Under the head of "7," giving only results; downwards thus: 5, 8, 12, 6, 1, 2, 7, 10, 3, 4, 9, 11; upwards, 11, I. MULTIPLYING AND DIVIDING A FRACTION BY A WHOLE NUMBER. Note.-There will be no difficulty in lessons like the following, if the teacher will let technical terms alone, METHODS OF TEACHING. take only one thing at a time, and drill upon it until it is fixed in the mind by practice. The first steps must be illustrated by broken crayons or sticks. 1. What is one half of 4? 2. What is the product of 4 multiplied by †? 3. What is one half of 12? 4. 12 multiplied by =? 5. What is of 5 ? 6. Multiply 5 by 1. EXERCISES. 1. Find one half of each of the even numbers from 2 to 20. 20, 40, 60, 80, 100. 2. Slate and Blackboard Drill. 1. The question "What is one half of 4" is expressed thus in written arithmetic: Multiply 4 by 1. Slate Work.-4x=? 4÷÷÷2 =2. Ans. In a similar manner perform each of the following: 1. Multiply each of the even numbers from 2 to 100 by 1. 2. Multiply each of the odd numbers from 3 to 99 by 2. III. MULTIPLYING BY A FRACTION. 1. What is of 8? 2. Multiply 8 by 1. 1. Oral Questions. 3. What is the product of 8 multiplied by ? 4. How do you multiply 8 by ? Ans. By dividing 8 by 4. 5. Find of 12, 16, 20, 24, 28, 32, 36, 40, 44, 48. 8. Find of 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49. 2. Slate and Blackboard Drill. 1. Put each of the oral questions in the preceding lesson into slate work. 2. Multiply each of the even numbers from 4 to 100 by 1. 3. Multiply each of the odd numbers from 5 to 99 by . 4. Multiply every number that ends with a cipher from 10 to 100 by 1. 5. Multiply every number ending in 5 from 15 to 105 by 4. METHODS OF TEACHING. IV. DIVIDING BY A FRACTION. 1. Oral. 1. How many times is contained in 2? 2. How can you show it? Ans. By taking 2 crayons and breaking them into halves. Do it. 3. How many times is contained in 4? Show it by drawing on the blackboard a line four inches long, and then dividing into half-inches. 4. Divide 2 by 1. 5. Divide 4 by 1. 6. What is the quotient of 2 divided by . 7. Find the quotient of 4 divided by . 8.2÷? 4÷=? = EXERCISES. Rule.-Multiply the number by 2. 1. Divide each of the even numbers from 2 to 100 by 1. to 100. 4. Divide by each number from 15 to 105 ending in 5. 2. Slate and Blackboard Drill. Questions like the preceding are put into the form of written arithmetic according to the following Require the class to put each of the preceding questions into the form of written arithmetic, and then dictate ten examples, using larger numbers. SECTION VI.-ANALYTICAL WORK IN FRACTIONS, FOR GRAMMAR-SCHOOL GRADES. Note. In undertaking to train pupils to a clear conception of analytical processes in common fractions, it is desirable to proceed slowly, taking a great number of easy operations limited to small numbers upon each new process. In the following lessons the analytical method is pursued exclusively, and only one method is given. Teachers who desire to add other explanations can do so; but, in the beginning, it is best not to confuse the minds of pupils with too many things at once. I. MULTIPLYING AND DIVIDING BY A FRACTION. 1. What is of 20? Analysis. Since 2. How many times is 1. Oral Drill. of 20 is 5, will be 3 times 5, or 15. contained in 15? Analysis. Since is contained 4 times 15, or 60 times, will be contained of 60, or 20 times. 3. What is the product of 20 multiplied by ? 4. What is the quotient of 16 divided by ? 5. Multiply 12 by 4. 6. Divide 9 by 4. 7. What is times 24 ? 8. How many times is contained in 24? 9. Find of 100. 10. How many times is contained in 20? |