ARITHMETIC 



351 



ARITHMETIC 



FOURTH TEAR 



Oral and Written Expression. The reading and 

 writing of numbers below 1,000,000 and Roman 

 numerals to M ; the reading and writing of deci- 

 mals of two orders, including dollars expressed 

 decimally. 



Notation and Numeration. Drill for rapidity 

 and exactness in simple addition, subtraction, 

 multiplication and division. See NOTATION. 

 Written work in multiplication and division of 

 numbers of 2 orders. Simple problems in "long" 

 division and "long" multiplication. Further com- 

 parison of numbers and quantities. See MULTI- 

 PLICATION ; DIVISION. 



Fractions. Develop fundamental idea or mean- 

 ing of fractions. Simple operations in addition, 

 subtraction and comparison of fractions ; chang- 

 ing of fractions to whole or mixed numbers and 

 back again. See FRACTIONS. 



Denominate Numbers. Review of denominate 

 numbers learned in previous grades and in addi- 

 tion, the units of weight, square measure and 

 cubic measure ; problems in denominate numbers 

 involving all the fundamental operations. See 

 DENOMINATE NUMBERS. 



Measuring. Continue and extend the exercise 

 in the measurement of familiar objects, including 

 drawing and construction work. 



Practical Problems. Find dimensions of your 

 desk top in feet. What area of space is occupied 

 by your Readers, when placed flat upon your 

 desk? 



The work may be made interesting by corre- 

 lating the problems with other subjects such as 

 nature study, as in the following example : there 

 are 6 oak trees, 2 maple trees and 4 elm trees in 

 the school yard; what proportion of the trees 

 are oaks? What proportion maples? What pro- 

 portion elms? 



FIFTH TEAR 



Varied Processes. Review of addition, sub- 

 traction, multiplication and division with special 

 emphasis on division ; oral and written drill on 

 numbers of nine orders, and all Roman 

 numerals ; the comparison of quantities and ratio 

 of numbers continued ; sight factoring of simple 

 combinations. 



Fractions. Work in small fractions Involving 

 the four fundamental operations. The use of 

 cancellation in the reduction and multiplication 

 of fractions. See CANCELLATION. 



The decimal method of expressing common 

 Ions; addition, subtraction, multiplication 

 and division of decimal fractions to two places. 

 The multiplication and division of frac- 



tions by 10,000 or 1,000, by moving the decimal 

 point. See FRACTIONS. 



Mensuration. The actual mea* 

 areas, surface, perimeters and volume and the 

 use of these measurements In problems ; to be 

 used also with fractions. See MENSURATION. 



Denominate Numbers. Problems involving the 

 use of units of length, surface, volume, weight, 

 capacity and time. See DENOMINATE NUMBERS. 

 'ical Problems. The application of tho 

 processes of addition, subtraction, multlpllc 

 .111.1 division In fractions and denominate num- 

 ber*. In concrete problems based on subjects of 

 interest to or within the experience of the pupils ; 



the form of simple bills, how to foot and balance 

 them. Let the pupil tell how problems may be 

 solved without going through the actual work 

 or give the approximate answer before solving. 



SIXTH TEAR 



Varied Processes. Review of fundamentals, 

 short cuts and easy methods in the calculation of 

 interest; tests of divisibility (by 2, 5, 3, 9) ; mul- 

 tiplication and factoring of fractions and mixed 

 numbers. The equation. 



Fractions. Decimal expression of fractions 

 and percentage in drill ; in business problems. 

 See FRACTIONS. 



Mensuration. The measurement of larger 

 rectangular areas using larger units, such as 

 the rod; measurement of rectangular and tri- 

 angular solids. See MENSURATION ; TRIANGLE ; 

 SQUARE; etc. 



Denominate Numbers. The reduction of de- 

 nominate units in all tables learned in the pre- 

 vious grades ; drill in larger units of measure, as 

 rod, mile, cord, etc., including a generous num- 

 ber of concrete examples and problems. See 

 DENOMINATE NUMBERS. 



Practical Problems. Let the pupils make up 

 problems in fencing, flooring, painting and paper- 

 ing; excavation problems to find the volume of 

 prisms and cubes ; problems using current prices 

 and dealing with percentage, profit, loss and 

 simple Interest. 



SEVENTH TEAR 



Varied Processes. Review of per cent and drill 

 in short method of rapid calculations ; special 

 emphasis on the statement of problems and equa- 

 tions. See PERCENTAGE ; INTEREST. 



Fractions. A review and application of all 

 processes in fractions in both oral and written 

 work. See FRACTIONS. 



Mensuration. The practical application of 

 measurement of lines, quadrilaterals, triangles, 

 solids, circles and cylinders, as in problems In 

 the measurement of land, lumber, the capacity of 

 barrels, tanks, etc. See MENSURATION; TRIAN- 

 GLE ; etc. 



Denominate Numbers. Use of surface and 

 cubic measure ; comparison and reduction of for- 

 eign and United States money. See SQUARE 

 MEASURE ; CUBIC MEASURE. 



Practical Problems. Real problems applying 

 measurement, per cent and business forms to sub- 

 jects associated with the home and school life 

 and of Interest to the pupils, as: problems of 

 hired rum i.-ihor, acreage of ground, balance of 

 rations for cattle, etc, 



EIGHTH TEAR 



Varied Processes. Continue and extend study 

 of ratio and proportion ; principles of square 

 root. 



Fractions. Review with special emphasis on 

 decimal fractions, percentage and other business 

 uses. See FRACTIONS. 



Mensuration. Drill for rapidity and exactness 

 in in-ir Mi.it i..n work of seventh grade. 



Denominate Numbers. Extend work to include 

 units of metric system, longitude and standard 

 See LONGITUDE AND TIME; STANDARD; 

 METRIC SYSTEM. 



