METHODS OF TEACHING.

2. Slate and Blackboard Drill.

Multiplication.

Model 1. 20 × =? 2045.

5 X 3 = 15. Ans.

Analysis.-Divide 20 by 4 to find , and multiply the quotient 5 by 3 to find 2.

Division.

Model 2. 15÷=?

15 × 460. 60320. Ans.

Analysis.- Multiply 15 by 4 to find how many times is contained in 15, and divide the product 60 by 3 to find how many times is contained in 15.

2. How do you find

of any number?

Ans. By dividing it by 2.

3. How do you divide by 2?

Ans. By multiplying the denominator by 2.

4. In what other way can you show this?

Ans. 2, and 1 of 2 = 1.

5. How many times is contained in ?

Ans. a time.

6. How do you divide any number by ?

Ans. By multiplying it by 2.

7. How do you divide by ?

Ans. By multiplying by 2, and this is done by dividing the denominator 4 by 2.

8. In what other way can you show this?

Ans. 2, and is contained in as many times as 2 is con

=

Put each of the preceding examples into the form of written arithmetic.

1. What is of 2? Ans. 3.

2. How is the answer obtained?

Ans. By dividing by 2, which is done by multiplying the denominator.

3. How many times is contained in? Ans. of a time.

4. How is this answer obtained?

Ans. By multiplying by 2, which is done by dividing the

denominator.

5. What is of Ans. . Why?

6. What part of a time is contained in? Ans. § of a time. Why?

METHODS OF TEACHING.

7. What is the product of multiplied by? Ans. 3. Why? 号

8. What is the quotient of divided by? Ans. . Why?

9. Multiply by ? Ans. 4. Why?

10. Divide by ? Ans. §. Why?

IV. MENTAL MULTIPLICATION.

Principle.-Multiplying by a fraction gives a product less than the multiplicand.

Rule.-Divide the multiplicand by the denominator of the multiplier.
Examples.

1. What is the product of & multiplied by ? etc.
2. Dictate ten similar examples.

V. MENTAL DIVISION.

Principle.-Dividing by a fraction gives a quotient

greater than the dividend.

Rule.-Multiply the dividend by the denominator of the divisor.

Examples.

1. How many times is contained in ??
2. What is the quotient of divided by ?

3. Dictate ten similar examples.

VII. MENTAL MULTIPLICATION.

1. What is of ? Ans. Since of is, will be twice

or.

2. What is of

3. Multiply by 3.

Why?

4. Dictate twenty similar examples.

VIII. MENTAL DIVISION.

1. How many times is contained in ?

Analysis. Since is contained in 3 4 times 3, or §, of a time,

Analysis.—Divide by 3 to find †, | Analysis.—Multiply by 3 to find

爻=

X. WRITTEN MULTIPLICATION.

Analysis. Since of is, is 3 times, or 2;

which process is equivalent to multiplying the two

numerators together for a numerator, and the two denominators for a denominator.

Rule.-Place the product of the numerators over the product of the denominators.

METHODS OF TEACHING.

1. Divide by 4.

XI. WRITTEN DIVISION.

Explanation. Multiply 3 by 4 in order to find how many times is contained; and divide that result by 3 in order to find how many times is contained.

XII. METHOD BY INVERTING THE DIVISOR.

Analytical Model.

1÷4=?

8×4=8

3. Ans.

Practical Model.

多÷星=?

Rule.-Invert the divisor, and place the product of the numerators over that of the denominators.

SECTION VII.-WORKING MODELS IN MENTAL ARITHMETIC, FOR GRAMMAR-SCHOOL GRADES.

Directions. Read each question to the class, allow from one quarter to one half a minute for the mental solution, and require each pupil to write his answer on the slate. When the ten questions have been given, let pupils exchange slates, and credit the work as the teacher reads the correct answers.

1. What is of 84?

SET I.

2. How many times is contained in 6?

3. Divide by 4.

4. Multiply by 3.

5. Divide by 1.

6. How many times is contained in §?

7. Multiply 14 by 11.

8. Divide 5 by 51.