SUBJECT MATTER AND METHODS 163 



tions are reviewed and completed, special attention being 

 given to pure decimals. As in the drills on integers, in- 

 numerable problems are given in fractions to develop speed 

 and accuracy. Much stress is placed on cancellation, actual 

 multiplication and division being performed by the shorter 

 process whenever possible. 



Believing that any one, " good at figures," can readily 

 adapt himself to his environments when placed on his own 



resources in business, only a few tables in 

 Denominate , . , , , , 



Numbers denominate numbers are required; but, by 



a concrete use of linear, surface, and cubic 

 measures, weights, money, and counting, pupils are led to 

 make more and more definite their ideas of number rela- 

 tions. Constructive diagrams, drawn to scale, illustrative 

 of the assigned problems, are required very frequently. In 

 objective work, measurements of lumber at the lumber 

 yards, of excavations being made, of special points in 

 houses under construction, of fences, sidewalks, streets, are 

 usually obtained through efforts of the class as a whole. 

 An individual or a committee takes the measurements when- 

 ever it is not convenient for the whole class to do so. This 

 work is very interesting and instructive for both teacher 

 and pupils. 



As we are working for mathematical power, its develop- 

 ment is not retarded by forcing unnecessary assistance upon 



the pupils. In percentage, for instance, 

 Percentage . 



where the problems are similar in every 



respect to those given the fifth grades in fractions and the 

 sixth grades in decimals, the pupils are expected to reason 

 out their own work. Knowing this, the children respond 

 to the requirement, usually with readiness and success. 



