Math Background

Division by One-Digit Divisors: When Students Ask

  • How do I regroup in division?
    Base-ten blocks can be used to show regrouping in division.

    To model division problem, first show 174 with 1 hundred block, 7 tens blocks, and 4 ones blocks.

    Base-ten blocks

    Since the hundred block cannot be put into 3 equal groups without regrouping, regroup the hundred as 10 tens. Now there are 17 tens. Put an equal number of tens in each of the three groups.

    Base-ten blocks

    There are now 2 tens and 4 ones. Regroup the 2 tens as 20 ones. Now divide the 24 ones blocks into the three groups, putting an equal number in each group.

    Each of the 3 groups has 5 tens and 8 ones.

    Base-ten blocks

    So 174 ÷ 3 = 58.

    Ask students to compare the model to the division algorithm.

    division problem
  • What do I do with a remainder?
    The remainder is the number that is left over after dividing. It is always less than the divisor. The remainder is an essential part of the answer and is shown in the quotient preceded by the letter R.
    division problem

    So 58 ÷ 4 = 14 R2.

    The remainder is often used to answer questions in word problems involving division. Sometimes the remainder is the answer to a question, sometimes the remainder is dropped, and sometimes the quotient is increased.

  • Where do I place the first digit in the quotient?
    Knowing where to place the first digit in the quotient is an important skill. Use base-ten blocks to model division. Students can then see when regrouping is necessary to divide. If hundreds must be regrouped as tens in order to divide, then the first digit in the quotient should go in the tens place. Likewise, if tens must be regrouped as ones, then the first digit in the quotient should go in the ones place.

    If students are having problems, use estimating and compatible numbers to place the first digit in the quotient.

  • When do I need to place a zero in the quotient?
    After every subtraction in the division algorithm, the difference must be less than the divisor. The next digit is then brought down. If the result is still less than the divisor, then a zero must be placed as the next digit in the quotient.
    division problem

Houghton Mifflin Math Grade 4