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arrangement of the product with the first class of multipliers is more nearly like that with multipliers of one place.
Facility in the mechanical work of multiplication requires not only a ready knowledge of the several products, but also the ability to find readily the sum of the product and some given number, the number to be "carried." This is provided for in the drill exercises that follow each set of facts in multiplication. This furnishes a constant review of the addition combinations as well as the desired practice in adding a number to each product.
Each lesson in multiplication is followed by a corresponding lesson in division. The study exercises in both should be thoroughly mastered before attempting the exercises which follow. With one place divisors, short division is used. The pupils should acquire the habit of using the shorter method with divisors of one place. The several steps in long division are taught when occasion arises for their use. A special method is employed in the subject of long division. Much time is usually wasted by the pupil in the attempt to find the correct quotient figure, with the result that pupils become discouraged and acquire a dislike for the work. A method is here presented by which the correct quotient figure may be found with little difficulty. (See pp. 178-186.) The teacher should acquaint herself with the method and should see that the pupils are perfectly familiar with it before they are required to use it. Time spent in mastering it will be time saved. A study of divisors with reference to determining the quotient figure is given in the text. The pupils should be taught to inspect closely each new
divisor before attempting to use it. Use only such divisors as properly belong in each of the classes into which they are grouped in the text.
A divisor of one place is used in presenting the several steps in long division. This is accompanied by a second illustration in which the divisor consists of two places.. The authors are quite certain that many teachers will secure better results by teaching the steps in long division in connection with divisors of two places. Until the process has been thoroughly learned, use as divisors numbers in which the second figure is the same as or less than the first figure; as, 44, 55, 84, 32, 43, 75, 97, etc.
ADDITION AND SUBTRACTION
NOTATION, NUMERATION, OBJECTIVE FRACTIONS, COMPOUND NUMBERS, MULTIPLICATION, AND DIVISION
1. 1. One ten and two ones are how many ones? 2. One ten and seven ones are how many ones? 3. Twelve ones are one ten and
7. Twenty-five ones are — - tens and
8. Two tens and seven ones are ones.
11. Nine tens and six ones are
13. Ten ones are ten.
Ten tens are ones.
14. How many tens are there in seventy ones? 15. How many tens are there in eighty ones? tens. Eighty ones are
16. Sixty ones are
4. Thirty-six ones are thirty ones and ones. 5. Twenty-three apples are twenty apples and apples.
6. Thirty-seven cents are thirty cents and cents. 7. Forty-eight children are forty children and
8. Sixteen boys are ten boys and boys.
9. Eighteen oranges are ten oranges and-oranges. 10. Twenty girls and six girls are — - girls. 11. Thirty marbles and eight marbles are marbles.
12. Forty girls and ten girls are — girls. 13. Twenty cents and ten cents are - cents. 14. Twenty-four days and ten days are — - days. 15. Thirty-six days and ten days are — days. 16. Sixteen boys and ten boys are- boys. 17. Seven boys and ten boys are — 18. Nine birds and ten birds are birds.
19. Ten oranges and six oranges are —
20. Ten books and four books are books.
21. Eight pencils and ten pencils are — pencils. 22. What number is ten more than thirty?
23. What number is ten more than seventy?
24. Thirty-five is ten more than -. Thirty-six is ten more than
25. Forty-six is how many more than thirty-six? 26. Sixty-eight is how many more than fifty-eight?
3. 1. There are
2. There are
100's in 400. There are - l's
100's in 1000. Count by 100's
3. What number is one hundred more than 60? 4. What number is one hundred more than 67? 5. What number is one hundred more than 167? 6. What number is one hundred more than 625 ? 7. Write a number that tells 9 tens and 4 ones. 8. Write a number that tells 2 hundreds, 6 tens, and 8 ones.
4. 1. What number is one more than 6?
2. What number is one more than 16?