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DEAN OF THE SCHOOL OF EDUCATION, NEW YORK UNIVERSITY, NEW

YORK

LYONS AND CARNAHAN

CHICAGO

NEW YORK

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3.

GENERAL PREFACE

The organization of the junior high school implies that pupils are classified in such a manner as to enable them to do more and different work in a given time than was possible under the former plan. They can do more work because it is possible under this organization to place pupils of relatively equal mental ability in the same group. They will do different work because the junior high spirit demands it in the light of modern psychology and of modern social requirements.

Inasmuch as the Third Book of Arithmetical Essentials contains the essence of the junior high mathematics as recommended by the national committee on the reorganization of mathematics for the seventh and eighth grades, the authors feel justified in making the matter of the above text the basis for the first two books of a new series of junior high mathematics texts.

This series of texts is intended to give junior high pupils the essentials of mathematics necessary to intelligent citizenship and at the same time to prepare those who continue their algebra and geometry to do the advanced work with a degree of success at least equal, if not superior, to that achieved by pupils who have followed the traditional algebra during the ninth year.

The transition from arithmetic to algebra and from arithmetic to geometry is made easy and natural, in the first case through problem solving with graphs and equations, and in the second case through drawing to scale and measuring such lines, angles, and surfaces as are needed in arithmetic.

The range of material used and suggested is wide enough to permit reduction for average and for slow pupils.

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ACKNOWLEDGMENTS

The authors wish to acknowledge their indebtedness to many teachers, principals, school superintendents, bankers, and other business and professional men and women who have aided greatly in the preparation of this series of texts by their helpful criticisms and suggestions.

Thanks are due Mr. W. C. Reavis, Principal of the University High School, School of Education, University of Chicago, for the use of his Problem Tests without Numbers and for his kindly counsel in the preparation and standardization of other tests.

Special acknowledgment is due Miss Genevieve Apgar and Miss Mary Doan Spalding, both of the English Department of Harris Teachers College, St. Louis, Mo., for their kindly interest in reading critically the text matter both in manuscript and in proof.

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SUGGESTIONS TO TEACHERS

Scope of This Book

This book is intended to provide the largest possible opportunity for self instruction in general mathematics for pupils of the second year junior high school. The text matter is written to the pupils. Sufficient material is provided for the superior pupils of the class. The teacher should be the judge of how much the slower pupils can accomplish. The lesson assignment, if the text is followed, can be of such a character as to keep all the members of the class working at their full capacity.

Computation Practice

Chapter II is intended to be used both for practice and test purposes. A short daily practice period of a few minutes as a part of the regular arithmetic recitation has been found productive of excellent results. In case a given exercise is used for practice and test purposes, the time limit should be the same in both cases. Those pupils who finish their practice work in less than the assigned time should spend the remainder of the period in checking their work.

When a given exercise is to be used for test purposes, it should be mimeographed in order that all members of the class may do the work under standard conditions.

The Value of Short Methods

It is the purpose of the authors of this series to encourage pupils to take the shortest road to the answer in the computing part of problem work. The habit of using short computing processes makes for accuracy and speed. Pupils who wish to develop a high degree of computing skill will find it worth while to do all the work in this chapter. Others should do those processes

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