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how many times of 42? As many times of 42 as of 42 is contained times in the number of which of of 36 is . Such exercises may be good discipline, but there is no need of consuming time on exercises merely for discipline, as the opportunities for it in acquiring useful knowledge are abundant.

8. When practicable, it is best that the whole class should stand at recitation. At any rate, the pupil who recites shoulil stand, and, if the teacher reads the example, the pupil should repeat it after him, before giving the explanation.

9. Never proceed with the recitation unless every member of the class is giving attention, but do not try to keep the atten. tion too long. Many expedients must be employed to keep the attention awake. Sometimes the pupils may *« take places, sometimes they may be permitted to correct each other, and sometimes a pupil may be called at random to finish a solution commenced by another.

10. Aim at thoroughness in every step. This is much promoted by frequent and judicious reviews. With every lesson in advance the preceding should be reviewed; and there should be monthly and quarterly reviews beside.

11. If you suspect that a solution has been committed to memory without being understood, give a similar original question with different numbers.

12. Where it is practicable, illustrate problems and principles by sensible objects. Let fractions be illustrated by dividing an apple, a line, a square, or some other object. The tables of weights and measures should be taught according to the method of object-teaching, and not abstractly committed to memory.

13. As an occasional exercise, let each pupil, from memory, propose to the pupil next above him some question embraced in the part of the book which has been studied, the pupil failing to solve the question put to him losing his place; or, where "place taking” is not practiced, let there be a forfeiture of merits for failure, or a gain for success.

14. Original questions similar to examples 32 and 33, page 28, to be answered simultaneously by the class, should be proposed frequently and enunciated rapidly.

15. The learner should seldom if ever be told directly how to perform any operation in Arithmetic. Much less should he have the operation performed for him. Instead of telling the pupil directly how to go on, examine him, and endeavor to discover in what his difficulty consists, and then, if possible, remove it.

16. The recitation should be conducted briskly, and it should be so managed, if practicable, that each pupil shall endeavor to solve every question proposed; but it is not necessary that the whole lesson should be actually recited by each pupil.

17. But the most important requisite to success is to create and to sustain an interest in the study. How can this be done? In the first place you must be really very much interested yourself. In the second place, you must teach well. And if you are deeply interested in the subject, you will be very likely to find out how to teach it skillfully.

CONTENTS.

I.

SECTION I, pp. 9-25, contains addition, subtraction, mu'tiplication,
and division, and numbers are expressed only by words. The very
young pupil will be aided in solving the examples by sensible objects,
such as knives, cents, marbles, apples, fingers, etc.

II.

SECTION II, pp. 26 - 47, introduces the Arabic figures and Arith-
metical signs. The examples are similar to those in Section I, and
a little more difficult.

IlI.
SECTION III, pp. 48 – 75, presents the elements of fractions, and op-
erations upon whole numbers are continued and extended.

IV.

SECTION IV, pp. 75 – 92, defines fractions, the fractional form isin-
troduced, and the principles of fractions are still further developed.

v.

SECTION V, pp. 93 - 101, gives the tables of compound numbers and
practical examples on the same.

VI.

SECTION VI, pp. 101 - 124, gives a variety of practical examples,
together with the more complicated combinations of fractions.

VII.

SECTION VII, pp. 125 - 138, introduces several notes, giving more or

less minute suggestions with reference to the various operations in

fractions.

SECTION VIII, pp. 139–148, develops some of the more important

principles in per centage.

SECTION IX, pp, 149 – 163, consists of a few. Lessons composed of

miscellaneous examples, together with Multiplication and Review

Tables,

X.

In pp. 164 – 176, a few of the more simple principles of Written
Arithmetic are given. These pages may be studied with or after the
preceding pages.

INTELLECTUAL ARITHMETIC.

SECTION FIRST.

LESSON 1.

1. HENRY had one knife, and he has found another; how many

knives has he now? 2. Charles bought an orange for two cents, and an apple for one cent ; how many cents did he pay for both ?

3. Mary gave two peaches to Sarah, and kept two herself; how many peaches had she at first ?

4. If you have four marbles in one hand, and three in the other, how many have you in both ? 5. If you

have four fingers on each hand, how many fingers have you on both hands ?

6. James found five apples under one tree, and four under another; how many apples did he find under both trees?

7. Addie has five canaries, and Ella has three ; how

many canaries have they together? 8. Robert had three peaches, but he has given one of them away; how many peaches has he now?

9. John having four cents, spent two of them for an orange; how many cents has he now?

10. David has five cents in one hand, and two cents in the other; how many cents has he in both hands ? How many more in one hand than in the other?

11. Frank has six gray squirrels, and Herbert has three; how many squirrels have they both ?

12. Edwin has six figs, and Philip has four; how many more figs has Edwin than Philip? How many have they both ?

13. William having eight plums, gave five of them to Louisa; how many did he keep? How many less did he keep than he gave away?

14. Edward has six doves, and Charles has eight; how many more has Charles than Edward ? How many have they both ?

13. Lewis bought a pig for eight dollars, and sold it for ten dollars ; how much did he gain ?

16. A man bought a sled for ten dollars, and sold it for seven ; how much did he lose ?

17. A man owing ten dollars, paid four dollars ; how much did he still owe?

18. A man owing ten dollars, paid all but four dollars ; how much did he pay ?

19. Mr. Adams sold a pig for three dollars, and a sheep for six dollars ; how many dollars did he receive for both ?

20. Albert has eight rabbits, and Arthur has two; how

many rabbits have they both ? 21. George found seven eggs in one nest, and three in another; how many eggs did he find?

22. Frank gave three cents for an orange, and had seven cents left; how many cents had he at first?

23. If a melon is worth ten cents, and an orange is worth four cents, how many cents are they both worth? How much more is the melon worth than the orange?

24. Mary had nine cents, and her mother gave her three; how many cents had Mary then ?

25. Robert had ten peaches, but he has given four of them to David ; how many peaches has Robert now?

How

many more than David ? 26. Mr. Day bought a barrel of flour for ten dollars, and sold it for two dollars more than he gave for it: how much did he receive for it?

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27. A boy having twelve walnuts, gave away five of them ; how many had he left?

28. Bought a ton of coal for ten dollars, and a cord of wood for six dollars ; what did I pay for both ? How much more for the coal than for the wood ?

LESSON II.

1. Two and one are how many?
2. Three and one are how many ?
3. Four and one are how many ?
4. Five and one are how many

?
5. Six and one are how many ?
6. Seven and one are how many ?
7. Eight and one are how many ?
8. Nine and one are how many ?
9. Ten and one are how many ?
10. Two and two are how

many

? 11. Three and two are how

many

? 12. Four and two are how many

? 13. Five and two are how

many

? 14. Six and two are how

many

? 15. Seven and two are how many ? 16. Eight and two are how many ? 17. Nine and two are how many ? 18. Ten and two are how many ? 19. Two and three are how

many

? 20. Three and three are how many ? 21. Four and three are how many ? 22. Five and three are how many ? 23. Six and three are how many ? 24. Seven and three are how many ? 25. Eight and three are how many

? 26. Nine and three are how many ? 27. Ten and three are how many ? 28. Two and four are how many ? 29. Three and four are how many ?

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