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D. H. CRUTTENDEN'S MATHEMATICAL SERIES.

No. 1.

THE

TABLE.BOOK AND MENTAL

SYSTEMATIC ARITHMETIC,

FOR BEGINNERS;

ARRANGED TO EXHIBIT THE PRINCIPLE THAT

THINGS ARE PLAINER THAN WORDS.

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PREFACE.
Definition. Arithmetic is the Science and Art of Numbers.

Division. There are two kinds of Arithmetic, viz., the PRIMARY and the ADVANCED.

PRIMARY ARITHMETIC is for the use of beginners. It includes Counting and Numbering, the Tables, and what are commonly called Mental or Intellectual," and " Primary Arithmetic.”

Primary Arithmetic, in common with all other primary studies, should be taught synthetically, i. e., beginning with things, or objects, it should finally end with the Abstract.

In the “School of Nature,” the child becomes familiar with persons and things long before it begins to distinguish sounds, and it distinguishes sounds or names before it begins to use them. Hence we see that naturally our knowledge of language depends on our preconceived ideas of that, to which the language relates. How absurd then, if not cruel and wicked, the attempt to teach beginners the meaning of one hard word, by compelling them to learn several other hard words. Show the thing, and the child will soon learn its name, no matter how hard that name may be. With beginners the thing defines the name and the name is the definition of the thing.

This book, No. I., is introductory to the No. II. which contains the only complete Synthetic system of any science, ever yet offered to the public. The No. I. supplies the place of the common Table-Books.

METHOD OF CONDUCTING THE RECITATIONS. 1st ; Let the pupils read the preceding day's lesson, and if the reading be satisfactory, then

2d; Explain orally, by the aid of the Numerical Frame, or Abacus, and Black Board, or such other things as are at hand, the advance lesson of the day, and then

3d; Let the pupils read the same lesson in the book, being careful to have it well read, and then

4th; Devote some time to practical exercises, either oral or on the slates and Black Boards.

CAUTION : Do not make your teachings all Oral, nor yet all Written, but make the pupil familiar with both ways of gaining knowledge, and Remember " never to do that for the pupils, which the pupils ought to do for themselves.Entered, according to Act of Congress, in the year 1854, by D. H. CRUTTEN

DEN, in the Clerk's Office of the District Court of the United States, in and for the Southern District of dew, York,

HARVARD
UNIVERSITY

LIBRARY

or

Applying the 2d, 3d, and 4th Directions (see Preface). 2D DIRECTION. The teacher is supposed to have a number of similar objects at hand, to which he calls the attention of the class. The regular piece of apparatus for this is the “ Numerical Frame,Abacus.' Each pupil should have a Book and a slate.

Teacher. Wha: do you see ? (showing the frame.)
Pupil. A thing, Balls, etc.
T. How many balls ? (showing 1.) P. One ball.
T. How many now ? (showing 2.) P. Two balls.
T. Why do you say balls instead of ball ?
P. Because there are two.

Questions of this kind call the pupil's attention to grammatical forms, etc. (See VI. Third Lesson.)

T. How many now?" (showing 3.) P. 3 balls ; and so on, until ten or twelve have been shown. Then ask the question again by taking the balls away one by one, finally it will be, T. How many now ? (showing 1 ball.) P. 1 ball. T. How many balls now ? (showing none.) P. No ball. T. Very well! we will write it on the board, (writes.) No ball.

T. Now we will write it by a shorter mode. 0 ball.

Thus he shows the words, one, two, three, etc. and also the figures 1, 2, 3, etc., placing the latter in a line across the up: per part of the board. Then show that ten is 1 before 0, etc., as in the II. Lesson, thus :0, 1, 2, 3, 4, 5, 6, 7, 8,

, 30 Direction. Now let the pupils read the First Lesson. Each pupil answers the questions, which he reads. If the tables, have been committed by the pupils, or if the pupils be but just beginning, let them read the tables. In reading let the pupil spell each new term, thus: Charles can find no book; 0, Naught, spells naught, etc. to twenty.

4TH DIRECTION. Now give them some of the numbers to be written on their slates, and write some on the board for them to read and to see if you can read them correctly.

8, 9,

I. FIRST. Charles can find no book. 0, Naught. Jane sees one star in the sky.

1, ONE. Ann can see two stars.

* *, 1,2, Two. William has three large knives.

H, 1,2,3, THREE. John has four sharp knives. HH, 1,2,3,4, Four. Can you count five things ? $8899, 1,2,3,4,5, FIVE. Susan counted six marks. IIIIII, 1,2,3,4,5,6, Six. Count seven dots.

......., 1,2,3,4,5,6,7, SEVEN. Count eight stars.

********, 1,2,3,4,5,6,7,8, Eight. Nine rings.

oQ0000000, 1,2,3,4,5,6,7,8,9, NINE. Count the letters in ARITHMETIC,

10, TEN. II. SECOND. Count and 'spell 10, ten. 11, eleven. 12, twelve. 13, thirteen. 14, fourteen. 15, fifteen. 16, sixteen. 17, seventeen. 18, eighteen. 19, nineteen. 20, twenty.

III. THIRD. Read these; 3 balls, 5 tops, 2 slates, 4 pens, 1 book, 16 pencils, 9 caps, 18 coats, 10 cents, 17 marbles, 11 apples, 6 cakes, 13 pins, 8 chairs, 19 boys, 7 girls, 15 desks, 0 bad boys, 14 horses, 12 guns, 20 arithmetics.

IV. FOURTH. NUMERATION TABLE. Used in counting. A single THING, or unit is one thing

l or 1. 10 units, or single things, make 1 ten

X. 10 tens

1 hundred 100 hun. C. 10 hundreds

I thousand 1,000... thou. M. 10 thousands

1 ten-thous. 10,000 .. t.thou. X. 10 ten-thousands

1 hund.-thou. 100,000 hun.thou. 10 hundred-thousands

1,000,000 . . mill. M V. FIFTH. What is a single thing or unit? How many hundreds make one thousand ?. How many tens make one hundred ? How many units, or single things, make one ten? How many ten-thousands make one hundred-thousand ? How many hundred-thousandr make one million ?

1 million

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First Decade 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, Second- 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, Third 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, Fourth 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, Fifth 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, Sixth *50, 51, 52, 53, 54, 55, 56, 57, 58, 59, Seventh 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, Eighth 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, Ninth 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, Tenth 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, Eleventh 100, 101, 102, 103, 104, 105, 106, 107, 108, 109,

- III. One hundred and two. 102, 506, 903, 809, 401, 604, 205, 708, 340, 460, 580, 620, 710, 838, 950.

IV. Read these ; 245, 706, 860, 607, 670, 845, 854, 485, 458, 990, 584, 548, 8, 868, 84, 848, 7, 74, 874, 917, 17, 7, 900, 10, 7, 6, 86, 986, 9, 98, 987, 7, 70, 700, 801, 920, 263, 834.

V. FEDERAL MONEY. Used in the United States. Its names are double-eagles, eagles, dollars, dimes, cents, and mills. 10 mills (m.) make 1 cent .

ct. 10 cents 1 dime.

D. 10 dimes 1 dollar

$. 10 dollars 1 eagle.

E. 2 eagles i double-eagle

D.E. VI. Read these ; $5 20ctš.; 19E. $7 2D. 7cts. 2m.; $18'15cts. 7m.; 16D.E.; 1E. $9 7cts. 6m.

VII. STERLING MONEY. Used in Great Britain. It names are guineas, pounds, crowns, shillings, pence, and farthings. 4 farthings (far.) make 1 penny

d. 12 pence

1 shilling 5 shillings

1 crown 20 shillings 1 pound

£. 21 shillings I guinea

gui. VIII. Read these; £9 10s. 2d. 1far.; £10 2s. 6d. 14gui. 5cr.'3s. 11d. 2far. ; £26 9d. ; 17gui. 138. 1far.

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