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HAMILTON'S ESSENTIALS

OF ARITHMETIC

MIDDLE GRADES

BY

SAMUEL HAMILTON, PH.D., LL.D.

Superintendent of Schools, Allegheny County, Pennsylvania

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PREFACE

THIS series of “ Essentials of Arithmetic” consists of three books, which cover the arithmetical work from the second to the eighth year.

The two important ends sought in the teaching of arith metic are (1) to give the pupil such a mastery of number combinations and processes as will enable him to perform with accuracy and speed all common numerical operations; and (2) to train him in the skillful application of these proce esses to the problems that he is likely to meet in his daily experiences. This series has aimed to lay equal stress on both these important phases of arithmetic.

The frequent drills in numbers in their abstract relations develop habits of accuracy and speed. Efficiency is encouraged by advising the use of short methods, by frequent timing of the drill work, and by insisting on checks for accuracy.

The problems have been framed with a view to the pupil's interests. Beginning with data drawn from his immediate environment, they reach out gradually to include his contact with the larger spheres of social and industrial life. The problems are of two types, - first, isolated problems, which provide direct application of a principle to some need or experience of the pupil; and, second, groups of related problems, called “Everyday Use of Numbers,” which center about an idea or a situation in which the pupil feels a vital interest. These related problems serve as a review of vari. ous principles previously taught. The problems are all real because they are true to life. They carefully avoid unpractical conditions and all questions that have no relation to common experience. The business problems follow present

business usage.

The pupil's self-activity is utilized in constructive work. His initiative is exercised by leading him to discover many arithmetical truths for himself. The importance of the correct interpretation of problems and of the choice of the best methods for their solution is emphasized. The “ Problems Without Numbers” tend to develop the power of generalization.

This book for Middle Grades covers the work that is usually taught in the fifth and sixth years, each chapter representing one half year's work.

By the end of the sixth year, this book aims to give the pupils a knowledge of all the arithmetical principles that are essential for success in the ordinary affairs of life.

The effort to follow prevailing prices has been limited by their rapid fluctuations and by their variation in different parts of the country. Teachers should encourage pupils occasionally to substitute current local prices, thereby vary. ing the problems in the book.

SAMUEL HAMILTON

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Review

Addition

Subtraction

Multiplication

Division

Everyday Use of Numbers

91,

Reduction of Fractions

Addition and Subtraction of

Fractions

Multiplication of Fractions

Cancellation

Division of Fractions

Fractional Relations.

Parts of One Dollar and of One

Hundred

Everyday Measurements

Short Methods of Solving

Problems.

125

Reduction to Decimals

128

94 Measuring Length.

130

96

Drawing to Scale

132

97 Bills and Receipts

135

99 Making and Solving Problems 138

100 Everyday Use of Numbers

Daily Marketing

143

104 Four H Clubs.

144

107 Pig Clubs.

145

Problems Without Numbers 146

111 Tests for Accuracy and Speed 147

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