14. 74 divided by 21, means, find how many times 2i is contained in 1\. I can change 21 and 71 to halves; 2i = halves; 7i = halves. halves are contained in halves times. Story—A farmer put 71 bushels of oats into bags, putting 2\ bushels in each bag; there were bags. 15. 5| tons divided by 2, means, find 1 half of 5| tons. 1 half of 5} tons = and tons. Story — 5§ tons of coal were divided equally between two families; each family received and tons. 16. 12? multiplied by 2|, means, take 2 times 12? plus 3 fourths of 12? (2| times 12?). 2 times 12? plus 3 fourths of 12? = cents. Story—At 12$ a pound 2\ 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. Story— A 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. 12J multiplied by 3, means, take 3 times 121 (3 times \, plus 3 times 12). 3 times 12 J = . Story—One side of a triangle having equal sides is 12\ft.; the perimeter of the triangle is and feet. 20. 15 feet divided by 21 feet, means, find how many times 21 feet are contained in 15 feet. I can change 15 ft. and 21 ft. to half-feet; 15 ft. = half-feet; 2i 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 2J ft. long; there were pieces. 21. 271 feet divided by 3, means, find 1 third of 27i feet. 1 third of 27J feet = and feet. Story—The perimeter of a triangle having equal sides is 27%feet; each side is ■ and feet. 22. 121 multiplied by 2i, means, take 2 times 121, plus 1 of 12J. 2 times 121, Plus h of 121 = and . Story—At $12% per ton, 2\ tons of hay cost and dollars. 23. 131 DU- divided by 2J bu., means, find how many times 2\ bu are contained in 13-1 bu. I can change 2\ and 131 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 2\ bu. in each bag. There were bags. 8. 20 multiplied by .2, means, find 2 tenths of 20. One tenth of 20 = ;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 bushel; I bought ■ bushels. 10. $6.36 divided by 3, means, And 1 third of $6.36. One third of 86.36 = . Story—I paid $6.36 for 3 barrels of apples; 1 barrel cost . 11. The sum of 176.4 and 148.75 is . 12. The difference of 276.4 and 148.23 is . 13. 20 multiplied 3.2, means, take 3 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 (5*) 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—/ paid $2.5 for pencils at $.05 (5t) 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 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 S8.2 ($8.20) = . Story—I paid $8.2 for 5 yards of cloth; 1 yard cost . SUGGESTIONS TO TEACHERS. 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 slowreading 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. 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 i\ acres of land into lots each containing ^ of an acre. There were 95 lots. 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. |