Educe T109.22 450 HARVARD COLLEGE LIBRARY GIFT OF GINN & COMPANY COPYRIGHT, 1921, BY D. C. HEATH & Co. 2J 2 PREFACE THIS book is the first of a series presenting a reorganized course in mathematics. It is designed for grade seven or the lowest junior high school year. The following principles have been observed in the preparation of it. I. The course must be practical. In grade seven, this means that: 1. There must be continued drill upon the fundamentals. In this text, the first forty-seven pages contain a systematic review of the fundamental operations. No short cuts or special devices are taught because most of the pupils of this grade are too inexpert with ordinary methods of computation to justify encouraging them to use special devices. The review is made systematic so that the teacher can easily assign work for the whole class or for individuals of the class without "dictating examples," and so that the pupils themselves can refer to it for self-instruction whenever necessary. On pages 211-219, are abstract drill exercises which can be used as suggested on page 211. This material and the miscellaneous review problems on pages 201-210 will be found particularly useful while the class is studying the geometry of Chapters VIII-XIII. 2. The instruction on new topics must be limited to processes and applications encountered by the average person. By thus rigidly limiting the instruction to the common problems and processes, these are taught more thoroughly and time is gained in which to accomplish the other purposes of the course. In this text, Chapters IV and V are devoted in an unusual manner to "finding the percentage" and its applications. These are the most common percentage problems. The discount problems in |