This textbook is a fourth-grade course in arithmetic. It contains a review of the principles taught in Book III, with their extension to problems of greater difficulty. A few new principles are introduced from time to time, the aim being to introduce the new thought side by side with the review of those already taught. Realizing that the highest function of arithmetic is to develop thought power, the author's aim has been to accomplish this by many concrete examples suited to the child mind. To quicken the thought power they have found it useful frequently to give only statements of certain problems, leaving the pupils to determine first, what can be found, and then how to find it.