Teaching Models

Divide by One-Digit Divisors

The division algorithm for dividing whole numbers is based on the base-ten numeration system. Proficiency in division requires proficiency in multiplication and subtraction. When discussing division, correct vocabulary is essential.

Example: Divide 59 by 8.

23 × 7 = 164
← 7 is the quotient.
← 8 is the divisor and 59 is dividend.


← 3 is the remainder.

Example: Divide 164 by 7.


23 × 7 = 164

Look at the hundreds place. 1 < 7, so there will be no hundreds digit in the dividend. The first digit will be in the tens place.
Think: 7 × n ≤ 16
2 is the greatest possible value of n.

Multiple 2 × 7.

Subtract 16 − 14. Compare to make sure the remainder is less than the divisor. If the remainder is greater, an error has been made.

 

164 ÷ 7 = 23

Rename remainder of 2 tens as 20 ones. Bring down the 4 ones in the divisor and add to the 20 ones
Think: 7 × n ≤ 24
3 is the greatest possible value of n.

Multiple 3 × 7.

Subtract 24 − 21. Compare to make sure the remainder is less than the divisor. If the remainder is greater, an error has been made.

 

23 × 7 = 161
To check a division problem, multiply the quotient by the divisor and add to the remainder. The result should be equal to the dividend.

Since division problems with zeros in the quotient cause some students difficulty, extra practice with such examples should be provided. When dividing money, point out to students that the decimal point in the quotient should be placed directly above the decimal point in the dividend.

Division examples

Patterns can be used when dividing with multiples of 10.

63 ÷ 7 = 9
630 ÷ 7 = 90
6,300 ÷ 7 = 900

Think: (63 ÷ 7) × 10
Think: (63 ÷ 7) × 100

Teaching Model 9.2: Place the First Digit of the Quotient


Houghton Mifflin Math Grade 4