Thus, 9+5=14 is read: 9 and 5 are 14, or 9 plus 5 equals 14. Beginners should adopt the first reading. Again, 8+3=? is read: 8 and 3 are how many. 56. Express by signs: 1. 3 and 5 are 8. 6. $6 + $3 = ? 7. 7 men +4 men = 11 men. 8. 5 pins + 6 pins =? 5. 6 balls added to 3 balls are 9 balls. 57. PRINCIPLE.-Only like numbers can be added. 58. The Complemental Parts of a number are the numbers whose sum equals that number. Thus the complemental parts of 7 are 3 and 4, or 1, 2, 3 and 1. 59. By Addition we find a number when its complemental parts are given. Complemental will frequently be denoted by the letter C. Thus, the c parts of 8 are 5 and 3, or 6 and 2. SUGGESTION TO TEACHERS.-In all the examples in Addition, the pupil should be required to point out the c parts and the whole. 60. The following table should be thoroughly committed to memory : 6 1+1= 2 | 2+1= 3 | 3+1= 4 | 4+1= 5 5. 5+1= 6 5+2=7 5+3=8 5+4= 9 5+5=10 5+6=11 5+7=12 5+8=13 5+9=14 3+9-12 4+9=13 8. 6+17 7+1= 8 8+1 9 9+1=10 10+1=11 9+2=11| 10+2=12 9+3=12 10+3=13 6+28 7+2= 9 8+2=10 6+39 7+3=10 8+3-11 6+4=10 7-+4-11 8+4-12 9+4-13 10+4=14 6+5=117+5=12 8+5=13 9+5=14 10+5=15 6+6 12 7+6=13 8+6-14 9+6-15 10+6=16 6+7=13 7+7=14 8+7=15 9+7-16 10+7=17 6+8=14 7+8=15 8+8=16 9+8=17 10+8=18 6+9-15 7+9-16 8+9-17 9+9=18 10+9=19 NOTE.-Pupils should read the tables thus: 1 and 1 are 2, 1 and 2 are 3, 2 and 1 are 3, 1 and 4 are 5, 4 and 1 are 5, etc. The table is expressed in signs to familiarize the pupil with their use and meaning. DRILL EXERCISES. 61. The following, read vertically, are the two complemental parts of the number written under them: 6 7 8 543 654 7654 8765 98765 123 123 1234 1234 12345 10 9 SUGGESTIONS TO TEACHERS.-These parts and their sum should be thoroughly committed to memory, so that they will be recog 213749625813749 925713648. COMBINATION BOARDS. nized at a glance. For this purpose the following is recommended: Procure two boards of convenient dimensions and dress them smoothly, so that one will slide freely on the other. Mark, number, and place them as shown in the diagram, and require the class in daily drill, to name the sum of the opposite numbers. Then shift the position of the upper board, and proceed as before, until all the combinations have been reached. These boards, especially with the addition of two or three similar ones, will afford abundant drill exercises in Addition, Subtraction, and Multiplication. We shall subsequently refer to them as the Combination Boards. See Art. 104. MENTAL EXERCISES. 62. 1. Frank is 10 years old, and his sister is 3 years older; how old is his sister? 2. John has 6 pears, and William has 5 more than John; how many pears has William ? 3. Susan has 7 roses and Lucy has 3 roses; how many roses have both girls? 4. Thomas killed 6 squirrels on Monday, and 8 squirrels on Friday; how many squirrels did he kill on both days? 5. 7 rabbits are in the garden, and 4 rabbits are in the yard; how many rabbits in all? 6. 1 hen has 8 chicks, and another hen has 5 chicks; how many chicks have both hens? 7. A boy worked 9 hours on Tuesday, and 6 hours. on Wednesday; how many hours did he work on both days? 8. John caught 5 fishes, and Ben caught 8 fishes; how many were caught by both boys? 9. Moses is 9 years old now; how old will he be 7 years from now? 10. Emma has 8 tulips, and Ann has 8 tulips more than Emma; how many tulips has Ann? 11. A man traveled 6 miles, and then went 3 miles further; how far did he travel in all? 12. Henry spent 10 cents for oranges, and 6 cents for apples; how much did he spend in all? 13. How many are 2 and 2? 3 and 4? 4 and 5? 6 and 6? 14. 7 and 7? 8 and 8? 9 and 9? 5 and 6? 7 and 3? 8 and 4? 15. 9 and 2? 5 and 7? 6 and 8? 7 and 9? 2 and 5? 1 and 8? 16. 6 and 4? 5 and 5? 8 and 2? 5 and 3? 9 and 9? 6 and 7? 17. What is the number whose complemental parts are 2 and 3? 3 and 4? 4 and 5? 5 and 6? 9 and 4? 7 and 8? 1, 3, and 4? 2, 3, and 7? 3, 5, and 8? 1, 2, 3, and 4? 18. How many are 5 and 6? 15 and 6? 25 and 6? 35 and 6? 45 and 6? 55 and 6? 65 and 6? 75 and 6? 85 and 6? 95 and 6? 20. How many are 9 and 8? 19 and 8? 29 and 8? 39 and 8? etc., to 107. 21. How many are 4 and 9? 14 and 9? 24 and 9? etc., to 103. 22. How many are 7 and 5? 17 and 5? 27 and 5? etc., to 102. 23. How many are 4 and 10? 14 and 10? 24 and 10? etc., to 104. 24. How many are 4 and 5? 5 more than that? 5 more than that? 5 more than that? 5 more than that? 3 more than that? 3 that? etc., to 22. 25. How many are 7 and 3? more than that? 3 more than 26. How many are 8 and 4? 4 more than that? etc., to 32. 27. How many are 9 a's and 6 a's? 6 a's more than that? etc., to 33 a's. 28. How many are 6 c's and 7 c's? 7 c's more than that? etc., to 41 c's. 29. How many are 2 n's and 8 n's? 8 n's more than that? etc., to 32 n's. 30. How many are 3 cows and 6 cows? 7 tens and 4 tens? 9 fives and 3 fives? 5 thirds and 2 thirds? 8 tenths and 4 tenths? |