Division by One-Digit Divisors

• Review the terms divisor, dividend, quotient, and remainder.

• Remind students that ÷ and are symbols used in division. The equation 45 ÷ 3 = 15 can be written as
  

  Give students division equations that use the division sign (÷), and ask them to rewrite the equation using the long-division symbol. Have students label the dividend, divisor, and quotient.

• Explain the concept of dividing and model regrouping in division by using base-ten blocks. Once students understand the concept, they will have greater success with the algorithm.

• Make sure that students know the relationship between multiplication and division, and show students how to check a division problem by using multiplication.

• If students learning the division algorithm are having trouble placing the first digit in the quotient, you may wish to teach them how to use compatible numbers to estimate the quotient. In the problem , students can estimate the quotient by using 120 as the dividend. When finding a compatible number, look for a number that is close to the actual dividend but is easily divided by the divisor. This number is compatible with the divisor because 3 x 40 = 120. If the estimate of the quotient is 40, then the first digit in the quotient must be in the tens place.

• Students must realize that when they are trying to find the quotient, they are looking for a number that when multiplied by the divisor will give a product that is closest to the dividend without being greater than the dividend. Reinforce that after every subtraction in the division algorithm, the difference must be less than the divisor. If it is not, then the digit in the quotient must be increased.

• An important but often difficult skill to master is that of placing zeros in the quotient. Impress upon students that once the subtraction is done, and the next digit is brought down, if division is not possible, then a zero must be placed as the next digit in the quotient.

• Students often omit the last digit in the quotient if that digit is a zero. In the problem below, tell students that if the first digit placed in the quotient is in the hundreds place, then there must be a digit in the tens place and the ones place.