Math Background

Lesson: Dividing Two-Digit and Three-Digit Numbers
Developing the Concept

After showing students how to model division problems with base-ten blocks, have them work together in groups to model division problems with play money.

Materials: play money, paper and pencil for each student

Preparation: Divide the class into small groups. Designate a “banker” for each group. Give each banker a bag of 30 pennies to be used for regrouping only. Then give each group 4 one-dollar bills, 3 dimes, and 2 pennies.

  • Say: The banker in each group is holding 30 pennies to be used for regrouping only. Each group has 4 one-dollar bills, 3 dimes, and 2 pennies. We are going to divide this amount into 4 equal groups.
  • Ask: How can you write this amount by using a dollar sign and a decimal point? ($4.32) How can you write $4.32 divided by 4 by using the long-division symbol? division problem
  • Say: Dividing money by a whole number is just like dividing whole numbers. The only difference is that the quotient will be an amount of money. Simply write the dollar sign and decimal point in the quotient directly above the corresponding places in the dividend.
    You may wish to demonstrate this on the board.
  • Say: Write division problem on a sheet of paper. As you model the division by using play money, complete each corresponding step in the division algorithm.
  • Ask: Can you divide 4 dollars into 4 equal groups? (yes) How many dollars will be in each group? (1 dollar) Where will you place the first digit in the quotient of the division algorithm? (in the place representing dollars) What is the first digit in the quotient? (1)
    Make sure that students place the first digit in the correct place in the quotient, and check to be sure that they have placed a one-dollar bill in each of the four groups.
  • Ask: How many dollar bills were used? (4) Are there any dollar bills left? (no) How do we show this by using the algorithm? (subtract: 4 − 4 = 0)
    Make sure that students complete this next step of the algorithm correctly.
  • Say: How many dimes do you have? (3) Represent this by bringing down the 3 in the division algorithm. Can you divide the 3 dimes into 4 equal groups? (no) What digit must be placed next in the quotient? (0)
    Check students' work to make sure the zero is placed correctly in the division algorithm.
  • Ask: What must be done with the 3 dimes in order to divide? (Regroup the 3 dimes as 30 pennies.)
  • Say: Ask your banker to regroup.
  • Ask: Now how many pennies do you have altogether? (32)
    Represent this in the division algorithm by bringing down the 2.
  • Ask: How can 32 pennies be divided into 4 equal groups? (Place 8 pennies in each group.)
    Make sure that students place 8 pennies in each of the four groups.
  • Ask: What number is placed next in the quotient? (8) How many pennies were used? (32) How many were left over? (0)
  • Say: Complete the algorithm by using this information. Place 8 in the quotient. Subtract 32 from 32. The remainder is 0.
    Check to make sure that students have completed the algorithm correctly and that their models reflect 4 groups with $1.08 in each group.
  • Ask: How much money is in each group? ($1.08) What is $4.32 ÷ 4? ($1.08)

Wrap-Up and Assessment
Review with students when it is necessary to place a zero in the quotient. Reinforce that after every subtraction in the division algorithm, the difference must be less than the divisor. If division is not possible after bringing down the next digit, then a zero must be placed as the next digit in the quotient.

You may wish to give students another division problem to model by using money or base-ten blocks. Have students use the model to complete the division algorithm. As you assess students, check to see whether they have a clear understanding of the division algorithm, the regrouping process, and the placement of zeros in the quotient. Note also those students who have not mastered the division facts.

Houghton Mifflin Math Grade 4