SUGGESTIONS TO TEACHERS In order to make the arithmetic in the intermediate grades of the greatest practical benefit to the pupil, the teacher will find it necessary to give especial attention to the particular occupations that are prominent in the vicinity. The collecting of information concerning the business operations actually met with in his community, and the solving of problems, the making out of bills, etc., such as the boat-builder, merchant, and others of his acquaintance find necessary, will greatly increase the pupil's interest in the study of arithmetic. The pupil might be requested to collect information regarding the building of a house to find out the amount of material needed, the prices of the same, the cost of labor, etc.—and to make out a bill for the whole. If the district is agricultural, the particular crop raised will furnish rich material for problems. The cost of preparation of the soil, of planting, cultivating, harvesting, and marketing, the amount produced per hektar, the price obtained for the produce, etc., may be used for this purpose. In a seacoast town or city, fishing and boat-building might well be investigated. The amount and value of the various exports and imports, the units of measure involved, the cost of shipping, the time required for transportation, the number of men employed on the wharves, etc., vary so greatly in the different localities that original investigation by teacher and pupils will add very much to the value of the problems made and discussed. Other local interests, such as rope-making, dyeing and bleaching, hat and mat weaving, working in silver, mining, etc., should be given due consideration. The making out of household accounts, and dressmakers' and tailors' bills, with local prices inserted, would be of practical value in any community. viii INTERMEDIATE ARITHMETIC PART II Review of fundamental processes; factors and multiples; common fractions; decimals; bills and accounts; metric system; longitude and time; practical measurements; percentage and its applications; Postal Savings Banks. REVIEW OF FUNDAMENTAL PROCESSES As an aid to the advanced work, a review of the fundamental operations is recommended. The first 12 pages of this volume are designed to furnish material for such a review. If the review is not thought to be desirable, it may, of course, be omitted. 1. Oral. NOTATION AND NUMERATION Notation is the writing of numbers. Numeration is the reading of numbers. Notation by figures was introduced into Europe by the Arabs; therefore it is called Arabic notation. Notation by letters is called Roman notation from the ancient Romans who used it. It is the place value of the figures that makes the Arabic system better than the Roman. In the Roman system VIII means 5+3, while 53 in the Arabic system means 5 tens + 3, the 5 having the value five and the place value tens. I 1. How many different figures are used in the Arabic system? 2. Give the name of each period in 2,304,568,721. the place value of each figure. Give Any number can be expressed in the Roman notation by the use of the following capital letters, combined according to the three principles given below: = 40. (2) When a letter is placed before another of greater value, its value is taken from that of the greater; IX = 9, XL (3) When a letter follows another of greater value their values are added; XI = 11, LII 52. 3. Read the following: XVII, XXV, LXVI, DCIX, XCV. 4. Write in Roman notation: 37, 84, 111, 1008, 1890, 2195. 5. Write in both systems the number of the present year. |