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ontinue z ing 8 marks, and another containing 6 marks, and

count them together.

How many are 17 and 5? Keeping 17 in the m with ten

mind, select a rectangle containing 5 marks, and ee are eligt add them thus :-17 and 1 are 18, and 1 are 19, and

1 are 20, and I are 21, and 1 are 22.

If you take 4 from 9, how many will remain ? assemblag

Select a rectangle containing 9 marks, and take him cous

away four of them.

18 less 5 are how many ? Keeping 18 in mind, example

select a rectangle containing 5, and take them away I at a time.

In this manner all the examples in this section may be solved.

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B & C. The articles B and C contain the common addition table as far as the first 10 numbers. In the first the numbers are placed in order, and in the second out of order.

The pupil should study these until he can find the answers readily, and then he should commit the answers to memory.

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D. In this article, the numbers are larger than in the preceding, and, in some instances, three or more

numbers are added together. In the abstract exst examp amples, the numbers from one to ten are to be added

to the numbers from ten to twenty,

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E. This article contains subtraction.

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F. This article is intended to make the pupil familiar with adding the nine first numbers to all others. The pupil should study it until he can answer the questions very readily. G. In this article, all the preceding are combined

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together, and the numbers from 1 to 10 are added to all numbers from 20 to 100; and subtracted in the same manner.

18. 57 and 6 are 63, and 3 are 66, and 5 are 71, and 2 are 73, less 8 are 65.

H. This article contains practical questions which show the application of all the preceding articles.

6. 37 less 5 are 32, less 8 are 24, less 6 (which he kept himself) are 18; consequently he gave 18 to the third boy,

SECTION II.

This section contains multiplication. The pupil will see no difference between this and addition. It is best that he should not at first, though it may be well to explain it to him after a while.

A. This article contains practical questions, which the pupil will readily answer.

1. Three yards will cost 3 times as much as 1 yard.

N. B. Be careful to make the pupil give a similar reason for multiplication, both in this article, and elsewhere.

This question is solved on the plate thus : in the second row, count 3 rectangles, and find their sum. 2 and 2 are 4, and 2 are 6.

11. A man will travel 4 times as far in 4 hours as he will in 1 hour. In the third row, count 4 times %, and ascertain their sum.

15. There are 4 times as many feet in 4 yards as in 1 yard, or 4 times 3 feet.

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B. This article contains the common multiplica10 are a tion table, as far as the product of the first ten subtracted

numbers. The pupil should find the answers once

or twice through, until he can find them readily, and 5 are' and then let him commit them to memory.

43. 6 times 3. In the third row count 6 times 3, and then ascertain their sum. 3 and 3 are 6, &c.

59. 7 times 9. In the ninth row count 7 times 9, or 7 rectangles, and ascertain their sum. 9 and 9 are 18, &c.

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C. This article is the same as the preceding, except in this the numbers are out of their natural order.

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D. In this article multiplication is applied to practical examples. They are of the same kind as those in article A of this section.

12. There are 8 times as many squares in rows as in 1 row. 8 times 8 are 64.

13. There are 6 times as many farthings in 6 pence as in 1

penny.

6 times 4 are 24. 17. 12 times 4 are 48.

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Note. When a number is taken more than 10 times, as in the above example, after taking it 10 times on the plate, begin at the beginning of the row again, and take enough to make up the number. 23. There are 3 times as many pints in 3 quarts

3 times 2 are 6. And in 6 pints there are 6 times 4 gills, or 24 gills.

28. In 3 gallons there are 12 quarts, and in 12 quarts there are 24 pints.

31. In 2 gallons are 8 quarts, in 8 quarts 16 pints, in 16 pints 64 gills. 16 times 4 are 64.

35. In 1 gallon are 32 gills; and 32 times 2

as in 1 quart.

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cents are 64 cents. Or, 1 pint will cost 8 cents, and there are 8 pints in a gallon. 8 times 8 are 64.

38. They will be 2 miles apart in one hour, 4 miles in 2 hours, &c.

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SECTION IIJ.

A. This section contains division. The pupil will scarcely distinguish it from multiplication. It is not important that he should at first.

Though the pupil will be able to answer these questions by the multiplication table, if he has committed it to memory thoroughly; yet it will be better to use the plate for some time.

9. As many times as 3 dollars are contained in 15 dollars, so many yards of cloth may be bought for 15 dollars. On Plate I., in the third row, count fifteen, and see how many times 3 it makes. It is performed very nearly like multiplication.

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B. In this article the pupil obtains the first ideas of fractions, and learns the most important of the terms which are applied to fractions.* The pupil has already been accustomed to look upon a collection of units, as forming a number, or as being itself a part of another number. He knows, therefore, that one is a part of every number, and that every number is a part of every number larger than itself. As every number

may have a variety of parts, it is necessary to give names to the different parts, in order to distinguish them from each other.

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* As soon as the terms applied to fractions are fully comprehended, the operations on them are as simple as those on whole numbers.

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receive their names, according to the number of
parts which any number is divided into. If the
number is divided into two equal parts, the parts are
called halves ; if it is divided into three equal parts,
they are called thirds ; if into four parts, fourths,
&c.; and, having divided a number into parts, we
can take as many of the parts as we choose. If a
number be divided into five equal parts, and three
of the parts be taken, the fraction is called three
fifths of the number. The name shows at once into
how many parts the number is to be divided, and
how many parts are taken.

The examples in this book are so arranged, that
the names will usually show the pupił how the ope-
ration is to be performed. In this section, although
the pupil is taught to divide numbers into various
parts, he is not taught to notice any fractions, ex-
cept those where the numbers are divided into their
simple units, which is the most simple kind.

It will be best to use beans, pebbles, &c. first; and then Plate I.

4. Show the pupil one of the rectangles in the second row, and explain to him that one is 1 half of 2.

7. In the second row count 3 units; it will take all the marks in the first, and 1 in the second rectangle. Consequently it is 1 time 2, and 1 half of another 2.

15. In the second row count 9. It will take all the marks in the four first rectangles, and 1 in the fifth. Therefore 9 is 4 times 2 and one half of another 2.

18. Show the pupil a rectangle in the third row,
and ask him the question, and explain to him that I
is 1 third of 3.

20. Since 1 is 1 third of 3, 2 must be 2 thirds of 3.
34. In the third row count 11. It will take 3

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