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EXERCISES.

ART. 27.—Copy and read the following numbers :

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ART. 28.- Write the following numbers in figures : 1. Six hundred forty-eight. 2. Three thousand five hundred twenty. 3. Twenty-four thousand two hundred sixty-four. 4. Thirty-eight thousand thirty-eight. 5. One hundred eight thousand five hundred five. 6. Six hundred forty-nine thousand nine hundred one 7. One million eight hundred thousand. 8. Nine million nine thousand two hundred twenty-four. 9. Twelve million ten thousand sixteen. 10. Fifty-eight million forty-one thousand eighteen. 11. Forty million thirty thousand twenty.

12. Eight hundred million seven hundred eighteen thouBand thirteen.

13. Nine billion eight million six thousand three.

Roman Notation.

In the Roman Method of Notation seven letters are employed. The method is rarely used, except to number chapters and divisions of books, and on the dials of clocks and watches.

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These letters are combined according to the following principles :

= 30.

Principles.-1. Repeating a letter repeats its value: as XX. = 20; XXX.

2. When a letter is placed before another of greater value, its value is taken from that of the greater ; as IX. = 9; XL. = 40.

3. When a letter is placed after another of greater value, their values are added ; as XI. = 11; LX.

= 60.

4. A bar placed over a letter multiplies its value a thousand times; as V. = 5,000 : L. = 50,000 ; M. = 1,000,000.

Write the following numbers in Roman notation : 5, 8, 6, 4, 10, 15, 18, 20, 35, 88, 121, 348, 610, 450, 832, 1,321, 2,453, 6,145, 3,853, 9,009.

C'lange the following numbers to the Arabic notatior : III., VI., VIII., IX., XI., LV., LXII., LXIX., XC., CX., CXX., CCXX., CCXXV., CXXXI., CCCXXXVIII., DICX., DCCXIX., DCCCXLIII., MDCXXXVII., V., M., MDCCCLXXXVI.

12

Addition,

Progressive Oral and Written Drills. SUGGESTION.—The pupil should be taught to count with and without objects. After counting, the first process in arithmetic is to add the digits to a given number. Let the given number be 2 and add to it 2, 5, 8; 1, 4, 7; 3, 6, 9 respectively.

2 2

SLATE AND BLACKBOARD EXERCISES.

2 2 2 2 2 2 2 2
5 8 1 4 7 3 6 9

2 0

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EXERCISES IN ADDING COLUMNS.
(1) (2)
(2) (3) (4)

(4) (5) (6) (7) (8) (9) (10)
2 1 2 1 2 2 1 2 1 1
1 2 1 1 2 0 2 0 2 2
0 2 1 2 1 1 1 2 2 1
2 1 2 2 2

2 1 2 0 1 2 2 1

1 2 2 1 2

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Begin with 0, 7, 4, 11, 8, 12, 9, 6, or 13, and add those columns up and down.

SUGGESTION.—Take 3 and add to it 1, 4, 7; 3, 6, 9; 2, 5, 8 respectively. Three combinations are enough for a lesson. Illustrate each fact, so that the child may think the result clearly.

3 2

SLATE AND BLACKBOARD EXERCISES.

3 3 3 3 3 3 3 3
5 8
4 ng 9

3

3
0

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Count by 3's to 30. Begin with 1 and count by 3's to 30. Be gin with 2 and count by 3's to 30.

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Begin with 0, 8, 4, 11, 5, 13, 16, 9, 12, or 21, and add these columns up and down.

SUGGESTION.--After adding the digits to 4, add 12 and 4, 22 and 4, 32 and 4; 15 and 4, 25 and 4, 35 and 4; and so on.

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(1)
3
4

EXERCISES IN ADDING COLUMNS.
(2) (3) (4) (5) (6)

(6) (7)

(7) (8) (9) (10) 4 4 1 3 4 4 4 4 2 1 3 4 2 3 2 3 3 4 4

2 3 2 4 3 3 4 1 4 4

2 4 2 3 4. 3 3 2 1 2

3
4

IF Add each of the above columns up and down, beginning with 0, 2, 13, 8, 17, 4, 16, 9, 15, 7, or 19.

SUGGESTION.

Abstract examples like the following, containing no figure greater than 4, should be dictated by the teacher:

(1) 423244 344432 412343 344234 421443 344324 412432 344343

(2) 342434 434241 340413 414043 342414 424123 341234 412432

(3) 243143 434432 142244 434422 342244 414422 341144 424422

344243
411402
324143
443404
342244
224434
443043
344234

@ For explanation, see Article 36.

SUGGESTION.—The process with the 5's is the same as with 2, 3 and 4. After adding the digits to 5, add 16 and 5, 36 and 5, 26 and 5, 46 and 5, and so on, until all combinations up to 49 and 5 are mastered.

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Explanation. The teacher or a pupil points to the dots on the right of the vertical line, while the pupils in turn name the results obtained by adding the number on the left of this line to the given number at the top. This exercise fixes the attention of each pupil, and may be introduced with the 2's, 3's, and 4's and also with the 6's, 7's, 8's and 9's. The numbers in parentheses should be used as review drills.

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