fourth of 5.6 = and tons. Story-A farmer sold 4 loads of hay, the entire weight of the hay was 5.6 tons; the loads averaged and tons. 16. .1 multiplied by .1, means, find 1 tenth of 1 tenth. One tenth of 1 tenth = 17. 2.5 divided by .05, means, find how many times 5 hundredths are contained in 2.5. 2.5 = 250 hundredths. 5 hundredths are contained in 2.5 (250 hundredths) times. Story-1 paid $2.5 for pencils at $.05 (54) each; I bought pencils. 18. $24.5 divided by 5, means, find 1 fifth of $24.5. One fifth of $24.5 Story-I paid $24.5 for 5 tons of coal; 1 ton cost SUGGESTIONS TO TEACHERS. 19. .3 multiplied by 2, means, find 2 tenths of 3 tenths. One tenth of 1 tenth One tenth of 3 tenths Two tenths of 3 tenths 20. $24.5 divided by $.5, means, find how many times 5 tenths of a dollar are contained in $24.5 (245 tenths dollars). 5 tenths are contained in 24.5 (245 tenths) times. Story-I paid $24.5 for apples at $.5 (5 dimes) a bushel; I bought bushels. 21. $8.2 divided by 5, means, find 1 fifth of $8.2. One fifth of $8.2 ($8.20) = Story—I paid $8.2 for 5 yards of cloth; 1 yard cost 1. ORDER OF PROCEDURE IN PART I. STEP 1.-Prepare the pupil by means of oral instruction for the work of a given page. This preparation may be, in part, the slow reading to the pupil of the figure problems* upon the page, the teacher hesitating at each blank for the pupil to supply the word. In this preparatory work, no book should be in the hands of the pupil. New words should be first presented through the voice of the teacher in the expression of thought. They may then be written upon the blackboard by the teacher, erased, and the pupil exercised in both oral and written reproduction. STEP 2.—The book should be put into the hands of the pupil, and he should read, first silently, then orally, the figure problems upon any page for which proper preparation has been made. STEP 3.—The pupil may attempt the letter problems* at his desk without further assistance. If he is unable to solve these, review the figure problems and give others similar to them. In some instances it may be well to have the figure problems solved upon the blackboard as preparation for the letter problems. 2. Wherever the word “story” follows a problem, as on pp. 12 and 13, require the pupil to make a statement showing how the problem might originate in business or other experience; thus, the story for problem (f), page 12, might be, A man divided 41 acres of land into lots each containing at of an acre. There were 95 lots. 3. The separatrix, as an aid in “pointing off” in multiplication and division of decimals, is mentioned in a note on page 133. Its use is illustrated on page 143. Its occasional use in blackboard work earlier in the course may be helpful; but a too early reliance upon formal rules is to be avoided if the purpose of the work is the development of the thought-power of the pupil. * The figure problems are those designated by figures; the letter problems, those designated by letters. |