Εικόνες σελίδας
PDF
Ηλεκτρ. έκδοση

20 =

[ocr errors]

=

8. 20 multiplied by .2, means, find 2 tenths of 20. One tenth of —; 2 tenths of 20

Story-At $20 an acre, .2 of an acre of land would cost dollars.

9. 8 divided by .4, means, find how many times 4 tenths are contained in 8. 8 = 80 tenths. 4 tenths are contained in 80 tenths

times. Story-I paid $8 for potatoes at $.4 (4 dimes) a bushel; I bought bushels.

10. $6.36 divided by 3, means, find i third of $6.36. One third of $6.36

Story-I paid $6.36 for 3 barrels of apples; 1 barrel cost

11. The sum of 176.4 and 148.75 is
12. The difference of 276.4 and 148.23 is

13. 20 multiplied 3.2, means, take 5 times 20, plus 2 tenths of 20. 3 times 20

2 tenths of 20 = 3 times 20, plus 2 tenths of 20

Story-At $20 an acre, 3.2 acres of land are worth dollars. 14. 4 divided by .05, means, find how many times 5 hundredths are contained in 4. 4 = 400 hundredths. 5 hundredths are contained in 400 hundredths times. Story-I paid $4 for tablets at $.05 (54) each; I bought tablets.

15. 5.6 tons divided by 4, means, find 1 fourth of 5.6 tons. One fourth of 5.6

and

tons. Story-A farmer sold 4 loads of hay, the entire weight of the hay was 5.6 tons; the loads averaged and

tons. 16. .1 multiplied by .1, means, find 1 tenth of 1 tenth. One tenth of 1 tenth =

17. 2.5 divided by .05, means, find how many times 5 hundredths are contained in 2.5. 2.5 = 250 hundredths. 5 hundredths are contained in 2.5 (250 hundredths) times. Story-1 paid $2.5 for pencils at $.05 (54) each; I bought pencils.

18. $24.5 divided by 5, means, find 1 fifth of $24.5. One fifth of $24.5 =

Story-I paid $24.5 for 5 tons of coal; 1 ton cost

19. .3 multiplied by .2, means, find 2 tenths of 3 tenths. One tenth of 1 tenth One tenth of 3 tenths =

Two tenths of 3 tenths

20. $24.5 divided by $.5, means, find how many times 5 tenths of a dollar are contained in $24.5 (245 tenths dollars). 5 tenths are contained in 24.5 (245 tenths) times. Story-I paid $24.5 for apples at $.5 (5 dimes) a bushel; I bought bushels.

21. $8.2 divided by 5, means, find 1 fifth of $8.2. One fifth of $8.2 ($8.20)

Story-I paid $8.2 for 5 yards of cloth; 1 yard cost

SUGGESTIONS TO TEACHERS.

1.

ORDER OF PROCEDURE IN PART I.

page, the

STEP 1.-Prepare the pupil by means of oral instruction for the work of a given page. This preparation may be, in part, the slow reading to the pupil of the figure problems* upon

the teacher hesitating at each blank for the pupil to supply the word. In this preparatory work, no book should be in the hands of the pupil. New words should be first presented through the voice of the teacher in the expression of thought. They may then be written upon the blackboard by the teacher, erased, and the pupil exercised in both oral and written reproduction.

STEP 2.-The book should be put into the hands of the pupil, and he should read, first silently, then orally, the figure problems upon any page for which proper preparation has been made.

STEP 3.—The pupil may attempt the letter problems* at his desk without further assistance. If he is unable to solve these, review the figure problems and give others similar to them.' In some instances it may be well to have the figure problems solved upon the blackboard as preparation for the letter problems.

2.

Wherever the word “storyfollows a problem, as on pp. 12 and 13, require the pupil to make a statement showing how the problem might originate in business or other experience; thus, the story for problem. (f), page 12, might be, A man divided 43 acres of land into lots each containing zo of an acre. There were 95 lots.

3.

The separatrix, as an aid in “pointing off” in multiplication and division of decimals, is mentioned in a note on page 133. Its use is illustrated on page 143. Its occasional use in blackboard work earlier in the course may be helpful; but a too early reliance upon formal rules is to be avoided if the purpose of the work is the development of the thought-power of the pupil.

* The figure problems are those designated by figures; the letter problems, those designated by letters.

ARITHMETIC.

PART 1.

SIMPLE NUMBERS.

[ocr errors]

and by

[ocr errors]

1. Three is an exact divisor of 6, of 9, of of of and of

Four is an exact divisor of
2. Eighteen is exactly divisible by 2, by by

28 is exactly divisible by
3. Two is an exact divisor of 4, 6,

etc. 4. A number that is exactly divisible by 2 is called an even number; 8, 10,

are even numbers. 5. Two is not an exact divisor of 1, 3, 5,

etc. 6. A number that is not exactly divisible by 2 is called an odd number; 9, 11,

are odd numbers. 7. 37 is an number.

24 is an

number. 8. Tell which of the following are odd numbers and which are even numbers: 375, 256, 320, 197, 281, 378, 584, 252, 323, 569.

(a) Copy the numbers given in problem 8 and find their

sum.*

(b) Find the sum of all the odd numbers from 1 to 15 inclusive.

(c) Find the sum of all the even numbers from 2 to 16 inclusive.

* Problems designated by letters are for the slate.

FRACTIONS.

1. When two or more fractions have denominators that are alike, they are said to have a common denominator. Io, 1o, 1., and 1, have a

and do not have

a

[ocr errors]
[ocr errors]

Reduce to equivalent fractions having a common denominator. 2. , , 1 (Change to 12ths.)

} À
3. }, { 1
(Change to
.) 1

I
(Change to .)
5. 1 4. (Change to .) 1 = 1 / 2 퓽 =
(a) and (b) and (c) s and

=

1
5 7

=

27

[ocr errors]
[ocr errors]

21

6. Add and I can change eighths and thirds to -ths.

twenty-fourths and twenty-fourths twenty-fourths.

(d) Find the sum of 5765 and 239 3.

7. From subtract ž. I can change sevenths and thirds to —sts.

twenty-firsts less 'twenty-firsts

twenty-firsts.
(e) Find the difference of 572, and 3681.
8. Divide by zo.

This means, find how many times 23 is contained in I can change to twentieths.

1 twentieth is contained in twentieths times. Story.*

(f) Find the quotient of 4 divided by zo. (Change 41 to twentieths.) Story.t

(g) 1474 +383. (h) 3745 -1813. (i) 27} bu. + 24 bu. I

3

[ocr errors]

* See Note (9) page 6.

† See paragraph 2, page 10. | Tell the meaning. Change 27% and 2to halves. Story. See note (14) page 7.

DECIMALS—THOUSANDTHS.

1. .125 and .006 are
2. .125 and .06 are
3. .125 and .6 are
4. .275 less .006 are
5. .275 less .06 are

thousandths. thousandths. thousandths.

thousandths. thousandths.

6. 2.4 and 3.104 are and thousandths. (a) Add 27.006, 14.8, and 25.06.

7. 36.025 less 1.008 equals and thousandths. (b) From 8.175 subtract 3.023.

8. 3 times 2.005 is and thousandths.
(c) Multiply 26.008 by 4.
9. Divide .035 by .007. This means

4* (d) Find the quotient of .375 divided by .005. Story.t 10. Divide .035 by 7.

This means

5* (e) Find the quotient of 35.049 acres divided by 7. Story.

11. At $.05 each, for $1.25 I can buy pencils. 1.25 •.05 =

12. At $.05 each, for $2 I can buy pencils. 2+.05 = (f)

(h)
(i)

(j) Add. Subtract. Multiply. Divide.

Divide. 46.27 54.75 7.0541 $.005)$.3859 5)$.3858 25.308 8.326

5

*These figures refer to notes on page 8. † See page 10, paragraph 2.

Write the decimal point in the product immediately after writing the tenths' figure of the product.

" Point off” in division of decimals by thinking what the problems mean. Problem (i) means, find how many times 5 thousandths arc contained in 385 thousandths. 5 thousandths are contained in 385 thousandths 77 times. Problem (j) means, find 1 fifth of 385 thousandths. A of 385 thousandths is 77 thousandths, or .077.

« ΠροηγούμενηΣυνέχεια »