 # The Teaching of Arithmetic: The Work of the Sixth School Year

The Leading Mathematical Features: The leading features of this year should be percentage and its applications, particularly to discount, profit and loss, commission, and interest. Ratio and simple proportion may also be included. The General Solution of Problems: Since the work in percentage introduces the pupil to the problems of business, some of which become rather intricate in the later school years, it is well at this time to take up rather systematically questions of the solution of problems in arithmetic. To this end there should be considered exercise in analysis in general and in unitary analysis in particular, and the equation may well begin to find place in the mental equipment of the child. As to the matter of analysis no question will be raised, but as to introducing the letter x some teachers are in doubt. When, however, we come to consider that it merely replaces an awkward symbol that has long been used, and makes the work much clearer, the objection cannot be maintained. For example, 2 + (?) = 7 is sometimes used as early as the first school year; this, however, is only a complicated way of writing 2 + x = 7, the two meaning exactly the same thing. Similarly, 4 : 7 = 12 : (?) is only an awkward way of writing what is equivalent to: