DRILL FOR RAPID

COMBINATIONS.

TO TEACHERS.-These exercises, if properly conducted, will secure tw objects: First, the habit of fixing the attention; Second, rapidity in the combination of numbers. They should be dictated slowly at first, increasing in speed as the class acquire ability to follow. The answers may be given individually, or by the class simultaneously.

ORAL.-I. From 12, subtract 5; add 6; subtract 4; add 3; add 4; subtract 10; add 9; subtract 4; add 2; subtract 5 what is the result?

EXPLANATION.-The teacher says, "from 12 subtract 5," the "add 6," the class think 13; "subtract 4," the class "add 3," the class think 12, and so on.

class think 7;

think 9;

2. To 9, add 4; subtract 2; add 5; subtract 6; add 3; subtract 5; add 7; add 3; subtract 5: the result? 3. From 17 take 15; add 10; take 2, add 9; add 6; take 5; take 10; 4. To 23 add 5;

add 7;

take 2

take 6; add 9;

result?

add 4; take 10; add

9; take 4; add 7; add 10; take 9; add 4: result?

5. From 24 take 6; add 8; take 10; add 5; add 7; add 5; add 3: result?

take 3; add 7; take 6;
6. To 35 add 4; take 6;
add 3; take 9; add 7;

5;

take 3; add 8; take 7; add take 8; add 10 result?

SLATE.-I. To 375 add 123; subtract 47; add 23; add 47; subtract 36; add 87; subtract 68: the result?

2. From 62 take 34; add 76; take 40; add 78; take 99; add 76; add 24; take 43: result?

3. Add 344 to 65; take 64; add 784; take 678; add 407; take 309; add 860: result?

4. From 780 take 607; add 788; add 28; take 19; add 976; take 306; add 1000: result?

5. To 4678 add 6246; take 4004; add 5020; take 508; add 1700; take 468; add 2500: result?

6. From 8640 take 3476; add 4578; take 5065; add add 608; take 47: result?

87;

take 1000;

MULTIPLICATION.

MENTAL EXERCISES.

To TEACHERS.-The object of this Exercise is to develop the idea of "times," as used in Multiplication, preparatory to learning the Table.

1. If your father gives you 3 books at one time, and

3 at another, how many books will you have?

3 books and 3 books are 6 books."

2. How many times 3 books will you have? "Two times."

3. How many are 2 times 3 books? "6 books." 4. How many are 2 times 2 pencils?

5. Show this by counters or unit marks.

6. How many are 2 cents, and 2 cents, and 2 cents? 7. How many are 3 times 2 cents? Show it.

8. If you have 4 fingers on each hand, how many have you on both hands?

9. How many are 2 times 4? 10. John has 5 apples, and many how many has Henry?

:

Show it.

Henry has 2 times as
Show it.

11. If I orange costs 6 cents, what will 2 oranges cost?

ANALYSIS.-If I orange costs 6 cents, 2 oranges will cost 2 times 6 cents; and 2 times 6 cents are 12 cents. Therefore, 2 oranges will cost 12 cents.

12. How many are 7 slates and 7 slates? Show it. 13. If 1 yard of braid costs 7 cents, what will 2 yards cost? Show it.

14. At 8 cents each, what will be the cost of 2 inkstands? Show it.

15. If I writing-book costs 9 cents, what will 2 writingbooks cost? Show it.

16. How many are 2 times 10 dollars? Show it.

DEFINITIONS.

1. What is Multiplication?

Multiplication is finding the amount of a number taken or added to itself a given number of times.

2. What is the number to be multiplied called?

The Multiplicand.

3. What the number by which you multiply?

The Multiplier; and shows how many times the multiplicand is to be taken.

4. What is the number obtained by multiplication called? The Product.

When it is said that 3 times 4 are 12, which is the multiplicand? The multiplier? The product?

When it is said that 4 times 3 are 12, what is the 4? The 3? The 12?

5. What else are the multiplier and multiplicand called? Factors; for they make or produce the product. The number 12 is made up of four 38, or three 48; hence, 3 and 4 are factors of 12.

REMARK.-The product is the same in whatsoever order the factors are multiplied. Thus, if 4 be represented by

*

a horizontal row of unit marks upon the blackboard, **** and 3 by a perpendicular row of 3 unit marks, it is plain that the horizontal row taken 3 times, is equal ✰

to the perpendicular row taken 4 times.

*

6. When the multiplicand contains only one denomination, what is the operation called?

Simple Multiplication.

7. How is Multiplication denoted?

By an oblique cross, called the sign of multiplication (×). Thus, 6 x 4 shows that 6 and 4 are to be multiplied together, and is read "6 times 4," "6 into 4," or "6 multiplied by 4."

Read the following expressions: 2 x 63 × 4; 4 × 5 = 10 X 2; 2 × 2 × 6 = 12 × 2.

MENTAL EXERCISES.

1. What will 4 pears cost, at 3 cents apiece?

ANALYSIS. Since I pear costs 3 cents, 4 pears will cost 4 times 3 cents; and 4 times 3 cents are 12 cents. Therefore, 4 pears will

cost 12 cents.

**It is important for the pupil to analyze every concrete example in a concise, distinct, and scholarly manner.

2. What will 5 oranges cost, at 6 cents apiece?

3. If I hat costs 6 dollars, what will 4 hats cost? 4. At 7 dollars a barrel, how much will 3 barrels of flour come to?

5. If you obtain 6 credit-marks each day for 5 days in succession, how many will you have?

6. In 1 week there are seven days: how many days are there in 6 weeks?

7. George has 7 marbles, and Henry has 4 times as many: how many marbles has Henry?

8. At 8 cents apiece, what will 6 tops cost?
9. At 9 dollars each, what will 4 trunks cost?

SLATE EXERCISES.

Copy and multiply the following, setting each result

under the figure multiplied:

(9.) (10.) (11.) (12.) (13.) (14.) (15.) (16.)

96

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9

7

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II

9