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It is the purpose of this manual to make plain to teachers in the elementary schools and the junior high school the purpose of teaching arithmetic, and to outline in a simple way the fundamental ideas and methods of presenting the subject in the various grades. It is strictly a teacher's book and not designed for the use of the child. It can be used most successfully as a supplement to the arithmetic, giving valuable suggestions for an enlargement of the subject. It has been generally felt that arithmetic stands aloof from other studies, but the attempt is made here to show the very inti mate and important relation that it bears to the other studies; like wise to present some practical applications not fully treated in the text. Teachers should use this manual much in the same way as the good and experienced teacher uses the text-book or the course of study; namely, as a supplementary device which offers suggestions a plicable to the teaching of the subject, for after all the teacher's c eif purpose is to teach the student the subject rather than to teach the subject. With these suggestions it is hoped that teachers will read fully this text preceding that portion which gives the solution to the various problems, in order that the point of view as well as the objective in teaching arithmetic be correctly understood. Grateful acknowledgement is hereby made to the teachers and supervisors of the Tulsa City Schools who have given many helpful suggestions and assisted in the solution of problems contained in this volume.