PROBLEMS IN ARITHMETIC BY GEORGE E. GAY Superintendent of Schools, Malden, Mass. BOOK I FOR GRADES III AND IV οὐ πόλλ ̓ ἀλλὰ πολύ BENJ. H. SANBORN & CO. PREFACE. This little book, the first of a series, furnishes without counting numerous combinations, one thousand problems designed for written work. They are nearly all "concrete," and no definitions or rules are given. Oral and abstract work can be furnished by the live teacher almost without limit. Carefully selected written problems are hard to find, and more difficult to make. To furnish these in an attractive but inexpensive form this series is projected. Of the problems it can be said, they are: 1. Practical. Every problem furnished by competent grade teachers to represent the problems which they have been in the habit of assigning to pupils for solution. 2. Comprehensive. Covering problems of every kind suitable for pupils of these grades. 3. Simple. Pertaining to matters with which children have acquaintance. 4. Systematic. Arranged in such a way as to develop the logical faculties of children, and to secure accuracy in arithmetical computation. 5. Progressive. Beginning with problems requiring one operation, and using only the smallest numbers, they end with problems of two conditions and larger numbers. The first one hundred and fifty lessons of this book consist of five problems each, and generally, but not always, each problem is of a different kind from the others in the same lesson. Lesson 151 contains problems in addition; lesson 152, in subtraction; lesson 153, in multiplication; lesson 154, in division; lesson 155, in fractions; lesson 156, in mensuration; lesson 157, miscellaneous problems. The first one hundred and twenty-five lessons contain problems of one condition, the remaining lessons contain problems of one and of several conditions. Before assigning problems to the class, the teacher should examine them carefully in order to determine how many make a suitable lesson, and what facts or principles used in their solution need to be taught to the class. Every pupil should be given an opportunity to solve every problem by his own unaided efforts. If he is unable to solve a problem, he should be encouraged to solve first a similar problem with very small numbers. Frequent oral reviews of from five to twenty problems will be found very helpful. In this oral work the pupil should read the problem, and proceed thoughtfully to tell how he would solve it. Many teachers wisely ask pupils in such oral work to state in what denomination the answer will be found, what the question in the problem is, and what processes must be used. Pupils should make problems similar to those given in the book for solution by their classmates. For supplementary oral work, problems may be changed by using small numbers. Abstract work in great variety should accompany the concrete work outlined in this book. The problems in the same lesson vary much in difficulty. This fact should be considered in ranking. All problems in mensuration should be illustrated. The author is indebted to the teachers of Malden for most of these problems and for assistance in preparing the book. Malden, Mass., June, 1898. G. E. G. |