Practice in Federal Money, Compound Division, Questions on the foregoing, To change an Improper Fraction to a Whole or Mixed Number, To multiply a Fraction by a Whole Number, To multiply a Whole Number by a Fraction, To find the Greatest Common D.visor of two or more Numbers, (reference,) 115 To reduce Fractions of Different Denominators to a Common Denominator, 117 To reduce Compound Numbers to Decimals of the highest Denomination, 142 To reduce Decimals of higher Denominations to Whole Numbers of lower Concise Rule for calculating Interest in New York State, Commission, Insurance, Stock, Loss and Gain, Time, Rate per cent., and Amount, given, to find the Principal, Time, Rate per cent., and Interest, being given, to find the Principal, The Principal, Interest, and Time, being given, to find the Rate per cent., 166 The Principal, Rate per cent., and Interest, being given, to find the Time, 168 The Diameter of a Circle being given, to find the Circumference, The Circumference of a Circle being given, to find the Diameter, To find the Solid Contents of a Globe, To find the Solid Contents of a Cylinder, To find the Solid Contents of a Pyramid, SUGGESTIONS TO TEACHERS ON THE METHOD OF USING THIS WORK. For a course of mental arithmetic, adapted to the capacities of very young pupils, they may take the mental exercises in each rule, as far as the first example for the slate. This course is not meant to include any of the exercises styled "Questions on the foregoing.” This course embraces the whole of the first 20 pages, together with the arithmetical tables, extending to the Appendix. The necessity of impressing these tables on the minds of pupils at an early age is sufficiently obvious. When the pupil is perfect master of this course, as will, most probably, be the case after one or two reviews, the teacher will find no difficulty in making him understand the operations by slate. He may then take the whole in course. In every school, it would be well to institute classes; and as there are seldom any answers given to the mental questions, the pupils may be allowed to read in their turns the questions from the book; thus giving the teacher no further trouble than occasional corrections. By this, the reader will perceive, that the work may be used to advantage in monitorial schools, as the former editions have been. In large schools these corrections may be made by an advanced scholar, instead of the teacher. Whenever an advanced scholar takes up the book with a view of profiting from it, he should omit nothing as he progresses, but make it his practice to qualify himself to answer any question, in the mental exercises, rules, or respecting the reason of the operations. Teachers will find it to be a useful occupation for their scholars, to assign them a morning lesson, to be recited as soon as they come into school. With little exertion on the part of teachers, pupils in this way may be made assiduous and ambitious, very much to their advantage, and to the credit of their teachers. The mental questions, under the head of "Questions on the foregoing," will, intelligently answered, furnish to committees an admirable test of the pupil's knowledge of this subject. The Appendix is designed for those who have time and opportunity to devote to the study of the more abstruse parts of mathematics. Note. Lest some may mistake the object of the figures in the parentheses, it may here be remarked, that these figures are separate answers, left without assigning any value to them, reserving this particular for the discretion of the pupil, which he must necessarily exercise, in order to obtain the answer which follows, that being the aggregate of the whole. The above directions are those which seem the best to the author; hut as every intelligent teacher has a way of his own, which, though not intrinsically the best, is, perhaps, the best for him, the subject is respectfully submitted te his own choice. ARITHMETIC. MENTAL EXERCISES. ADDITION. ¶ I.* 1. How many little fingers have you on your right hand? How many on your left? How many on both? 2. How many eyes have you? 3. If you have two apples in one hand, and one in the other, how many have you in both? How many are two and one, then, put together? 4. How many do your ears and eyes make, counted together? 5. If you have two nuts in one hand, and two in the other, how many have you in both? How many do two and two make, put together? 6. If you have three pins in one hand, and James puts another in, how many will you have in your hand? How many are three and one then? 7. If you have three pins in one hand, and James_puts two more in, how many will you have in your hand? How many are three and two then? 8. If you have four apples in one pocket, and two in the other, how many will you have in both? How many are four and two then? 9. Thomas has four cents, and William has three; how many have they both together? How many are four and three then? 10. You have five pins in one hand, and three in the other; how many have you in both? How many are five and three then? 11. You have four nuts in one hand, and four in the other how many have you in both? How many are four and four then? *The questions in TI and T II are intended for very young children. Older pupils may omit these. But the two remaining sections, and the four tables, will claim an attentive perusal. |