7. NOTATION TO THOUSANDS. Teach children that nine and one make ten, and that two figures are required to express ten (10). Figures are used to spell numbers, just as letters are used to spell words. Thus: a, an, ant, Nat, and tan, are spelled by combining the three letters, a, n and t, variously; so, by means of the figures, 1, 2 and 3, the numbers 1, 12, 123, 213 or 312 are expressed. Nine and one is ten, which requires the two figures 1 (one) and 0 (cipher) to express. As o and n will spell either on or no, so 1 and 2 will express either 12 or 21. The relative position in which the ten figures are placed makes it possible to spell all numbers with ten characters. Fix this thought in the child's mind as early as possible Figures are the Alphabet of Arithmetic. 8. Numbers increase ten-fold from right to left. Thus: Units....................... 1 2 3 4 5 6 7 8 9 10 20 30 40 50 60 70 80 90 100 200 300 400 500 600 700 800 900 Tens Hundreds Units, Tens and Hundreds : 111 222 333 444 555 666 777 888 999 9. Teach numbers from 10 up to 100, and that all numbers between 9 and 100 consists of UNITS and TENS. A numeral frame with a hundred balls is needed for this purpose. The right-hand figure expresses units, and the next figure on the left, tens. Thus: three tens and seven units is expressed by writing three to the left of seven 37, which is called thirty-seven. Count off tens and units on the numeral frame, and then express the number in figures. Require children to count by tens and units, until they realize in a general way the numbers from 9 to 99, and can represent them in figures. 10. Require children to read numbers from 1 to 99 written promiscuously and to realize them by means of the numeral frame. II. Teach numbers from 99 to 1000, and that all numbers between 99 and 1000 consist of UNITS, TENS and HUNDREDS. Three figures constitute a period. In reading numbers, do not use the word and. Thus: 896 is read: eight hundred ninety-six. 12. FUNDAMENTAL PROCESSES. Numbers may be increased or diminished. 1. Addition is the process of finding a number by putting two or more given numbers together. 2. Subtraction is the process of finding a number equal to the difference between two given numbers. 3. Multiplication is the process of finding a number which is a given number of times another number. 4. Division is the process of finding how many times one number is contained in another of the same kind. 5. Division is also the process of separating a number into parts of a given size, or of finding the size of given parts. This is the case whenever a concrete number is divided by an abstract number. Since the fundamental processes are intimately connected, one growing out of the others, arithmetical ideas are best |