THE THE LIBRARY ARITHMETIC HELP MANUAL of EXAMPLES AND PROBLEMS WITH EXAMINATION QUESTIONS FOR PUPILS AND TEACHERS From the Superintendents of Various Cities EDITED BY ALVORD D. ROBINSON Author of "The Worker'S ARITHMETIC," "MODERN METHODS IN CHICAGO THE CARNEGIE BOOK COMPANY 1903 INTRODUCTORY. THE HE quickest and best way to learn arithmetic is by solving practical problems, From the earliest number work until the subject is no longer studied, the pupil should solve enough problems on each part to fix firmly the principle involved. Principles and processes can, for the most part, be fixed by using small numbers, and the quantity of problems used depends upon the pupil's aptness. The more advanced the work of the pupil, the fewer the number of problems that should be needed to clear up the subject for him. Most of the pupil's work should be upon the fundamental operations and fractions. With proper understanding of these parts of arithmetic, and due consideration to accuracy and rapidity, the pupil is fitted to combat the arithmetic of any phase of practical life, once he understands the vocabulary of the phase of life considered. At every step of the pupil's work abundant oral problems. should be given. It is in this way only that he secures the greatest disciplinary value from the study. Another feature that should be emphasized is estimating results. As a rule, after the first few years of work let the pupil estimate the result in every case before doing the written work. This should follow as a result of outlining in the mind the operations needed to secure the result. The problems in this MANUAL will be found sufficient in number on the different subjects, for most pupils. If additional problems are needed those given in any good school arithmetic may be used. For advanced pupils the examination questions in (3) 193269 the concluding pages furnish work where the pupil's own ingenuity and understanding are called upon to decide how best to perform the work needed. Problems for advanced grades should largely be original, and made to include actual conditions in the surrounding life. None of the problems in this MANUAL or those from other sources should be given until the pupil has had all the explanation which the HELP gives, or some equally good presentation of the subject by teacher or parent. Do not be afraid of giving too much assistance. For most pupils the subject is difficult enough after all explanation possible has been given. You do not encourage a steed by showing him a high wall through which he sees no passage. Every effort has been made to have the problems correct in statement. Any error in the MANUAL or HELP proper if brought to the author's notice will receive his immediate attention. The concluding problems are representative of those given in the upper grammar grades and at teachers' examinations in the larger cities. The author here expresses his obligations to the city superintendents of the country for these questions and valuable suggestions. ALVORD D. ROBINSON. WORK IN NUMBERS FOR LITTLE PEOPLE. EXERCISE I. 1. If Ned had 1 hat and his papa gave him 1 more, how many would he have? 2. If Mary had 2 dolls and her mamma gave her 1 more, how many would she have? 3. If Tom had 1 top and his papa gave him 2 more, how many would he have? 4. If May had 2 books and her mamma gave her 2 more, how many would she have? 5. If Nat had 1 ball and his brother gave him 3 more, how many would he have? 6. If May had 3 books and her sister gave her 1 more, how many would she have? 7. If John had 1 top and his brother gave him 4 more, how many would he have? 8. If Nell had 2 dolls and her sister gave her 3 more, how many would she have? 9. Frank had 3 balls and he made 1 more; how many did he then have ? 10. Rob had 4 cents and his papa gave him 1 more; how many did he then have? 11. Ella had 2 dolls and her mamma gave her 1 more; how many did she then have ? 12. If Sam had 2 rabbits and his papa gave him 2 more, how many would he have? 13. Nat had 2 marbles, and his big brother gave him 3 more. How many has he now ? (5) 43 |