35 less 9? 55 less 9? 75 less 9? 65 less 9? 85 less 8? 95 less 9 ? 17. 9 and 7 are how many? 16 and 7? 36 and 7? 26 and 7? 46 and 7? 66 and 7? 56 and 7? 86 and 7? 76 and 7? 96 and 7? 18. 16 less 7 are how many? 26 less 7? 46 less 7? 36 less 7? 56 less 7? 76 less 7? 86 less 7? 66 less 7? 96 less 7? 19. 7 and 8 are how many? 15 and 8? 25 and 8? 45 and 8? 35 and 8? 55 and 8? 75 and 8? 65 and 8? 85 and 8 ? 95 and 8 ? 20. 15 less 8 are how many? 25 less 8? 45 less 8? 35 less 8? 55 less 8? 65 less 8? 85 less 8? 75 less 8? 95 less 8? 21. 8 and 4 are how many? 18 and 4? 48 and 4? 38 and 4? 68 and 4? 58 and 4? 88 and 4? 78 and 4? 98 and 4? 4 are how 32 less 4? 22 less 4? 82 less 4? 72 less 4? 92 less 4? 23. 7 and 6 are how many? 17 and 6? 37 and 6? 27 and 6? 57 and 6? 47 and 6? 67 and 6? 97 and 77 and 6? 87 and 6? 6? 24. 23 less 6 are how many? 33 less 6? 53 less 6? 73 less 6? 63 less 6? 83 less 6? 93 less 6? 25. 9 and 8 are how many? 17 and 8? 27 and 8? 47 and 8? 37 and 8? 57 and 8? 77 and 8? 67 and 8? 87 and 8? 97 and 8 ? 26. 17 less 8 are how many? 27 less 8? 47 less 8? 37 less 8? 57 less 8? 87 less 8? 77 less 8? 67 less 97 less 8? 8? LESSON XII. TO TEACHERS.-This Lesson is intended as a "Drill Exercise" in adding and subtracting, and can not be made too familiar. Increased interest will be given to it, if occasionally the figures are written in a perpendicular or horizontal line upon the blackboard, the teacher pointing at each as the class name the results in concert. 1. Count by 2s till the sum is 50.* four, six, eight, ten, twelve, etc. Thus: two, 36. 48. 36. 48. 40. 50. 42. 60. 35. 63. 40. 64. 2. Count by 38 till the sum is 24. 3. Count by 4s till the sum is 24. 4. Count by 5s till the sum is 30. 5. Count by 6s till the sum is 24. 6. Count by 78 till the sum is 21. 7. Count by 8s till the sum is 24. 8. Count by 9s till the sum is 27. 9. Count by 10s till the sum is 50. 10. Begin at 50 and count backward by 28. fifty, forty-eight, forty-six, forty-four, etc. 45. 63. Thus: II. Begin at 48 and count backward by 38. 12. Begin at 48 and count backward by 4s. 13. Begin at 50 and count backward by 5s. 14. Begin at 48 and count backward by 6s. 15. Begin at 49 and count backward by 78. 16. Begin at 48 and count backward by 8s. 17. Begin at 45 and count backward by 9s. 18. Begin at 100 and count backward by 10s. 19. Add 7, and 2, and 5, and 3, and 8, and 4, and 6. 20. Add 8, and 3, and 6, and 4, and 7, and 5, and 2. 21. Add 9, and 4, and 3, and 6, and 7, and 8, and 5. *This and the other numbers should be extended to 100 as soon as the progress of the class will warrant it. MULTIPLICATION. LESSON I. TO TEACHERS.-The design of this Lesson is to develop the idea of "times," as used in Multiplication. 1. First boy hand me a counter, as a pencil. How many times have you passed a counter? Ans. One time. 2. I time I counter is how ? many 66 I counter." 3. Pass me another counter. How many times have you now passed I counter? Ans. Two times. 4. 2 times I counter are how many? "2 counters." 5. Next boy hand me another counter. How many times has I counter been handed me? Ans. Three times. 6. How many are 3 times 1 pencil? "3 pencils." 7. Next, hand me another counter. times has I counter been handed me? Ans. Four times. 8. How many are 4 times 1 hat ? 66 How many 4 hats." 9. Hand me I counter more. How many times has I counter been handed me? Ans. Five times. 10. How many are 5 times 1 book? "5 books." 11. Pass another counter. How many times now? Ans. Six times. 12. How many are 6 times 1 apple? 13. Pass another counter. How many times now? Ans. Seven times. LESSON II. TO TEACHERS.-The object of the next eight lessons is to make the class masters of the "Multiplication Table." 1. First pupil, make a unit mark upon the blackboard; now make another on the right, with a space between them; as in the margin, *, * 2. How many times have you made 1 unit mark? Ans. Two times. 3. How many are two times I unit? "Two." 4. Next pupil, make 2 unit marks, and on the right 2 more; as in the margin, * *, ** 5. How many times 2 unit marks have you? Ans. Two times. 6. How many are 2 times 2 units? "Four." 7. Make 3 unit marks, and 3 unit marks. ***, ** 8. How many times 3 unit marks are there? Ans. Two times. 9. How many are 2 times 3 units? "Six." The class may illustrate and complete the Table, as below: 1. What will 2 apples cost, at 1 cent each? ANALYSIS.—If I apple costs I cent, 2 apples will cost 2 times I cent; and 2 times 1 cent are 2 cents. Therefore, 2 apples will cost 2 cents. 2. What will 2 peaches cost at 2 cents apiece? 3. Show me 2 times 2 fingers. 4. Lucia bought 2 yards of braid, at 3 cents a yard: how much did she pay for her braid? 5. Show me 2 times 3 fingers. 6. If lemons are 4 cents apiece, what will 2 cost? 7. Show me 2 times 4 fingers. 8. If Howard can write a line in 5 minutes, how long will it take him to write 2 lines? 9. Show me 2 times 5 fingers. 10. If a man can saw a cord of wood in 6 hours, how long will it take him to saw 2 cords? II. At 7 cents each, how much will 2 oranges cost? 12. At 8 cents a quart, what will 2 quarts of chestnuts cost? 13. If I inkstand costs 9 cents, what will 2 cost? 14. What must I pay for 2 writing-books, at 10 cents apiece? 1. George bought 3 tops, at 4 cents apiece: how much did he pay for his tops? ANALYSIS.-Since I top costs 4 cents. 3 tops must cost 3 times 4 cents; and 3 times 4 cents are 12 cents. Therefore, he raid 12 cents for his tops. |