Entered according to Act of Congress, in the year 1838, by Frederick Emerson, in the Clerk's Office of the District Court of the District of Massachusetts. PREFACE. In a systematic course of general education, Arithmetic claims a place among the primary objects. Its elementary exercises, when rationally conducted, are adapted to the capacities of children at a very early age. Its influence on the character of children, in developing the reasoning faculties, and habituating the mind to investigation, is highly conducive to progress in every other branch of knowledge. Notwithstanding the obvious truth of this remark, the practice of postponing arithmetic till children arrive at the age of nine or ten years, still prevails in many of our schools, and calls for the attention of those whose influence may correct the error. The purpose of this manual is, to facilitate the instruction of the younger classes. It contains the first part of a Course of Exercises in Arithmetic, which is published in three books, severally denominated, Part First, PART SECOND, and Part THIRD. The method employed for illustrating the subject, it will be seen, is original and peculiar. Part First is confined to the simple elements, and it may be advantageously used as an introduction to the subsequent study of arithmetic from any larger book now in common use. Learners will, however, find the steps of progress to be most gradual, easy, and certain, in passing from this book immediately into Part Second. The lessons contained in Part First are all to be performed orally; the slate and pencil not being required. In the title-page will be seen a drawing of an improved structure of the Abacus. It is a convenient apparatus for illustrating the combinations of numbers; although it need not be used in teaching from this book: its use is superseded by cuts and unit marks. F. E. Boston, August 1, 1838. Do This book is adopted in the Public Schools of the cities of Boston, Salem, Portland, Providence, New York, Philadelphia, and Louisville, by orders of the respective Boards of School Tutto ARITHMETIC. NUMERATION. Note to Teachers. The learners are to have their books open before them, while performing the lessons in Numeration. Do not omit any lesson. LESSON FIRST. I. five, eight, nine, four, seven, ten. See this flock of black-birds: they have lighted upon the bars of a gate, and are all singing together. Find how many there are on each separate bar. Lesson Second. II. Note to Teachers. In this lesson, the teacher may read the questions, and the children give the answers; or, if the children can read with fluency, they may read the questions to each other, by turns; each one reading a question to be answered by the scholar next below him, and thus proceeding ihrough the class. This lesson should pass through the class several times at one recitation, until each scholar has had several turns in answering. The chief purpose of the lesson is to show, that nunbers are formed, successively, by adding one unit to the next preceding number. How many stars are one star and one star ? * * How many stars are two stars and one star? * How many stars are three stars and one star ? * * * * How many stars are four stars and one star? * * * * * How many stars are five stars and one star? * * * * * * How many stars are six stars and one star ? * * * * * * * How many stars are seven stars and one star? * * * * * * * * How many stars are eight stars and one star? * * * * * * * * * How many stars are nine stars and one star? LESSON THIRD. III. Note to Teachers. The design of the preceding lessons has been, to teach the names, and the comparative magnitude of numbers, from one to ten. The teacher should now inform the learners, that numbers are represented by FIGURES. He may direct them, to obtain the names of the figures by counting the unit marks, (from left to right,) which stand against the figures severally, in the following table. As this exercise will tend to fix a mental association of each figure with the number of units, which it represents, the lesson should not be omitted, even by children, who are already able to read figures. LESSON FOURTH. IV. Note to Teachers. Make two exercises of this lesson. First, let the chile dren read the words in the columns. Then, let the words be covered with a slip of paper, and the reading be performed on the figures. While reading the figures, lead the children to observe the analogies, two-twenty ; three — thirty; four - forty; five-fifty; &c. 1 One, 2 two, 3 three, 4 four, 5 five, 6 six, 7 seven, 8 eight, 9 pine, 10 ten, 11 eleven, 12 twelve, 13 thirteen, 14 fourteen, 15 fifteen, 16 sixteen, 17 seventeen, 18 eighteen, 19 nineteen, 20 twenty, 21 twenty-one, 22 twenty-two, 23 twenty-three, 24 twenty-four, 25 twenty-five, 26 twenty-six, 27 twenty-seven, 28 twenty-eight, 29 twenty-nine, 30 thirty, 31 thirty-one, 32 thirty-two, 33 thirty-three, 34 thirty-four, 35 thirty-five, 36 thirty-six, 37 thirty-seven, 38 thirty-eight, 39 thirty-nine, 40 forty, 41 forty-one, 42 forty-two, 43 forty-three, 44 forty-four, 45 forty-five, 46 forty-six, 47 forty-seven, 48 forty-eight, 49 forty-nine, 50 fifty, 51 fifty-one, 52 fifty-two, 53 fifty-three, 54 fifty-four, 55 fifty-five, 56 fifty-six, 57 fifty-seven, 59 fifty-eight, 59 fifty-nine, 60 sixty, 61 sixty-one, 62 sixty-two, 63 sixty-three, 64 sixty-four, 65 sixty-five, 66 sixty-six, 67 sixty-seven, 68 sixty-eight, 69 sixty-nine, 70 seventy, 71 seventy-one, 72 seventy-two, 73 seventy-three, 74 seventy-four, 75 seventy-five, 76 seventy-six, 77 seventy-seven, 78 seventy-eight, 79 seventy-nine, 80 eighty, 81 eighty-one, 82 eighty-two, 83 eighty-three, 84 eighty-four, 85 eighty-five, 86 eighty-six, 87 eighty-seven, 88 eighty-eight, 89 eighty-nine, 90 ninety, 91 ninety-one, 92 ninety-two, 93 ninety-three, 94 ninety-four, 95 ninety-five, 96 ninety-six, 97 ninety-seven, 98 ninety-eight, 99 ninety-nine, |