NOTE TO TEACHERS. A variety of expedient methods may be pursued, in examining written operations in arithmetic; and perhaps no one system can be adopted, from which it will not be found advantageous, occasionally, to depart. My own practice for several years, with occasional variation, has been as follows. A certain number of examples having been assigned for a lesson the day previous, each scholar is supposed to be prepared with the solutions upon his slate, and the class are paraded for recitation. Every scholar passes his slate into the hands of the scholar next above him, except the head scholar, who hands his to the foot scholar. The first scholar then reads from the slate he holds, the answer to the first example; and the teacher, holding the key, declares the answer to be right, or wrong. When the answer has been pronounced right, it is the duty of every scholar who finds a different answer upon the slate he holds, to signify it, and the error is noted against the owner of the slate. The first example being disposed of, the answer to the second example is read by the second scholar, and disposed of in like manner. Thus the reading of answers goes through the class, and each scholar detects the errors of his neighbour. Individual scholars are occasionally called upon to explain their work in a particular example, and to give their reasons for the operation adopted. By this mode of examination, the work of a large class is particularly inspected, in nearly thesame time that would be required to inspect the work of one scholar. Besides the advantage of despatch in this mode of examination, the exercise itself is beneficial to the pupils.-Each scholar acts the part of an inspector- he is interested to be critical- he acquires a facility in deciphering the work of others- and thus his perceptive powers are cultivated, and a habit of alertness is attained. [The KEY, alluded to above, is published separately.] In teaching the principles of Numeration, teachers will find an advantage in the use of Mr. Shaw's Visible Numerator. It is a recent invention, for which Mr. Shaw has secured a patent: it consists of a series of blocks, corresponding, in comparative magnitude, with the comparative value of the dif ferent orders of units. Before the learners attempt to perform operations by figures, they should be able to write figures with facility, and to arrange them regularly. To attain this object, the arrangement of figures below, may be repeatedly copied upon the slate, until a good degree of despatch and accuracy is acquired. 423456 7 8 9 0 1 2 3 4 5 6 7 8 901234 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 1 2 3 4 5 6 123456 7 8 9 0 1 2 345678 901234 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 89 WRITTEN ARITHMETIC. CHAPTER 1. NUMERATION. SECTION 1. THE UNIT, which is the first thing to be considered in numeration, signifies One. The figure 1 stands for one unit; 2, for two units; 3, for three units; 4, for four units; 5, for five units; 6, for six units; 7, for seven units; 8, for eight units; 9, for nine units. The TEN is a number which is made up of ten units. One ten is expressed thus, 10; two tens, thus, 20; three tens, thus, 30; four tens, thus, 40; &c. The HUNDRED is a number which is made up of ten tens. One hundred is expressed thus, 100; two hundreds, thus, 200; three hundreds, thus, 300; &c. Suppose the balls below, which are arranged in three places, to represent 8 units, 3 tens, and 1 hundred. HUNDRED TENS UNITS 138 Learn from the figures above, that the first or right hand figure expresses units, the second figure expresses tens, and the third figure expresses hundreds. H* of ten The THOUSAND is a number, which is made up hundreds. One thousand is expressed thus, 1000; two thousand, thus, 2000; three thousand, thus, 3000; &c. Observe, that a figure expresses thousands, when it stands in the fourth place from the right; therefore ten thousand is expressed thus, 10 000; and a hundred thousand, thus, 100 000. Examine the following Numeration Table. Begin at the right hand, and observe, that every three figures may be viewed by themselves;— the first three express so many units, tens and hundreds; the second three, so many Thousands; the third three, so many Millions; the fourth three, Billions; the fifth three, Trillions.* To read the line of figures in this table, begin with the left hand figure, and proceed as follows. Tens - UNITS 472 156 795 841 526 This character, 0, called nought, or cipher, expresses nothing of itself-it stands only to occupy a place, where there is none of the denomination belonging to that place to be expressed. For example, in the number 240, there are no units; therefore a cipher stands in the units' place. In the number 407, there are no tens; therefore a cipher stands in the tens' place. * The old method of embracing six figures in a period, is of late abandoned. Note to Teachers. Require the learners to copy upon their slates the following figures expressing numbers. Then require them to read from their slates the several numbers expressed. Note to Teachers. The following numbers written in words, are to be written upon the slate in figures. If the learner meet with difficulty in denoting the larger numbers, he may be instructed to repeat the Numeration Table, from units up to the highest denomination in the number to be denoted; and, while repeating the table, he may make a dot for each denomination, arranging the whole in a line. Then, the figure to express the highest denomination may be written under the left hand dot, and there will be no difficulty in arranging the figures of other denominations under their respective dots. 1. Seventy. 2. Forty-eight. 3. One hundred and twenty-four. 4. Six hundred and nine. 5. Three thousand, and six hundred. 6. Two thousand, four hundred and fifty. 7. Nineteen thousand, and sixty-eight. 8. Five thousand, seven hundred and thirty-one. 9. Thirty-six thousand, seven hundred and forty. 10. Two hundred and sixty-eight thousand. 11. Nine hundred five thousand, and one hundred. 12. Eighteen thousand, seven hundred and thirty-five. 13. Seven hundred thousand and nine. 14. Thirteen million, sixteen thousand, and nineteen. 15. One hundred five million, two thousand, and one. 16. Six billion, forty million, and six thousand. 17. Twenty-one billion, and one hundred million. 18. Five trillion, fourteen billion, seventy million, one thousand, two hundred and thirty-six. 19. One hundred twenty-two trillion, eight hundred and forty-seven thousand. 20. Ten billion, nine hundred eighty-seven thousand, seven hundred and thirty. 21. Seven hundred trillion, and thirty-six thousand. 22. Twelve billion, eight hundred forty-two thousand, seven hundred and eighty. 23. Twenty-nine trillion, eight hundred nine billion, one thousand, and eighteen. 24. Eight hundred twenty-three billion, ten million, eight thousand, and fifteen. Questions to be answered Orally. (1) What is a unit? (2) What is the greatest number, that can be expressed by one figure alone? (3) In what situation must the figure 9 stand, to express 9 tens ? (4) What is the greatest number that can be expressed by two figures? (5) Recite the several denominations of numbers, from units to trillions, as they stand in the Numeration Table. (6) What denominations are expressed in the 1st. three places of figures? (7) What denominations are expressed in the 2nd. three places? (8) Where must the figure 7 stand to express 7 tens of thousands -that is, seventy thousand? (9). What denominations are expressed in the 3rd. three places? (10) Where must the figure 2 stand, to express two hundred thousand? |