Math Background

Lesson: Regrouping to Divide
Introducing the Concept

After students learn the concept of division and the basic division facts, it is time for them to move on to dividing greater numbers. Manipulatives will help students grasp this concept. In this lesson, we'll introduce students to the division of greater numbers with no regrouping.

Materials: play money: ten $1 bills, 10 dimes, and 10 pennies for each student or pair of students, or use 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 understand the concept of division, know the basic division facts, and know how to model amounts of money with $1 bills, dimes, and pennies.

  • Write 96¢ ÷ 3 = n on the board.
    Have a volunteer read the division sentence aloud.
  • Say: Show 96¢ with your play money. Put the rest of the money aside.
    Students should show 9 dimes and 6 pennies.
  • Ask: Into how many equal groups will we divide 96¢? (3)
  • Say: When we divide, we start with the greatest place value. Divide the 9 dimes equally into 3 groups.
  • Ask: How many dimes are in each group? (3)
  • Say: Divide the 6 pennies equally into 3 groups.
  • Ask: How many pennies are in each group? (2)
  • Ask: What is the value of the money in each group? (32¢) What is 96¢ ÷ 3? (32¢) Replace n with 32¢.
  • Write $8.25 ÷ 2 = n on the board.
    Have a volunteer read the division sentence aloud.
  • Say: Show $8.25 with your play money. Put the rest of the money aside. Students should show eight $1 bills, 2 dimes, and 5 pennies.
  • Ask: Into how many equal groups will we divide $8.25? (2)
  • Say: Divide the eight $1 bills equally into 2 groups.
  • Ask: How many $1 bills are in each group? (4)
  • Say: Divide the 2 dimes equally into the 2 groups.
  • Ask: How many dimes are in each group? (1)
  • Say: Divide the 5 pennies equally into the 2 groups. Put any leftover pennies aside.
  • Ask: How many pennies are in each group? (2) How many pennies are left over? (1)
  • Say: The amount left over in division is the remainder.
  • Ask: What is the value of the money in each group? ($4.12) What is the value of the money left over? (1¢) What is $8.25 ÷ 2? ($4.12, remainder 1¢)
  • Provide students with additional examples of dividing money with no regrouping. Start with examples that do not have remainders, such as $8.40 divided by 4, and then move to examples with remainders, such as $6.95 divided by 3.

Houghton Mifflin Math Grade 3