5. Let us make a new lesson. How many times one are three times three? Look at the three parcels of three one, two, three, four, five, six, seven, eight, nine. Answer, nine.

6. How many times one will four times three make? Three, and three are six, and three are nine, and three are twelve. Answer, twelve.

7. How many times one are there in four times four? Look at the parcels of four, place your finger down at the end of the fourth parcel; now count how many there are till coming to your finger. Sixteen. Right. Then four times four make sixteen, or sixteen times one.

8. How many times one are two times eight: Look at two parcels of eight: count them: how many do they make? Sixteen. Right. Then two times eight are equal to four times four. Can you tell me how many eight times two will make? Count off eight parcels of two: how many do they make? Sixteen, the same as two times eight. That is right; figures will prove one and the other when reckoned right. Four times four are sixteen, two times eight are sixteen, and eight times two are sixteen.

9. I wish to know how many times one three times five will make? Count off the first, second, and third parcels of five: how many? Fifteen. Well, how many times one will five threes make? Count off five parcels of three. Five threes make fifteen also, the same as three fives. All right.

10. DIVISION.

Now we will try to perform Division with our checker-board.

How many times two are contained in eighteen ? Place your finger at the end of eighteen on the range

of twos; how many times two are there in that space or range till coming to your finger? Ans., nine. 11. Count off thirty on the parcels of five: How many times five in thirty? Answer, six.

12. How many times eight in forty? Count off forty on the parcels of eight: how many times eight? Five. Count off forty-eight on the same range. How many times eight? Six times.

13. In forty-nine, how many times seven? Count off forty-nine on the range of sevens; how many times seven are there? Seven times. Then seven times seven are forty-nine: all right.

14. I have sixty-four chesnuts, and wish to divide them among eight boys; how many times eight are there in sixty-four, and how many will each boy have? Count off sixty-four on the range of eights: how many times eight are there? Eight times. Then each boy must have eight. Give eight to each one and see if the operation will prove in the result.*

15. Suppose I have forty-two walnuts, and wish to divide them equally among six boys; how many can each one have? Count off forty-two on the range of sixes: how many times six are there? Seven.

16. Nine cakes cost forty-five cents: how much was that apiece? Count off forty-five on the range of nines; how many times nine are there? Five times. Right, the cakes cost five cents each.

17. I have fifty-six pencils; how shall I divide them that seven boys may have an equal number each ? Count off fifty-six on the range of sevens: how many times seven are there? Eight times. Very well, each boy must have eight pencils. But, here comes little George Sprightly; will you all sonsent that I divide them again and give him an equal share? Agreed.

* Here explain result, and use no technicle terms without expla nation.

Now there are eight of you: how many must each one have? Count off fifty-six on the range of eights: how many times eight are there? Seven. Right, each one must have seven pencils, because seven times eight are fifty-six.

18. These questions are only a small number of specimens for the Teacher; he may exercise his ingenuity in forming different lessons, and of such variety, as his judgment will direct from time to time for the benefit of pupils. Exercising questions similar to the following, may be given out occasionally to advantage. As, four more three, that is, four added to three, equal how many?

19. Four, more three, more two, equal how many? 20. Four, more three, more two, less one; that is, one substracted, equal how many?

Six, more three, more two, less one, equal how many times five?

21. Eight, multiplied by two, equals how many? Eight, multiplied by three, less four, equals how many times ten?

22. Four, more the half part of two, equal how many?

23. Fifteen, less five, gives a certain sum for a remainder how many times five equal that remainder ?

24. The third of twelve, more the one half the third of twelve, equal how many?

25. The third of forty-eight, and half the third of forty-eight, are equal to how many times six? The fourth part of eight, more the third of fifteen, more the half of eighteen, equal how many times the half part of eight? 4.

26. The younger classes, under the inspection of some one from a senior class, may be exercised with such simple, easy, and diverting questions, and save

much time, which otherwise would be worse than lost; for this employment at home and at school, will often keep them out of mischief; it will exercise their mental faculties, and teach them how to distinguish truth from error; it will facilitate an attainment of the knowledge of the multiplication table suspended by the wall, and it will aid in expediting, that which is already an expeditious mode of teaching and learning arithmetic.

22 Apples.

34

21

33

12

23

145 Ap.

in all.

KEY TO CARD NO. 6.

SIMPLE ADDITION.

LESSON 1.

I begin first by writing down in figures, twenty-two, thirty-four, twenty-one, thirty-three, twelve, twenty-three: I place them exactly one number under another as on the card.

Now I begin at the first right hand 3, and say, 3 and 2 are 5, and 3 are 8, and 1 are 9, and 4 are 13, and 2 are 15; I set down 5 and carry one; because there is once 10 in 15, and 5 over.

Then I begin at the lower left hand 2, and say, 1 that I carry and 2 are 3, and 1 are 4, and 3 are 7, and 2 are 9, and 3 are twelve, and 2 are 14; I set down 14 on the left side of the 5. Total in figures 145 apples-In words-One hundred and forty-five. Let each scholar write the sum total or answer in words as well as in figures.

NOTE. To prove Addition, begin at top and reckon downward. See Simple Addition, Lesson 10.

LESSON 2.

34 Peaches. Write down on your slate 34, under that 41, then 52, 35, 24, 34:

41

52

35

24

34

220 Peaches.

Begin at the lowermost right hand 4, and say, 4 and 4 are 8, and 5. are 13, and 2 are 15, and 1 are 16, and 4 are 20: set down 0 under the 4, and carry 2; because there are twice 10 in 20.

Now begin at the lowermost 3, and say, 2 that I carry and 3 are 5, and 2 are 7, and 3 are 10, and 5 are 15, and 4 are 19, and 3 are 22. Set down 22 on

the left side of the cipher.

Total in figures, 220 peaches. Write down in. words Two hundred and twenty.

152 Pears.

343

444

561

324

444

2268 Prs.

in all.

LESSON 3.

Place the figures on your slate as they are on the card. Then say 4 and 4 are 8, and 1 are 9, and 4 are 13, and 3 are 16, and 2 are 18: set down 8 and carry 1.

One that I carry to 4 makes 5, and 2 are 7, and 6 are 13, and 4 are 17, and 4 are 21, and 5 are 26: set down 6 and Scarry 2.

Two that I carry to 4 are 6, and 3 are 9, and 5 are 14, and 4 are 18, and 3 are 21, and 1 are 22: set down 22 on the left side of 68. Total in figures, 2268. In words, Two thousand two hundred and sixty-eight.