The 45 is 4 tens and 5 units; or 3 tens, and 1 ten, and 5 units. The 1 ten and 5 units are 15 units; now take away the 6 units, and there are 9 units left. In the next column as it stands, we have to take 2 tens from 4 tens; but one of those 4 tens is already disposed of; so there are but 3 tens left; and 2 tens from 3 tens leaves 1 ten. The answer is, therefore, 1 ten, 9 units, or 19, as before. Of course only one of these methods should be taught; the teacher should make up her mind previously as to which she will adopt, and adhere to it. Third Method: subtracting from Ten. Using the same example as before 45 26, let the six be taken from the borrowed ten, before adding on the 5; thus 6 from 10 leaves 4, and 4 and 5 are 9; 3 from 4 leaves 1 as before. This method is very useful at a later stage, in Compound Subtraction; thus, in 13s. from 12s. take 13s. from 20, this leaves 7, and 7 and 12 are 19, and similarly with the borrowed 1d. (4 farthings) and 1s. (12 pence.) SIMPLE MULTIPLICATION TO 6 × 12 72. = First Stage.-Nearly all these exercises should be concrete; as 4 rows of panes, and 6 in a row = 24, etc. Second Stage. In this the multiplier should be no larger than 6, and there should be no carrying, as 213 2 Third Stage.-Same as 2, with carrying. 246 3 426 738 The children should also be exercised in writing out, and repeating, the Multiplication Table (see Part I.). As a matter of fact the children in Standard I. readily learn to do simple Mental Division; as, Share 12 marbles among 3 boys:-answer, 4 marbles to each. If this is done the children readily see that Multiplication and Division are the opposites of each other; thus 4 × 5 = 20. Fours in 20, 5; and Fives in 20, 4. In the Mental Arithmetic of Standard I., the Arithmetic of 2s. is readily taught, and much enjoyed; as, How many shillings, sixpences, fourpenny, threepenny pieces, pence, half-pence, in 1s. and 2s. ? What part of 2s. is ls. 6d. ? This introduces the meaning of,,,, etc., and, after a little practice, Standard I. children readily grasp the meaning of these fractions. The same remarks apply to the Arithmetic of a yard, and of a foot. Finally, very interesting questions are made out of "shopping," spending a 1s. and 28.; as, A man had ls. in his pocket, and bought 2 cakes worth 3d. each: how much had he left ? It will be sufficient for the writer merely to indicate the lines along which the young teacher should travel, but the latter should prepare before the lesson sufficient typical examples to interest and instruct the class. As the teacher will experience the most difficulty in preparing exercises in Mental Arithmetic for Standard I., typical kinds are appended below: MENTAL ARITHMETIC (STANDARD I.). Notation and Numeration. I. What figures must be used to write the following? Seven hundred and seven. A hundred and eleven. One hundred and ten. Nine hundred and ninety. II. Say in written : A hundred and thirteen. Five hundred and ten. Seventy tens. words how the following numbers are 111 713 110 303 1000 330 770 907 III. What is the tens figure in Six hundred and twenty-four, One hundred and ten, Six hundred and six, Thirty-three, Nine, One hundred and eleven ? IV. 6 + 4 + 3 + 2 7+ 4 + 6 + 3 6+ 9 + 3 + 7 6 + +7+0 8 + 0 + 9 + 7 12 + 3 + 7 + 4 13+ 7+ 8+ 9 148 +12 + 3 V. Give the sum of Two+three + four. Three four + five. Six + seven + eight. Addition. 15+ 7+ 8+ 6 Seven sixteen + nine. VI. Give in words, without writing on slates, the sum VII. How many fingers have you on one How many on both hands? How many fingers have three boys? How many toes and fingers have you? hand? How many legs have three boys and four horses? How many eyes in a class of seventeen boys? How many eyes and ears in a class of twelve boys? How many legs have three cows, two horses, and three men ? If 0 stands for nothing, how can 2 and 0 be twenty? What do three twos, standing side by side, stand for? VIII. In adding up odd numbers of figures that run in order, take the middle one and multiply it by the number of figures given. Thus in 2, 3, 4, the middle figure is 3, and 2+ 3+ 4 is 3 × 3 = 9. X. How many times does the clock strike from one to three o'clock? How many times does the clock strike from one to five o'clock ? How many times does the clock strike from one to seven o'clock ? How many times does the clock strike from one to nine o'clock? How many times does the clock strike from one to eleven o'clock ? How many times does the clock strike from one to twelve o'clock ? XI. A man owes 17 shillings and 6 shillings and 5 shillings: how much does he owe altogether? A man bought a cow for £24, a horse for £36, and a pig for £7: how much must he pay? PART II. E |