2. The simple forms of checking the work in addition and subtraction. 3. The emphasis placed on the estimate of the result and on rational methods of locating the decimal point in multiplication and division. 4. The early use of the equation as a simple mathematical tool. 5. The natural introduction to the idea of ratio, and the simple development of its use in the solution of analytic problems. 6. The rational development of measurement, and the extension of the decimal idea to this field, by the use of the protractor and decimalized ruler. 7. The interpretation of number data by means of graphs. 8. The revised treatment of the fundamentals of percentage, wherein the idea of per cent is first made clear. 9. The restriction of the treatment of percentage to simple direct applications. 10. The application of the equation to formulas of mensuration. 11. The emphasis on reasoning throughout the work in mensuration. 12. The selection of problem material from situations of interest to the child. 13. The presentation of all problem material in the form of direct statements followed by direct questions as to the results required. WILLIAM LEDLEY VOSBURGH. FREDERICK WILLIAM GENTLEMAN. JUNIOR HIGH SCHOOL FIRST COURSE CHAPTER I REVIEWS OF ARITHMETIC I. THE READING AND Writing of INTEGERS 1. In our system of notation, which is called the Hindu-Arabic system, there are ten separate symbols used; namely, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0. These symbols are called digits, or figures, or numerals. = Each symbol by itself represents a single numerical value. Thus 2 || (two); 5 = ||||| (five); etc. 2. When two or more of these symbols are written together, however, the number value then represented by each symbol depends also upon the place it occupies. Thus, using 2 and 5, the numbers twenty-five (25) or fifty-two (52) may be written. In the first number 2, by the place it occupies, represents two tens, 5 represents five units; in the second number 5 represents five tens, 2 represents two units. Using 2, 3, and 5 together six numbers may be written; as, 235, 253, 523, 532, 325, 352. Noting the place that each figure occupies in each of the above numbers, tells the number that it represents. 3. The number value that a figure may express by reason of the place (or order) that it may occupy in a number is spoken of as its place value; the value that it denotes individually as its figure value. 4. Since the symbol 0 (zero) when used alone does not express any number value it is called zero, cipher, or naught. When 0 (zero) is used with other symbols it may help to place them and so express number value; as, 230, 320, 302, 203, 023, 032. Read each of the above numbers. In which of them does the 0 help to express number values? Since the O serves no purpose in writing the last two numbers it is generally not written. Read the following numbers: 560, 506, 605, 650, 2650, 2600, 2065, 2605, 2005. Do not use and in reading whole numbers (integers). 5. For convenience in reading numbers of four or more figures, in the Hindu-Arabic system, the figures are generally separated by commas into groups of threes, called periods. The table at the top of page 3 shows the arrangement of periods and orders in our system (the Hindu-Arabic system) of writing numbers. Read each of the numbers from the table. How many orders in each period? Name the orders in each period. Name the periods, beginning at the right. Read each number from the table. Note that in reading a number each period is named after the number in that period has been read except in units' period. |