ADDITION. INDUCTIVE EXERCISES. 1 23. 1. How many are 2 pounds and 3 pounds? 3 pounds and 4 pounds? 5 pounds and 3 pounds? 2. Can you unite 6 books and 4 pounds? 3. Can you unite 3 pounds and 7 pounds? 4. How many are 6 units and 4 units? 5. How many are 3 tens and 4 tens? 5 tens and 3 tens? 6. How many are 4 hundreds and 5 hundreds? 7. What is the unit of 3 men? Of 12 rods? Of 8 tens? 8. What is the unit of 4 tens? these units be united? Why not? Of 6 hundreds? Can 9. What kind of numbers only can be united? What orders of units? Why not? 10. How many are 9, 3, and 6? 6, 3, and 9? 3, 6, and 9? 11. Is the result changed by uniting the same numbers in a different order? 12. A farmer sold 6 sheep to one man, and 9 to another. How many did he sell to both? 13. If a coat costs 10 dollars, and a pair of boots 8 dollars, what is the cost of both? 14. James gave 4 pears to George, and 5 to Belle, and kept 7. How many pears had he at first? 15. In a shop are 8 men, 6 boys, and 7 girls at work. How many persons in all are at work? PRINCIPLE.-Only like numbers and units of the same order can be added. DEFINITIONS. 24. Addition is the process of finding a number equal to two or more like numbers. The sum or amount is the number found by addition. 25. The sign of addition is +. It is read plus, and signifies more. 26. The sign of equality is, It is read, "equals," or "is equal tc." Thus, 5+6=11 is read, 5 plus 6 equals 11. It may also be read, 5 and 6 are 11. Name the members and the terms of each of the following equations: 1. 7+10=17. 6. 12+8=16+4. 11. 8+9+?=25. 2. 8+12=20. 7. 14+6=12+? 12. ?+6+8=15+8. 3. 15+6=21. 8. 9+20=?+%. 13. 10+?+5=20+10. 4. 30 20+10. 9. 25+? 5+30. 14. 21+7+6=?+25. 5. 9+6=10+5. 10. 36+0=?+20. 15. 9+13+10=24+? The expression "?" is read "equals how many?" or "equals what?" The pupil may be exercised on the above table as follows: first, by columns, at sight, give the sum of each number and the one below it; then, by lines, give the sum of each number and the one to the right of it. In like manner, practice with sets of three figures, then of four, and so on, until each column from bottom to top, and from top to bottom, and each line from left to right, and from right to left, can be added with rapidity and accuracy. Next start with 1, and add to it each column and each line successively; then start with 2, 3, etc., to 10. The pupil should be required always to add as he counts: thus, in column A, beginning at the bottom, say, 3, 11, 16, 22, 29, 30, 34, 37, 39. The above and all other subsequent drill and oral exercises are designed for daily practice in numbers. Not more than five minutes should be given to this kind of work in connection with the regular lesson. DRILL EXERCISES. 29. 1. Add or count by 3's from 3 to 36. Written, 3+3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3, etc. Read, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, etc. Next, form a new combination, commencing with 1, and then another, commencing with 2, thus: 2, 5, 8, 11, 14, 17, 20, 23, 26, 29, etc. Add, or count, 2. By 2's from 4 to 50. 3. By 3's from 1 to 43. 4. By 3's from 6 to 51. 5. By 4's from 1 to 53. 6. By 4's from 5 to 45. 7. By 5's from 7 to 82. In like manner, treat the remaining digits 6, 7, 8, and 9. 8. Add by 2's and 3's alternately to 32. Written, 2 + 3 + 2 + 3 + 2 + 3 + 2 + 3 + 2 + 3, etc. Read, 2, 5, 7, 10, 12, 15, 17, 20, 22, 25, etc. In like manner add, 9. By 2's and 4's to 48. 10. By 4's and 5's to 72. 11. By 5's and 3's to 69. 9+0+6= 12+ 4+4= 4+12+4= 6+9+3= 12+7+6= Add the following rapidly, from the open book, naming only results, thus: 9, 15; 12, 16, 20; etc. Then the teacher may dictate the first member, and the pupil give the second. 12. By 3's and 6's to 75. 13. By 5's and 6's to 88. 14. By 10's and 5's to 100. 8+ 9+ 6 = 9+ 6+ 8 = 10+7+5= 2+11+10= 16+0+10= 21+7+ 6 = 9+13+10= 7+20+ 5 = The teacher may add to these last exercises, or the pupil be required to place upon the slate or the blackboard, original work of the same kind. 15+ 3+ 6 = 3+15+ 4 = ORAL EXERCISES. 30. 1. How many units are 8, 6, and 7? 9, 5, and 8? 2. How many tens are 4 tens, 6 tens, and 7 tens? 3. How many tens are 40, 60, and 70? 50, 20, and 80 ? 4. How many hundreds are 4 hundreds, 6 hundreds, and 7 hundreds? 5. How many hundreds are 400, 600, and 700? 6. How many thousands are 4000, 6000, and 7000 ? It will be observed that the sum of 4, 6, and 7 is the same, whether they represent tens, hundreds, or thousands. 7. How many tens and units are 30, 25, and 13? 8. How many hundreds, tens, and units are 200, 30, and 8? Ans. 2 hundreds 3 tens 8 units; read, two hundred thirtyeight, 238. Give the sum of each of the following at sight: 9. 200+50+7. 10. 400+60 +5. 11. 12. 900+40+9. 13. 1000+ 500+20. 16. 17. A barrel of flour cost 10 dollars, a ton of coal 6 dollars, and a caddy of tea 9 dollars. What was the cost of all? ANALYSIS.-The sum of 10 dollars, 6 dollars, and 9 dollars, which is 25 dollars. 18. There are 9 birds sitting on one limb, 6 on another, and 8 on another. How many birds on the three limbs? 19. An orchard contains 50 apple trees and 46 pear trees. How many trees in the orchard? In all the drill and oral exercises, little more than models can be given. The teacher is expected to give such additional examples for practice as may be required. |