Column Division
Column division connects a manipulative-based approach to paper-andpencil. Making this connection allows students to conceptually understand
the division process as they move to the symbolic level. This process
encourages students to utilize base-10 blocks and language that breaks the
dividend into separate digits. For example, 583 would focus on 5 things,
8 things, and 3 things rather than 583 items. The student breaks each
part into hundreds, tens, and ones, with only one place value being
considered at a time.
Even those students whose basic-facts knowledge and estimation skills
are limited can find correct answers using this approach to division. In
the process, students can move from the concrete to the paper-and-pencil
level once they feel comfortable. This graphic column presentation greatly
reduces error.
Build Understanding
Divide the class into groups of three. Provide each group with base-10 blocks
and direct them to model the number 53 (5 tens, 3 ones). Tell students that the
blocks represent 53 pieces of candy and direct them to divide the pieces equally
among two students. When dividing the 5 longs among 2 students, the groups
should see that they have to exchange one long for ten ones. The groups should
determine that each student would receive 26 pieces of candy with 1 left over.
The sharing of base-10 blocks at each place value is the conceptual basis for
this division algorithm. Explain that it is best to always begin with the largest
base-10 blocks. If they can’t be shared evenly, they should be exchanged for
smaller base-10 blocks, as in the example above.
Using page 71, walk students through an example of the column-division
algorithm.
Error Alert Watch for students who do not trade in one of the longs for
10 ones when dividing 53 into 2 groups. Do another example with these
students to make sure they understand the process of equal grouping.
Check Understanding
1. 151 R2
Give each group 2 or 3 additional problems to solve. Encourage each student
to explain his or her strategy while working so that the small group can
follow along. If many students are confused about a particular aspect of the
algorithm, do another problem as a whole class. When you are reasonably
certain that most of your students understand the algorithm, assign the
“Check Your Understanding” exercises at the bottom of page 71. (See answers
in margin.)
2. 121
3. 76
4. 66 R3
Division
5. 208
Copyright © Wright Group/McGraw-Hill
Page 71
Answer Key
6. 1,975 R1
7. 1,340 R3
8. 537 R11
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Teacher Notes
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Name
Date
Time
Column Division
In the example below, think of sharing $583 among 4 people.
1. Draw lines to separate the digits in the dividend.
Work left to right. Begin in the left column.
2. Think of the 5 in the hundreds column as 5 $100
bills to be shared by 4 people. Each person gets
1 $100 bill. There is 1 $100 bill remaining.
1
4
5
3⎯
8
-4
1
3. Trade the 1 $100 bill for 10 $10 bills. Think of the
8 in the tens column as 8 $10 bills. That makes
10 + 8 = 18 $10 bills in all.
1
4
5
3⎯
8
-4
18
1
4. If 4 people share 18 $10 bills, each person gets
4 $10 bills. There are 2 $10 bills remaining.
5. Trade the 2 $10 bills for 20 $1 bills.Think of the
3 in the ones column as 3 $1 bills. That makes
20 + 3 = 23 $1 bills.
6. If 4 people share 23 $1 bills, each person gets
5 $1 bills.There are 3 $1 bills remaining.
Record the answer as 145 R3.
Each person receives $145 and $3 are left over.
1
4
4
5
3⎯
8
-4
18
1 - 16
2
1
4
4
5
3⎯
8
-4
23
18
1 - 16
2
1
4
5
4
5
8
3⎯
-4
18
23
1 - 16 - 20
2
3
Division
Copyright © Wright Group/McGraw-Hill
4
5
8
3⎯
Check Your Understanding
Solve the following problems.
1. 455 ÷ 3
2. 726 ÷ 6
3. 532 7
4. 267 4
5. 832 4
6. 3,951 ÷ 2
7. 6,703 5
8. 8,603 16
Write your answers on a separate sheet of paper.
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