SUBJECT MATTER AND METHODS 155 



by a fraction. 10. To divide a mixed number by a mixed 

 number. 



It is desired that the pupil shall be able to do more than 

 " work " fractions ; he must be able to see them, to visualize 

 the operations so that he understands them perfectly. In 

 this ability will lie his real mastery of their use in later life. 



Compound numbers and tables are also a part of this 

 year's work, and the aliquot parts of a dollar are studied. 



f> > T f I0 cents are found mentally; 

 Money 



rib t> are worked out by diagrams. For 



|| an oblong is ruled, 6 by 4 inches in size, divided into 

 spaces one-half inch square. By inspection of the ruler 

 the children estimate J of an inch and add a strip that wide 

 to the width of the oblong. This gives a surface I2x8j 

 inches, or the equivalent of 100 squares. One row equals 

 TV of 100, or 8J squares ; two rows equal -fz of 100, or i6| 

 squares. 



For f an oblong is ruled, 4 inches wide by 6J long, di- 

 vided into half-inch squares. This gives a surface of 8x 

 12 J squares, or 100 squares. One row is of 100, or 12 J 

 squares. Two rows are f of 100, or 25 squares. 



For an oblong is ruled, ij inches wide and 4 inches 

 long, and divided into quarter-inch squares. By inspec- 

 tion of the ruler the children estimate f of a quarter-inch 

 space, and add that amount to the length of the line. This 

 gives a surface of 6 x i6| squares, or 100 squares. One 

 row is of 100, or i6| squares. Two rows are f of 100, 

 or 33^ squares. Some of the most important parts of 100 

 are learned by the pupils, as : 8J = ?V of 100 ; I2j = J of 

 100; i6f = of 100. Other aliquot parts are also mem- 

 orized, as: f, |, i, i, |, etc. 



