Math Background

Lesson: Regrouping to Divide
Developing the Concept

After students have explored the division of greater numbers with no regrouping, they can proceed to divide with regrouping.

Materials: play money: ten $1 bills, 10 dimes, and 25 pennies for each student or pair of students, or Learning Tool 6 in the Learning Tools Folder

Preparation: Distribute the play money to each student or pair of students.

Prerequisite Skills and Background: Students should know how to divide greater numbers with no regrouping.

  • Write56¢ ÷ 4 = n on the board.
    Have a volunteer read the division sentence aloud.
  • Say: Show 56¢ with your play money. Put the rest of the money aside.
    Students should show 5 dimes and 6 pennies.
  • Ask: Into how many equal groups will we divide 56¢? (4)
  • Say: Divide the 5 dimes equally into 4 groups. Put any leftover dimes aside.
  • Ask: How many dimes are in each group? (1) How many dimes are left over? (1)
  • Say: Regroup the 1 leftover dime as 10 pennies.
  • Ask: Now how many pennies do you have? (16)
  • Say: Divide the 16 pennies into 4 groups.
  • Ask: How many pennies are in each group? (4) Are there any left over? (no)
  • Ask: What is the value of the money in each group? (14¢) What is 56¢ ÷ 4? (14¢)
    Replace n with 14¢.
  • Write$9.84 ÷ 3 = n on the board.
    Have a volunteer read the division sentence aloud.
  • Say: Show $9.84 with your play money. Put the rest of the money aside.
    Students should show nine $1 bills, 8 dimes, and 4 pennies.
  • Ask: How many equal groups will we divide $9.84 into? (3)
  • Say: Divide the nine $1 bills equally into 3 groups.
  • Ask: How many $1 bills are in each group? (3)
  • Say: Divide the 8 dimes equally into the 3 groups. Put any leftover dimes aside.
  • Ask: How many dimes are in each group? (2) How many dimes are left over? (2)
  • Say: Regroup the 2 leftover dimes as 20 pennies.
  • Ask: Now how many pennies do you have? (24)
  • Say: Divide the 24 pennies into 3 groups.
  • Ask: How many pennies are in each group? (8) Are there any left over? (no)
  • Ask: What is the value of the money in each group? ($3.28) What is $9.84 ÷ 3? ($3.28)
  • Provide your students with additional examples of dividing with regrouping, such as $6.75 divided by 5 and $8.48 divided by 6. Include some examples of whole numbers modeled with base-ten blocks.

Wrap-Up and Assessment Hints
Students need a great deal of practice when learning to divide multidigit numbers. Do not be in a rush for students to put away their manipulatives when learning this concept. Assess students based on their understanding of skills that lead up to the division algorithm, such as what to do with a remainder and whether or not regrouping is necessary.

Houghton Mifflin Math Grade 3