Teaching Models

Divide by Two-Digit Divisors

The division algorithm for dividing by two-digit divisors is the same as that for one-digit divisors. Students must develop skill in estimating the first digit in the dividend, including making adjustments when the first estimate is too great or too small.

Example: Divide 1,138 by 23.

1,138/23
Look at the dividend. Since 11 < 23, there will be no thousands or hundreds digit in the quotient. The first digit will be in the tens place.
Think: 23 × n ≤ 113 so 4 is the greatest possible value of n.
Multiply 23 × 4.
Subtract 113 − 92. Compare to make sure the remainder is less than the divisor. If the remainder is greater, an error has been made.
1,138/23 = 49 r11
Rename the remainder of 21 tens as 210 ones. Bring down the 8 ones in the dividend and add to the 210 ones.
Think: 23 × n ≤ 218 so 9 is the greatest possible value of n.
Multiply 23 × 9.
Subtract 218 − 207. Compare to make sure the remainder is less than the divisor. If the remainder is greater, an error has been made.
 
To check a division problem, multiply the quotient by the divisor and add the remainder. The result should be equal to the dividend.
49 x 23 to check answer

Since division problems with zeros in the quotient cause some students difficulty, extra practice with such computations should be provided.


Teaching Model 5.1: Divide by Multiples of 10, 100, and 1,000


Houghton Mifflin Math Grade 5