SUBJECT MATTER AND METHODS 147 



by 3! inches. Tell what you did. Find the perimeter. 

 How long is it? 



Later, such examples as the following are mastered: I 

 have three pieces of string; one is 2j inches long, another 

 is 3J inches long, and the third is 2,\ inches long. If laid 

 end to end, how long a piece of string would I have? 



Towards the end of the school year the pupils will add 

 such numbers without actually drawing the lines, and many 

 can add them mentally. 



Comparisons of lines are also made. Lines are drawn 

 on the board with colored chalk or put on a square of card- 

 board. Different objects in the schoolroom are considered, 

 width, height, length, being compared one with the other. 

 The objects for drawing are reasoned out in the same way, 

 and proportion becomes easier. Thus the children become 

 accustomed to measuring and to estimating the perimeters 

 and surfaces of objects varying greatly in shape and size. 



Until Christmas, the end of the first term, the children 

 are busy with measurements, fractions considered con- 

 cretely, addition, subtraction, multiplication, and short 

 division. One problem is given every day and the children 

 are taught to read it and to reason it out. After the Christ- 

 mas vacation comes the real work of the year, long division. 



In the third grade, in learning the tables, the children 

 found J of 12; in the fourth grade they find f, f. Later, 

 they find mentally such parts as f of 480. 



For mental drill such combinations are given as: 



14 18 20 30 14 



+ 10 +10 +10 +10 +ii or 14 +10+ 1 



