THE YOUNG PUPILS' ARITHMETIC OBJECTIVELY OR SYNTHETICALLY ARRANGED BY D. H. CRUTTENDEN A.M. AUTHOR OF "THE RHETORICAL GRAMMAR" "THE NEW YORK PUBLISHED BY J. M. BRADSTREET & SON 18 BEEKMAN STREET 1869 Also for sale by Kiggins, Tooker & Co. 123 & 125 William Street HARVARD Entered, according to Act of Congress, in the year 1868, BY DAVID H. CRUTTENDEN, the Clerk's Office of the District Court of the United States, for the Southern District of New York. The Apparatus to be used in teaching Arithmetic is ; 1. Blackboard and Crayons. 2. Numerical Frame or Abacus. Note. For this purpose, a Numerical Frame having ten wires, with ten balls on each wire, is sufficient. The Abacus will soon be considered as essential as the blackboard in teaching Arithmetic, 3. Cruttenden's Arithmetical Charts. Note.-A Teacher ordering Arithmetics for introduction will be furnished with Charts gratis. 4. Each pupil must have a slate and pencil. 5. Young pupils may use "The Young Pupil's Arithmetic," or No. I.; older ones may begin with "The First Course or Objective Arithmetic," No. II. Entered according to Act of Congress, in the year 1867, by D. H. Cruttenden, in the Clerk's Office of the District Court of the United States, in and for the Southern District of New York. FIRST DIRECTION.-Teach your pupils to count and to number objects from nothing or none to twenty, from twenty back to nothing or none. Do this, at first, and tell the names of the objects; that is, teach counting and numbering in the concrete; next, teach them without telling the names, or in the abstract. Note. The best objects to be used in counting and numbering, are ;—first, the fingers; second, the balls of a Numerical Frame; but if this be wanting, use marks on the blackboard, placing ten in a row, and the second row under the first; finally, exercise the pupils in counting and numbering themselves, or any classes of objects, as desks, chairs, windows, panes of glass, pebbles, etc., etc. COUNTING with the names (CONCRETE) and without the names (Ar NUMBERING with the names (CONCRETE) and without the names (AB STRACT). In like manner, during each lesson, exercise the pupils a few minutes in counting and numbering, until as large numbers are reached as you think best. Lastly, instruct your pupils that when we consider the sounds used in counting and numbering we call them Words; but when we consider how many, or which one, each sound means, we call them Numbers. Next, teach your pupils to count marks, or balls; first, in ones or units, as one one, two ones, three ones, &c., to ten one or one ten; then, count in tens; as, one ten, two tens, three tens, &c., to ten tens, or one hundred then, count in hundreds to thousands, &c. SECOND DIRECTION.-The Written numbers may now be presented, first, in words, second, in the Roman letters, and third, in the Arabic figures. In presenting any one of these three kinds of written numbers, the following rule should always be observed;— RULE.-Make the written numbers in Decades, or setts of ten numbers each. The pupils should be required to make the word-numbers on the slate, in capitals, in small letters, and in script, or written numbers, It is well to introduce the written numbers by a conversation somewhat like the following: Teacher.-Pupils, would you like to see how the numbers appear when they are printed, or written on the blackboard? Pupils. We would? T-Very well, then I will show you. What word, or number did you use first in counting the balls? P.-We said no ball. T.-When you counted without using the name, or in the Abstract, what word did you use? P.-We said none, nothing. NOTHING, nothing, Nothing, T-If we had not said anything at all, how many would be meant? P.-Why, none would be meant—not anything. T-Very well, then we need not say anything; or, if we choose we may say, no thing, or nothing. Usually we do not say anything at all, when there is nothing. What do you say next after nothing? P-We say one, after nothing. T-Very well; I will place one on the blackboard. [The Teacher writes one on the board, as follows: ONE, one, One. In like manner present two, three, four, five, six, seven, eight, nine, so that the pupils may learn to read and spell these words readily. Before writing the second decade, cause your pupils to observe the composition of these word-numbers. Teacher.-Now you may count from nine to twenty. Pupils.-Ten, eleven,. teen. .... to nine T-What parts of these numbers are like those of the first ten numbers? P.-Four, five, six, seven, eight, nine, are exactly the same. T.-What other word is joined to these? P.-Teen, is joined to each of them. T.-Do you know what teen means? P. We suppose teen means ten. T.-You are right, teen does mean ten; why do we not say fourten, instead of fourteen? P. We do not know why we say fourteen instead of fourten. T.-You may say fourteen twice and fourten twice, and see which you can speak the more easily. P.-Fourten, fourten, fourteen, fourteen; we can say fourteen more easily than fourten. T.-Which sounds better, fourten or fourteen ? P.-Fourteen sounds better than four ten. T.-Very good; the reason why we say fourteen instead of fourten, is because fourteen is more easily spoken than fourten, and hence sounds better. The more easily a word is spoken, the more pleasantly it sounds to the ear, or it is more euphonious. Hence we say fourteen because it is more euphonious, or pleasant sounding than fourten. Now you may begin at nineteen and tell how each of these numbers back to ten is made, and how you can prove it. P.-Nineteen is nine and ten. We can count nine balls on one bar and ten on another, and they make nineteen. This proves it. (The pupils do the same with eighteen to twelve.) Twelve is made of tw for two, but we do not know what elve means. T. It is for the word leve, which means ten. P.-Then eleven must mean one and ten, for they make eleven. T-You are quite right; the first stands for en, which means one. Now we will write them on the board. We will write this ten in a row, below the first ten. Ten of these numbers we call a decade of numbers, as twelve things are frequently called a dozen things. (See arrangement of second decade below.) Note. Before giving a lesson in the book, it should be presented in oral instructions similar to the above. The teacher will find the substance of these oral instructions in the lesson as given in the book. Hence the teacher is advised to read the advanced lesson before giving it to the class. If the No. I be used by the class, the teacher is advised to read the corresponding lesson in the No. 2 also. |