This book is intended for students who know the numbers from one to thirty thoroughly, who can count to one thousand, who know something of the multiplication tables of two, three, four, five, six, ten, and twelve, and who understand the simplest facts about ratio and fractions. The purpose of the textbook is to conform numbers in their facts and principles to the usual processes and powers and interests of children's minds. The graded reader has opened the way for the graded arithmetic. Grading all books is part and parcel of the new education, which means to discover and to obey the facts of the child-mind, its methods, nascent periods, and order of growth. It also includes suggestions for teachers how to use the book for teaching. [Cover title varies: "Graded Arithmetics. Book Two--Grade III."]