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PREFACE

Book Three of the Pilot Arithmetics is for use in Grade Seven and Grade Eight. It has been the aim of the authors to select the material carefully and to present it in such a manner as to make it thoroughly teachable.

The work of the first six grades has carried the pupils through the fundamental operations, fractions, decimals, and percentage. This book builds on that foundation by extending the applications of the topics already studied and gradually leading into the broader fields of community and business life.

In dealing with topics drawn from the business world much care has been taken to make the problems and the situations true to life. Complicated problems which rarely, if ever, occur in daily experience and which would only tend to confuse a child, have been omitted. Problems which help to bring out clearly the underlying principles involved are used extensively.

This book, in common with the previous books of the series, appeals strongly to the interests of children by presenting many groups of problems in connection with topics and situations of especial interest to them, such as A Radio Club, Athletic Records, Air Mail Service, Sending Money by Radio, Pay Rolls, A Family Budget, Thrift Problems, and the Money Value of an Education. These topics furnish practical problems in arithmetic in connection with current, everyday situations.

Opportunities for reviews and practice in computation are found in the many drill exercises, time tests, general tests, improvement tests, tables of statistics, and review chapters. It is suggested that teachers turn to these review pages frequently during the year for drill material.

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The work in intuitive geometry has been made interesting and practical. Many topics, such as the area of a trapezoid and the volumes and surfaces of pyramids and cones, which have found a place in arithmetics for years but which are never used by the average person, have been omitted. Considerable work in graphs is presented and pupils should be encouraged to supplement it with the study and collection of graphs from outside sources. The treatment of indirect measurement gives an interesting application of geometry.

A chapter on algebra in the middle of the eighth grade work shows the use of the literal number and the equation as a new method of problem solving. It also furnishes excellent preparation for the work in algebra, as carried on more intensively in the next grade in most schools.

A brief treatment of the metric system serves to show the principle upon which it is built and its chief advantages. The problem work is confined to meters, liters, and grams with their English equivalents, and there is an interesting group of problems based on records in the latest Olympic games.

The authors desire to acknowledge the hearty coöperation of many town and city officials, bankers, business men, and government employees, who have furnished much practical material and offered many suggestions. They also wish to express their appreciation of the very valuable assistance given in the preparation of the manuscript by Miss Lou Belle Stevens, Supervisor of Arithmetic, New Rochelle, New York, and Miss Elizabeth Brockenbrough, Mathematics Department, John Marshall High School, Richmond, Virginia; and the constructive criticisms and suggestions of Dr. L. L. Jackson, Assistant Commissioner of Education, Trenton, New Jersey, and Prof. G. M. Wilson, Boston University, Boston, Massachusetts.

CONTENTS

PAGE

3

17

MAKING CHANGE

17

MULTIPLICATION

18

Practice Exercise

18

Multiplication Time Test

18

SHORT METHODS

18

PROBLEMS

19

DIVISION

20

Practice Exercises

20

Division Time Test

20

Division of United States Money

20

Estimating Results

21

The Solution of Problems

22

PROBLEMS

22

A Radio Club

24

DIVISIBILITY

25

ORAL EXERCISES

25

COMMON FRACTIONS

25

Adding Fractions .

26

Subtracting Fractions

27

Multiplying Fractions

27

Dividing Fractions

28

ALIQUOT PARTS OF A DOLLAR

29

ORAL EXERCISES

29

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