613401 HALL'S MATHEMATICAL SERIES THE WERNER ARITHMETICS A Three-Book Course for Graded Schools Book 1. For third and fourth grades, cloth, 256 pages, 40c. TEACHERS' HAND BOOK giving oral work preparatory for Book I., suggestions to THE HALL ARITHMETICS A Two-Book Course for Graded or Ungraded Schools 35c. 60c. Copyright, 1896, by FRANK H. HALL PREFACE. A book may be as noteworthy for what it omits as for what it contains. “Arithmetical conundrums," "mathematical monstrosities," "examples," in which the thing exemplified is lost to the pupil in long rows of figures, and problems suited only to maturity, are omitted from this book. The work presented can be thoughtfully performed by students ten to thirteen years of age if they have been properly prepared for it in the preceding years. As in Book I. of this series, classification is made subordinate to gradation. Every set of problems -every problem, has been selected with careful reference to the supposed thought-power of the pupil, and bears close relation to what precedes and to what follows. The decimal arrangement of the parts of the book whereby a topic is re-presented on every tenth page, insures at once systematic review and the proper relating of the new to the old. F. H. H. WAUKEGAN, ILL., December, 1896. CONTENTS. ..11, 21, 31, 41, 51, 61, etc. ..15, 25, 35, 45, 55, 65, etc. ..16, 26, 36, 46, 56, 66, etc. 271-288 TO THE TEACHER.—If the pupil into whose hands this book may fall has been trained along the lines suggested in the First Book of the Werner Arithmetics, “the foundation” upon which to make further arithmetical effort will have been properly laid, and but little attention to pages 5 to 9 of this book will be necessary. Otherwise much time must be devoted to securing a clear conception of the meaning and application of these fundamental problems before the work in the body of this book is attempted. Require the pupil, if necessary, to recite each problem again and again; 1st, reading it and telling its meaning; 2d, solving it; and, 3d, illustrating with a concrete problem. Then make other similar problems to be treated in a similar manner. Put great emphasis upon the meaning of the problem. If the child knows that the expression, 1: , means, find how many times 1 sixth is contained in 1 half, he solves the problem without difficulty. Do not permit the pupil to “juggle with figures” and then ask him to explain the juggling. Rather, see that he has a clear conception of what is to be done, and allow him the privilege of doing it in a thoughtful manner. TO THE PUPIL. - Read each problem and (a) tell its meaning, (b) solve it, and (c) tell the suggested number story. Do this until you can easily give the meaning of all problems similar to these, solve them, and tell the suggested number stories without reference to the notes that follow. MULTI- DIVISION. DIVISION. SUB 68 + 24 = * 64 — 2¢ =* 64 X 2=* 6% • 24 = 64 ; 2= * +1=(1) 4-3= (2) bu.X7= (3) 4 = 1= (1) { bu. • 4= (5) (9) 63+5=(6) 63-53= (7) 124 x = (8) 63 yd. = 2= (10) 71 • 21 = (14) 53 tons:2= (15) 2 bu. 3 pk. 5 bu. 1 pk. $% X =(18) 2 ft.)46 ft. (17) 2 bu. 2 pk. 1 bu. 3 pk. 124 x 29=(16) 24 ft.)15 ft. (20) 2)46 ft. (18) (11) (12) 123X3 =(19) 24 bu.)131 bu. 3)271 ft. 121X2=(22) (23) (21) * See First Book of the Werner Arithmetics, pp. 89 and 155. (1) plus 4, means, į and 1. I can change thirds and fourths to twelfths; twelfths; 1 twelfths; twelfths and twelfths = twelfths. Story-Harry played ball of an hour, and“ hide and seek” 1 of an hour; in all he played twelfths of an hour. (See First Book, pages 125, 135, 145, 147, 149.) (2) i minus 5, means, i less 3. I can change fourths and thirds to twelfths. twelfths; twelfths; twelfths 5 |