66 T. By what process have you taken 304 five times? "By multiplying it." T. What, then, is multiplication? "Multiplication is the process of taking one number T. How many times is the number taken in the above example? "It is taken five times, or as many times as there are units in the multiplier." 7. Now complete your definition. Multiplication is the process of taking one number as many times as there are units in another." These steps should be repeated with other examples, until the definition is clearly reached and accurately stated. It should then be written and compared with the author's definition, which should be thoroughly memorized. 4. Rules.--These should also be deduced and stated by the pupils. The true order is this: 1. A mastery of the process without reference to the rule. 2. The recognition of the successive steps in order, and the statement of each. 3. The combination of these several statements into a general statement. 4. A comparison of this generalization with the author's rule. 5. The memorizing of the latter. Take for illustration the rule for adding fractions. T. What is the first step? "Write the fractions, separating them by the plus sign." (Pupils write an example.) T. What is the second step? "Reduce the fractions to a common denominator." T. What is the third step? "Add the numerators of the new fractions." T. The fourth step? "Under their sum write the common denominator." These questions should be repeated until the answers are promptly and accurately given, and then they should be united in a general statement. The first step may be omitted in the rule. 5. Questions for Review.-These are designed as a final test of the pupil's knowledge. Before they are reached, the definitions, principles, and rules should be thoroughly mastered, and the pupils should be able to make a topical analysis of them and recite each in order. 6. Fractions. This section presents only the elements of Fractions, and these in the simplest manner. The subject is more exhaustively treated in the COMPLETE ARITHMETIC. The reduction of compound fractions is made introductory to the multiplication of fractions, as the two processes are best taught together. 7. One Method.-Elementary instruction in arithmetic should aim to make the pupil ready and accurate in the use of one method for each operation. This may not be the shortest method in every case; but, as a rule, the pupil will reach the result sooner by it than by a method that is less familiar. The attempt of the young pupil to use several methods, results in hesitation and confusion. For other suggestions see the MANUAL OF ARITHMETIC. rows. LESSON I. ORAL EXERCISES. Article 1.-1. Here are one hundred balls in ten How many balls are there in one row? How many balls in two rows? In three rows? In five rows? In eight rows? In ten rows? 2. How many ones in ten? How many ones in two tens? In five tens? Eight tens? Ten tens? 3. How many tens in ten? How many tens in twenty? In thirty? Forty? Sixty? Seventy? Eighty? One hundred? Art. 2. When a number is expressed by two figures, the first or right-hand figure denotes Units, and the second or left-hand figure denotes Tens. 4. Which figure in 25 denotes units? Which denotes tens? 5. How many tens and units are there in 37? In 57? 46? 33? 50? 45? 64? 88? 94? 99? Art. 3. In reading numbers, the tens and units are read together as so many units. Thus, 45 is read forty-five units, or, more briefly, forty-five. Read the following numbers, and give the number of tens and units in each: Art. 4. When a number is expressed by three figures, the third or left-hand figure denotes Hundreds. 12. Which figure in 245 denotes hundreds? Which figure denotes tens? Which denotes units? 13. How many hundreds, tens, and units in 426? 708? 340? 235? 406? 560? 666 ? Read the following numbers, and give the number of hundreds, tens, and units in each: |