The pupil's self-activity is utilized in constructive work and in the framing of original problems. His initiative is exercised by leading him to discover many arithmetical truths for himself. The importance of the correct interpretation of problems and of the choice of the best methods for their solution is emphasized.

The "First Book" covers the work that is usually taught in the second, third, fourth, and fifth years, each chapter representing one half year's work. The second year's work, contained in Chapters I and II, may be used as review for classes that begin the use of a text-book in the third year. Chapters III and IV comprise the third year's work, Chapters V and VI, the fourth year's work, and Chapters VII and VIII, the fifth year's work.

The effort to follow prevailing prices has been limited by their rapid fluctuations and by their variation in different parts of the country. Teachers should encourage pupils occasionally to substitute current local prices, thereby varying the problems in the book.

SAMUEL HAMILTON