CARD No. 5. Combination of Numbers. 11 and 6 are 17, and 7 are 24, and 5 are 29, and 4 are 33, and 4 are 37, and 5 are 42, and 3 are 45, and 4 are 49, and 6 are 55, and 6 are 61, and 7 are 68, and 2 are 70, and 6 are 76, and 3 are 79. 13 and 4 are 17, and 4 are 21, and 6 are 27, and 5 are 32, and 5 are 37, and 3 are 40, and 4 are 44, and 5 are 49, and 2 are 51, and 7 are 58, and 5 are 63, and 4 are 67, and 2 are 69, and 5 are 74. 8 and 7 are 15, and 4 are 19, and 5 are 24, and 3 are 27, and 4 are 31 and 9 are 40, and 1 are 41, and 7 are 48, and 5 are 53, and 6 are 59, and 5 are 64, and 3 are 67, and 4 are 71, and 5 are 76, and 5 are 81. 9 and 7 are 16, and 3 are 19, and 9 are 28, and 3 are 31, and 5 are 36. 5 and 7 are 12, and 5 are 17, and 6 are 23, and 4 are 27, and 5 are 32, and 7 are 39, and 5 are 44, and 4 are 48, and 5 are 53, and 5 are 58, and 3 are 61, and 7 are 68, and 2 are 70, and 5 are 75, and 8 are $3. 6 and 9 are 15, and 7 are 22, and 5 are 27, and 4 are 31, and 6 are 37, and 5 are 42, and 7 are 49, and and 3 are 52, and 6 are 58, and 7 are 65, and 4 are 69, snd 5 are 74, and 3 are 77, and 2 are 79, and 5 are 84. 7 and 6 are 13, and 4 are 17, and 3 are 20, and 3 are 23, and 7 are 30, and 8 are 38, and 7 are 45, and 4 are 49, and 5 are 54, and 8 are 62, and 5 are 67, and 4 are 71, and 8 are 79, and 7 are 86, and 5 are 91, and 7 are 98. 4 and 7 are 11, and 5 are 16, and 7 are 23, and 5 are 28, and 8 are 36. When boys become acquainted with the combination of numbers so that they can add easily, compel them to perform their operations without naming all the figures. For example, begin with lesson first; 3, 5, 8, 9, 13, 15; 5, and carry I to 2, [see lesson first in addition] 3, 4, 7, 9, 12, 14; set down 14 on the left side of 5. Again in lesson second say, 4, 8, 13, 15, 16, 20; 0 and carry 2 to 3 ;-5, 7, 10, 15, 19, 22; set down 22 on the left side of 0. Let a number of expert boys or girls practice by this mode of reckoning, and give preference to whom due, as in spelling classes. + ADDITION TABLE No. 1 3 4 5 6 7 8 9 7 8 9 9 8 7 6 5 4 3 2 1 9 9 8 7 6 5 4 3 2 1 9 1 8 7 6 8 9 9 8 7 6 5 2 This table must be reckoned to the right and left and perpendicularly, forward and backward, thus, 1, 3, 6, 10, 15, 21, 28, 36, 45, 54, 62, 69, 75, 80, 84, 67, 89, 90, 99. That is to say, 1 and 2 are 3, and 3 10, and 5 are 15, and 6 are 21, and are 28, and 8 are 36, and 9 are 45, and 9 are 54, and 8 are 62, and 7 are 69, and 6 are 75 and 5 are 80, and 4 are 84, and 3 are 87, and 2 are 89, and one will make 90, and 9 will make 99. are 6, and 4 are Let classes exercise by this table as in spelling, give ing preference to the most expert; but enjoin upon all to omit the words is and are, and the names of the figures, in order to reckon expeditiously, as 1, 3, 6, 10, 15, 21, &c. It is not, however, intended for those little gentlemen who first begin in calculation, unless they choose this mode of reckoning, by having previously familiarized their minds with the table. This mode of reckoning is intended for exercising the minds of scholars after they have made some small progress in addition-when they have learned to repeat this table readily, no class can vie with them, in even combat, without the same practical knowledge. This, as well as the other tables, ought always to hang in plain view. THE PESTALLOZZIAN PLAN. MODE OF OPERATION. First. Instead of figures, let boys make use of peas, beans, kernels of Indian corn, short pieces of sticks, leaves of grass, of weeds, or any other convenient materials. To a certain number of these objects, add another number, then count how many there are in the whole: call this the sum total, From another number of these objects, take away a certain number, and ascertain how many are left: call this number which is left a remainder. Thus we can perform Addition and Subtraction with real objects, instead of those which are imaginary. This exercise will afford children pastime when they are out of school; it will keep their minds intent on the business they are sent to perform, and will not disappoint their guardians, nor grieve their hard-labouring and frequently indigent parents. But these two rules are not all that can be performed by moveable objects without figures. Multiplication and Division, may be wrought with the same måterials on a checker-board about two feet square; and this may be done to a considerable greater degree of profit, than is commonly received from the operations played on that fascinating time-waster. 2 By this board we can solve the following problems, and perhaps thousands more. How many times one will two times two make? Two times two are four, and four times one are four. Answer, four times. 3. How many times one can we make of three times two? Three times two make six, and there are six times one in six. Answer, six times. B* This table must be suspended on a larger scale.. 4. How many times one are four times two? Count off four times two: now how many have you? Answer, eight. Then four times two are eight. Well, how many times one are two times four? Count the first parcel of four; this is one time four; count on five, six, seven, eight; now we are all through the second parcel of fours; how many are there? Answer, eight. Right, the same as the other; two times four are eight, and four times two are eight: this proves the work to be done right. |