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SECTION IV. Increase and Decrease by a Small Number,

causing a change in the ty or tens. (LET the Teacher show here, by means of the frame, that in this, as in other successive lessons, the sum of the units increases the number of tens by one ; and that, in the subtraction, the number of tens is, for a similar reason, decreased by one.]

1. Four and six are how many? Fourteen and six ? Twenty-four and six ? Forty-four and six ? Sixty-four and six ? Two hundred and thirty-four and six ? Take four from ten ? From twenty ? From fifty ? From a hundred ? From two hundred and fifty ? From two hundred and ten ? thousand and ten ? 2. Four and seven, how many ?

Fourteen and seven? Twenty-four and seven ? A hundred and fifty-four and seven? Five hundred and thirty-four and seven? Nine hundred and sixty-four and seven? Take four from eleven? Four from twenty-one? Thirty-one? Fifty-one? Eighty-one ? Sixtyone? A hundred and eleven? Two hundred and twenty-one ? Three hundred and forty-one? Five hundred and fifty-one ? One thousand and twenty-one ?

3. Nine and five, how many? Nineteen and five? Twentynine and five? Thirty-nine and five ? Fifty-nine and five ? Seventy-nine and five? A hundred and nine and five? Three hundred and nineteen and five? Take five from fourteen? From twenty-four ? From forty-four ? Sixty-four? A hundred and four? Two hundred and thirty-four ? Three hundred and fourteen ? A thousand and fourteen ?

4. Eight and three, how many ? Eighteen and three ? Twenty-eight and three ? Fifty-eight and three ? Eightyeight and three? Two hundred and seventy-eight and three ? Nine hundred and forty-eight and three ? One thousand and eighteen and three ? Take three from eleven? Three from twenty-one? From thirty-one ? From thirty-one ? Sixty-one ?

Sixty-one? Eighty-one ? A hundred and twenty-one ? A thousand and twenty-one ?

5. Four and nine, how many ? Fourteen and nine? Twenty-four and nine ? Forty-four and nine? Eighty-four and nine? Three hundred and twenty-four and nine? Nine hundred and eighty-four and nine ? Take four from thirteen? Four from twenty-three? Thirty-three? Sixty-three ? A hundred and thirteen ? A thousand and twenty-three ?

6. Six and eight, how many ? Sixteen and cight? Twenty

six and eight? Fifty-six and eight? Eighty-six and eight? Sixty-six and eight ? Nine hundred and seventy-six and eight? Také six from fourteen? Sis from twenty-four ? Thirty-four ? Eighty-four ? Fifty-four ? A hundred and fourteen ?. Seven hundred and twenty-four? Eight hundred and sixty-four ? Nine hundred and twenty-four ? A thousand and fourteen ?

SECTION V. Increase and Decrease by a Small Number, caus

ing a change in the Tens and the Hundreds. 1. Five and seven are how many ? Twenty-five and seven? Fifteen and seven ? Forty-five and seven? Eighty-five and seven? Fifty-five and seven ? Thirty-five and seven ? Ninetyfiv and seven? Two hundred and ninety-five and seven ? Seven hundred and ninety-five and seven? Nine hundred and ninety-five and seven ? Take seven from twelve ? Seven from twenty-two ? Seven from fifty-two ? Seven from ninety-two ? Seven from a hundred and two ? From four hundred and two ? A thousand and two ? Eight hundred and two ?

2. Two and nine, how many ? Thirty-two and nine ? Twelve and nine ? Fifty-two and nine ? Eighty-two and nine ? Ninetytwo and nine ? A hundred and forty-two and nine ? Five hundred and ninety-two and nine? Nine hundred and ninetytwo and nine ? A thousand and twelve and nine? Take nine from eleven? Nine from a hundred and one ? Nine from twenty-one? From fifty-one ? From two hundred and one ? From a thousand and one? From five hundred and twentyone ?

3. Six and four, how many? Thirty-six and four ? Sixteen and four ? Ninety-six and four ? Nine hundred and ninetysix and four ? Eighty-six and four ? A thousand and six and four? Two hundred and sixteen and four ? Take four from ten? Four from twenty ? From a hundred ? From three hundred ? From two hundred and sixty ? From a thousand ? From five hundred and ten? From nine hundred and eighty?

4. Seven and five, how many? Ninety-seven and five ? Two hundred and seventeen and five? Three hundred and ninety-seven and five? Five hundred and seventeen and five ? Eight hundred and seven and five ? Seven hundred and seven and five ? Take five from twelve ? From twenty-two ? From

a hundred and two ? From a thousand and two ? From two hundred and twenty-two ? From eight hundred and ninetytwo?

5. Eight and seven, how many? Twenty-eight and seven? Eighteen and seven? Forty-eight and seven? Ninety-eight and seven? A hundred and eight and seven ? Eight hundred and eight and seven ? Nine hundred and eighteen and seven? Nine hundred and ninety-eight and seven? A thousand and eight and seven ? Take seven from fifteen? From twentyfive? From ninety-five ? From a hundred and five ? From three hundred and fifteen? From six hundred and five? From four hundred and twenty-five? From a thousand and five? From a thousand and ninety-five ?

6. Eight and nine, how many ? Forty-eight and nine ? Eighteen and nine? Ninety-eight and nine? Sixty-eight and nine? Eighty-eight and nine? A hundred and eight and nine? Two hundred and twenty-eight and nine? Six hundred and fifty-eight and nine? A thousand and eight and nine ? Nine hundred and ninety-eight and nine ? Take nine from seventeen? From eighty-seven? From twenty-seven? From a hundred and seven? From two hundred and twenty-seven ? From three hundred and seven ? From eight hundred and eighty-seven? From a thousand and seven ? From a thousand and twenty-seven?

7. Seven and four, how many ? Forty-seven and four ? Seventeen sand four ? Ninety-seven and four ? A hundred and seven and four ? Eighty-seven and four ? Three hundred and ninety-seven and four ? Nine hundred and ninety-seven and four? A thousand and seventeen and four? Take four from eleven? From twenty-one ? From sixty-one ? From a hundred and one ? From a thousand and one? From six hundred and eleven? From nine hundred and twenty-one ? From three hundred and one?

SECTION VI. Increase and Decrease by Larger Numbers, the

Units causing no change in the Tens or Hundreds. 1. Two and two, how many ? Twelve and twelve ? [Let the units occupy a wire in the frame between the two series of wires representing the tens.] How many are twelve and

twenty-two? Twenty-two and twenty-two? Thirty-two and twenty-two ? Thirty-two and fifty-two? A hundred and twenty-two and forty-two? Two hundred and thirty-two and two hundred and forty-two ? Take two from four ? Twelve from twenty-four? Twelve from thirty-four? Twenty-two from thirty-four ? Twenty-two from forty-four ? Twenty-two from fifty-four ? Thirty-two from fifty-four ? Thirty-two from eighty-four ? Fifty-two from eighty-four ? A hundred and twenty-two from a hundred and sixty-four ? Forty-two from a hundred and sixty-four ? Two hundred and thirty-two from four hundred and seventy-four ? Two hundred and forty-two from four hundred and seventy-four ?

2. One and two, how many ? Eleven and two ? Eleven and twelve ? Eleven and fifty-two? Eleven and twenty-two ? Eleven and forty-two ? Eleven and sixty-two? Eleven and eighty-two? Eleven and a hundred and twelve ? Eleven and a thousand and two ? Eleven from thirteen ? Two from thirteen? Eleven from twenty-three ? Twelve from twenty-three? Eleven from sixty-three? Fifty-two from sixty-three? Eleven from thirty-three?_Twenty-two from thirty-three ? Eleven from fifty-three ? Forty-two from fifty-three? Eleven from seventy-three ? Sixty-two from seventy-three ? Eleven from a hundred and twenty-three ? A hundred and twelve from a hundred and twenty-three? Eleven from a thousand and thirteen ? A thousand and two from a thousand and thirteen?

3. Four and three, how many ? Fourteen and thirteen? Thirty-four and thirteen? Thirty-four and fifty-three ? A hundred and twenty-four and a hundred and fifty-three ? Fourteen from twenty-seven? Thirteen from twenty-seven? Thirteen from forty-seven ? Thirty-four from forty-seven? Thirty-four from eighty-seven ? Fifty-three from eighty-seven ? A hundred and twenty-four from two hundred and seventyseven ? A hundred and fifty-three from two hundred and seventy-seven?

4. Two and six, how many ? Twelve and sixteen? Twelve and thirty-six ? Twenty-two and fifty-six ? Forty-two and fifty-six ? Thirty-two and forty-six? A hundred and twentytwo and two hundred and forty-six ? Six from eight? Two

rom eight? Twelve from twenty-eight? Sixteen from twentyeight? Twelve from forty-eight? Thirty-six from forty-eight? Twenty-two from seventy-eight? Fifty-six from seventy-eight? Forty-two from ninety-eight? Fifty-six from ninety-eight ?

Thirty-two from seventy-eight? Forty-six from seventy-eight? A hundred and twenty-two from three hundred and sixtyeight? Two hundred and forty-six from three hundred and sixty-eight?

5. Three and six, how many ? Thirteen and sixteen? Twenty-three and thirty-six ? Twenty-six and fifty-three ? Fortythree and forty-six ? A hundred and thirty-three and forty-six ? Two hundred and twenty-six and three hundred and fifty-three? Three from nine ? Six from nine ? Thirteen from twentynine? Sixteen from twenty-nine? Twenty-three from fiftynine? Thirty-six from fifty-nine? Twenty-six from seventynine ? Fifty-three from seventy-nine ? Forty-three from eighty-nine ? Forty-six from eighty-nine? Forty-six from a hundred and seventy-nine ? A hundred and thirty-three from a hundred and seventy-nine ? Two hundred and twenty-six from five hundred and seventy-nine? Three hundred and fiftythree from five hundred and seventy-nine ?

6. Two and three, how many ? Twelve and thirteen? Twelve and twenty-three? Thirty-two and forty-three? Twenty-two and fifty-three ? A hundred and thirty-two and forty-three ? Two hundred and seventy-three and twelve ? Two from five ? Three from five ? Twelve from twenty-five? Thirteen from twenty-five? Twelve from thirty-five? Twenty-three from thirty-five? Thirty-two from seventy-five ? Forty-three from seventy-five? Twenty-two from seventy-five? Fifty-three from seventy-five? A hundred and thirty-two from a hundred and seventy-five? Forty-three from a hundred and seventyfive? Two hundred and seventy-three from two hundred and eighty-five? Twelve from two hundred and eighty-five?

7. Eight and one, how many ? Eighteen and eleven? Twenty-eight and thirty-one? Seventy-eight and eleven? Two hundred and eleven and three hundred and eight? Two hundred and twenty-one and eighteen ? Eight from nine ? One from nine? Eighteen from twenty-nine? Eleven from twenty-nine ? Twenty-eight from fifty-nine? Thirty-one from fifty-nine? Seventy-eight from eighty-nine? Eleven from eighty-nine? Two hundred and eleven from five hundred and nineteen? Three hundred and eight from five hundred and nineteen? Two hundred and twenty-one from two hundred and thirty-nine? Eighteen from two hundred and thirty-nine ?

8. Four and two, how many? Fourteen and twelve ? Twenty-four and twelve? Twenty-two and seventy-four ? A hun

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