A Division Algorithm

1. Partial Quotient A Division Algorithm

2. Partial Quotients • The Partial Quotients Algorithm uses a series of “at least, but less than” estimates of how many b’s in a. Students might begin with multiples of 10 – they’re easiest. This method builds towards traditional long division. It removes difficulties and errors associated with simple structure mistakes of long division. Based on EM resources

3. 12 158 Partial Quotients 13 R2 There are at least ten 12’s in 158 (10 x 12=120), but fewer than twenty. (20 x 12 = 240) - 120 10 – 1st guess Subtract There are more than three (3 x 12 = 36), but fewer than four (4 x 12 = 48). Record 3 as the next guess 38 - 36 3 –2nd guess Subtract Since 2 is less than 12, you can stop estimating. 2 The final result is the sum of the guesses (10 + 3 = 13) plus what is left over (remainder of 2 ) 13 sum of guesses

4. 36 7,891 Here is another one... 219 R7 There are at least 100 36’s in 7,891 (100 x 36=3600). Record it as the first guess. - 3,600 100 – 1st guess There is at least 100 more 36’s. Record 100 as the next guess Subtract 4,291 - 3,600 100 – 2nd guess 36 x 10 is 360. There are 10 more 36’s. Record 10 as the next guess. Subtract 691 There is not another 10 group in 331. 36 x 9 is 324. Record 9 as the 4th guess. - 360 10 – 3rd guess Subtract 331 Since 7 is less than 36, you can stop estimating. - 324 9 – 4th guess Subtract The final result is the sum of the guesses (100 + 100 + 10 + 9) plus what is left over (remainder of 7 ) 7 219 sum of guesses

5. 43 8,572 Try this one on your own! 199 R 15 Let’s see if you’re right. - 4,300 100 – 1st guess Subtract 4272 - 3870 90 – 2nd guess Subtract Way to go! 402 - 301 7 – 3rd guess Subtract 101 - 86 2 – 4th guess Subtract 15 Sum of guesses 199