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dred and twelve and two hundred and fourteen? Two hundred and two and eight hundred and forty-four ? Two from six ? Four from six ? Fourteen from twenty-six ? Twelve from twenty-six? Twenty-four from thirty-six? Twelve from thirty-six? Twenty-two from ninety-six? Seventy-four from ninety-six ? A hundred and twelve from three hundred and twenty-six ? Two hundred and fourteen from three hundred and twenty-six ? Two hundred and twenty-two from a thousand and sixty-six ? Eight hundred and forty-four from a thousand and sixty-six ?

9. Five and four, how many? Fifteen and fourteen? Thirty-four and fifteen? Twenty-four and thirty-five? Two hundred and twenty-five and three hundred and fourteen? Three hundred and seventy-five and seven hundred and fourteen? Five from nine ? Four from nine ? Fifteen from twenty-nine? Fourteen from twenty-nine ? Thirty-four from forty-nine ? Fifteen from forty-nine? Twenty-four from fifty-nine ? Thirty-five from fifty-nine ? Two hundred and twenty-five from five hundred and thirty-nine ? Three hundred and fourteen from five hundred and thirty-nine ? Three hundred and seventy-five from a thousand and eighty-nine ? Seven hundred and fourteen from a thousand and eighty-nine ?

10. Two and five, how many ? Twelve and fifteen? Twenty-two and thirty-five? Sixty-two and fifteen? Two hundred and thirty-two and fifteen? Four hundred and twelve and six hundred and fifteen? Two from seven? Five from seven? Twelve from twenty-seven? Fifteen from twenty-seven? Twenty-two from fifty-seven? Thirty-five from fifty-seven? Sixtytwo from seventy-seven ? Fifteen from seventy-seven? Two hundred and thirty-two from two hundred and forty-seven ? Fifteen from two hundred and forty-seven ? Four hundred and twelve from a thousand and twenty-seven? Six hundred and fifteen from a thousand and twenty-seven ?

11. Five and three, how many ? Fifteen and thirteen? Twenty-five and thirty-three ? A hundred and fifteen and a hundred and fifty-three ? Two hundred and forty-five and eight hundred and thirteen ? Five from eight? Three from eight? Fifteen from twenty-eight? Thirteen from twentyeight? Twenty-five from fifty-eight? Thirty-three from fiftyeight? A hundred and fifteen from two hundred and sixtyeight? A hundred and fifty-three from two hundred and sixty-eight? Two hundred and forty-five from a thousand and

sixty-eight? Eight hundred and thirteen from a thousand and sixty-eight?

SECTION VII. Practical Questions. [Tuis section is the first that requires very close attention on the part of the pupils. The class, therefore, should once more be warned that the questions are not to be repeated, one of the main objects of the course being to make good and correct listeners.]

1. John picked up an apple in the orchard. His father gave him another. How many apples had he then ? Ans. John had then two apples. How do you know? Because he picked up one in the orchard, and his father gave him one, and one

one make two. [Let the Practical Questions be resolved in this manner throughout. Use the frame when the child is at a loss.]

2. William's father gave him two plums, and his mother gave him two.

How many plums did they both give him ? Ans. They both gave

him
plums. How do

you

know? 3. If an orange cost five cents, and an apple two cents, how many cents will both cost?

How do you know? How many will the orange cost more than the apple? How do you

know? Ans. Because the orange cost five cents, and the apple two, and the difference between five and two is three.

4. Robert had six nuts, and gave two of them to his sister. How many bad he left? Why? 5. If

you had seven nuts in the one hand, and four in the other, how many would you have in the one more than in the other ? How many in both hands ? [Repeat “Why ?” after every question.]

6. A man had four apples, which he divided equally between his two boys. How many did he give them apiece ?

7. A lady gave two apples to each of her three children. How many did she give to them all ?

8. A man bought six peaches, and divided them equally among his three children. How many did they get apiece?

9. William gave two nuts to each of his three brothers. How

many did he give to them all? 10. If you had six cents in one pocket, and five cents in another, how many

would

you

have in both ?

11. If you had eleven cents, and were to pay away three, how many would you have remaining ?

12. There were four boys, each of whom had three cents. How many had they altogether?

13. A lady, who had five children, wished to divide fifteen apples equally among them. How many would they get apiece ?

14. A man, who had twenty-eight dollars in his pocket, paid away five of them for a barrel of flour. How much had he left ?

15. John had sixteen marbles in a bag, and four in one of his pockets.

How many were in both ? How many more in the bag than in the pocket?

16. James gathered nineteen apples, and put them in a basket to carry them home; but, when he got there, he found only fifteen in the basket. How many had he lost out ?

17. A man owing thirty-seven dollars, paid all but seven dollars. How much did he pay?

18. A man bought three calves for six dollars each. What did they cost him ? If he were to sell them for twenty dollars, how much would he gain?

19. A merchant bought a firkin of butter for twelve dollars; but, as it was found to be damaged, he had to sell it for eight dollars. How much did he lose ?

20. Three girls one day counted their needles, and put them into one cushion: one had five, another four, and the third cight. How many needles had they amongst them?

21. When the girls had finished sewing, they found that six of the needles had been broken, and agreed to share the loss equally among them. How many did each of them get, and how many had they in the whole? 22. A boy had twenty apples, which he divided among

his companions as follows: to one he gave three; to another two; to another four; and to another five. How

many

did he give away, and how

many

had he left ? 23. A man went to a provision store, and bought three pounds of beef for eighteen cents, and four pounds of mutton for twenty cents. He gave the man fifty cents. How much change should he receive ?

24. A man bought a cabbage for five cents, some turnips for eight cents, some carrots for six cents, and a head of celery for five cents, and gave the owner a twenty-five cent piece to pay for them. What was his change?

25. A man bought a sleigh for fifteen dollars, and gave

nine dollars to have it repaired and painted. He hired it to one of his neighbors for a few days for a dollar, and to another for a month for four dollars. He then sold it for twenty dollars. Did he gain or lose by the bargain, and how much ?

26. Dick had twenty-five plums? He gave seven of them to Harry, and half of the rest to John. How many had each of them then ?

27. A boy had twenty-five cents. He bought two oranges at six cents each, four apples at one cent each, and a lemon for four cênts. How much money had he left ?

28. Dick had ten peaches, Harry twelve, and Charles thirteen: Dick gave three to Stephen, Harry gave him six, and Charles

gave

him five. How many had Stephen, and how many had each left?

29. A boy, having received fifty cents for his work, bought a slate for ten cents, two pencils for a cent, a book of arithmetic for fifteen cents, and a book of geography for twenty cents. How many cents had he left?

30. John, having received fifty cents from his father, bought one of the Rollo books for twenty cents. His mother then gave him twenty-five cents, after which he bought for his sister one of the Lucy books for twenty cents, and a ribbon for six cents. How many cents had he left, and how many more did he spend for his sister than for himself?

SECTION VII. Increase and Decrease by Large Numbers,

the Units causing a change in the Tens. 1. Four and six, how many ? Fourteen and sixteen ? [Show, on the frame, that, when the units amount to ten or more, the number of ty or tens is increased by one.] Thirty-four and sixteen? Twenty-four and twenty-six ? Thirty-four and twenty-six? Fifty-four and twenty-six ? Forty-four and thirty-six ? Thirty-four and twenty-six ? Eighty-six and fourteen? A hundred and twenty-four and sixteen? Five hundred and fourteen and a hundred and sixteen? Fourteen from thirty ? [Here show, on the frame, that, when there are not a sufficiency of units for the subtraction, one of the tens must be broken. Repeat illustrations of this kind on the frame wher

ever necessary.] Sixteen from thirty ? Sixteen from fifty ? Thirty-four from fifty? Twenty-six from fifty? Thirty-four from sixty? Twenty-six from eighty ? Forty-four from eighty ? Thirty-four from ninety? Eighty-six from a hundred ? A hundred and twenty-four from a hundred and forty ? A hundred and sixteen from six hundred and thirty ?

2. Eight and five, how many ? Eighteen and fifteen? Twenty-eight and thirty-five ? Forty-eight and forty-five? Twentyeight and sixty-five ? Sixty-eight and fifteen? A hundred and eighteen and a hundred and fifteen? Five hundred and twenty-eight and a hundred and fifteen? Five from thirteen? Eight from thirteen? Eighteen from thirty-three? Twentyeight from sixty-three? Forty-five from ninety-three? Twenty-eight from ninety-three? Fifteen from eighty-three ? A hundred and eighteen from two hundred and thirty-three ? A hundred and fifteen from six hundred and forty-three?

3. Seven and four, how many ? Seventeen and fourteen ? Twenty-seven and fifty-four ? Thirty-seven and fifty-four? Thirty-seven and twenty-four? Sixty-seven and twenty-four ? A hundred and seventeen and thirty-four ? A hundred and fifty-seven and thirty-four ? Two hundred and thirty-seven and three hundred and fourteen? Fourteen from thirty-one ? Twenty-seven from eighty-one? Thirty-seven from sixty-one ? Twenty-four from sixty-one? Twenty-four from ninety-one ? A hundred and seventeen from a hundred and ninety-one ? A hundred and seventeen from a hundred and fifty-one? Thirtyfour from a hundred and ninety-one ? Two hundred and thirty-seven from five hundred and fifty-one ? Three hundred and fourteen from five hundred and fifty-one ?

4. Six and six, how many ? Sixteen and twenty-six ? Sixteen and sixteen? Thirty-six and forty-six ? Fifty-six and twenty-six ? Sixteen and fifty-six? A hundred and sixteen and a hundred and twenty-six ? Three hundred and sixteen and two hundred and fifty-six ? Six from twelve ? Sixteen from forty-two? Forty-six from eighty-two? Fifty-six from eighty-two? Sixteen from seventy-two? A hundred and twenty-six from two hundred and forty-two ? Three hundred and sixteen from five hundred and seventy-two? Two hundred and fifty-six from five hundred and seventy-two?

5. Seven and eight, how many ? Seventeen and eighteen? Seventeen and forty-eight? Twenty-seven and fifty-eight ? A hundred and twenty-seven and eighteen? Two hundred and

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