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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.

DIVISION

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.

CHAPTER III

ADDITION AND SUBTRACTION

NOTATION, NUMERATION, OBJECTIVE FRACTIONS, COMPOUND NUMBERS, MULTIPLICATION, AND DIVISION

ones.

7.

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
4. Eighteen ones are — ten and

ones.
5. Twenty ones are — tens.
6. Two tens and three ones are ones.
Twenty-five ones are tens and

ones.
8. Two tens and seven ones are ones.
9. Three tens are ones.

Four tens are

ones. 10. Eighty ones are how many tens?

Nine tens and six ones are ones. 12. Seventy-eight ones are — tens and

ones. 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 ?

16. Sixty ones are tens. Eighty ones are — tens.

11.

ones.

ones.

ones.

ones.

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2. 1. Five tens and no ones are
2. Five tens and nine ones are
3. Twenty-four ones are twenty ones and
4. Thirty-six ones are thirty ones and

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 children.

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 boys. 18. Nine birds and ten birds are birds. 19. Ten oranges and six oranges are — oranges. 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?

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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

100's in 400. There are l's in 400.

2. There are 100's in 1000. Count by 100's to 1000.

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 ?
3. What number is one more than 13 ?
4. What number is one more than 20 ?
5. What number is one more than 29 ?
6. What number is one less than 4 ?
7. What number is one less than 9 ?
8. What number is one less than 20 ?
9. What number is one less than 29 ?
10. What number is one less than 40 ?

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