Teaching Models

Divide by One-Digit Divisors

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

Example: Divide 59 by 8

59/8

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

Finding the Mean
One application of division is finding the mean, or average, of a set of numbers. The mean is found by adding the numbers and then dividing the sum by the number of addends. The mean tells what each number would be if the sum remained the same and the individual numbers were equal.

Example: Find the mean for 9, 19, 44, 8, 25, 4, 27, and 32.

Find the sum:
Divide the sum by the number of addends:
    9 + 19 + 44 + 8 + 25 + 4 + 27 + 32 = 168
   168 ÷ 8 = 21
The mean, or average, of the group is 21.

The mean is only one measure of central tendency of a set of data. Other measures of central tendency are discussed elsewhere.

Dividing by Multiples of 10
Patterns can be used when dividing by multiples of 10.

63 ÷ 7 = 9
630 ÷ 7 = 90
6,300 ÷ 7 = 900
63,000 ÷ 7 = 9,000
630,000 ÷ 7 = 90,000
 
630 ÷ 70 = 9
6,300 ÷ 700 = 9
63,000 ÷ 7,000 = 9
630,000 ÷ 70,000 = 9
    
 
Think: (63 ÷ 7) × 10
Think: (63 ÷ 7) × 100
Think: (63 ÷ 7) × 1,000
Think: (63 ÷ 7) × 10,000
 
Think: (63 ÷ 7) × (10 ÷ 10)
Think: (63 ÷ 7) × (100 ÷100)
Think: (63 ÷ 7) × (1,000 ÷ 1,000)
Think: (63 ÷ 7) × (10,000 ÷ 10,000)

Teaching Model 4.4: Divisibility


Houghton Mifflin Math Grade 5