Math Background

Lesson: Division
Introducing the Concept

As with addition, subtraction, and multiplication, students progress in division by learning algorithms that allow them to perform operations beyond basic facts. After students learn the basic division facts and the concept of division, it is time to introduce algorithms that will allow them to divide larger numbers. It is important to show students that there is a need to learn how to use algorithms to divide larger numbers.

Materials: overhead base-ten blocks, overhead projector, base-ten blocks for students

Preparation: Be sure to provide at least one set of base-ten blocks for each pair of students.

Prerequisite Skills and Concepts: Students should know the basic division facts and be at least familiar with base-ten blocks. Introduce students to the vocabulary dividend, divisor, and quotient prior to the lesson.

  • Ask: What does 54 represent in 54 ÷ 9?
    In the expression 54 ÷ 9, you have 54 items and are dividing the items into 9 groups, so you need to find how many items will be in each group. The 54 represents the total number of items you begin with.
  • Ask: What does 9 represent in 54 ÷ 9?
    In 54 ÷ 9, the 9 represents the number of groups you will be dividing 54 by.
  • Ask: What is the answer to 54 ÷ 9?
    The answer is 6.
  • Ask: What does 6 represent for 54 ÷ 9?
    It is the quotient, but more importantly, the 6 represents the number of items in each group when you divide the 54 items into 9 groups.
  • Say: Another way to write 54 ÷ 9 is division problem. The number 54 represents the total number of items you begin with, and 9 is the number of groups you want to make. The quotient, 6, or number of items in each group, is written above the 54. Write
    division problem
  • Ask: What does 68 represent in 68 ÷ 4?
    In 68 ÷ 4, you have 68 items divided into 4 groups. You need to find how many items you will have in each group. The 68 represents the total number of items you begin with.
  • Ask: What does 4 represent in 68 ÷ 4?
    The 4 represents the number of groups you will be dividing 68 by.
  • Ask: What is the answer to 68 ÷ 4?
    Since this is not a basic division fact, it is unlikely that students will be able to find an answer quickly. This will allow you to show the need for learning an algorithm to divide multidigit numbers that are not basic division facts.
  • Ask: If we want to write 68 ÷ 4 the same way we wrote  division problem, what number would go where 54 is and what number would replace 9?
    68 would go in place of 54, and 4 in place of 9.
  • Say: When we are dividing numbers too large for us to immediately know the answer, it is best to do the problem in several steps.
  • Say: When doing division problem, we can think of 68 as 6 tens 8 ones.
  • Place 6 tens 8 ones on the overhead using base-ten blocks.
    base-ten blocks
  • Ask: How can you divide the 6 tens into 4 equal groups?
    You can put 1 ten in each group. You have 2 tens left.
  • Say: Since you can put only one ten in each group, you write a 1 over the tens place in 68.
    division problem
  • Say: Since you cannot put another ten in each group, you will need to regroup the remaining 2 tens as 20 ones.
  • Show the regrouping on the overhead. Next, combine the 20 ones with the 8 ones.
    base-ten blocks
  • Ask: If we combine the 20 ones with the 8 ones, how many ones will we have?
    28 ones.
  • Ask: How can you divide 28 ones into 4 equal groups?
    We can make 4 groups with 7 ones in each group.
    base-ten blocks
  • Say: Since 4 groups of 7 ones can be made, we write 7 above the ones place in 68. Write
    division problem
  • Say: Since there are no ones remaining, our answer, or quotient, is 17. If we make 4 groups with 17 items in each group, we should have a total of 68 items. You and your partner need to make 4 groups with 17 items in each group. After you have done this, count the total number of items to see if there are 68.
  • Continue this activity, using slightly larger numbers. Have students use their base-ten blocks to determine the place value for the quotient. Then have them use their base-ten blocks to check the answers.

Houghton Mifflin Math Grade 4