Alternate Division Algorithms
SCMP September 2008
Partial-Quotients Method
Study the algorithm below and answer the following questions:
1. How does it work?
2. How does this method support student’s conceptual
understanding of division?
3. How can the teacher support students using this algorithm?
4. What difficulties might students have with this method?
16 1220 50
!800
420
20
!320
100
5
!80
20
1
!16
4
76
The answer is 76 R 4
Solve the following division problems using the Partial-Quotients
Method.
156 ÷ 12
264 ÷ 24
Page 1 of 4
1476 ÷ 123
Alternate Division Algorithms
SCMP September 2008
Array Division
Study the algorithms below and answer the following questions:
1. How do they work?
2. How do these methods support student’s conceptual
understanding of division?
3. How can the teacher support students using these
algorithms?
4. What difficulties might students have with these methods?
5. Compare the two different versions and discuss the pros
and cons of each.
Base-Ten Block
350 ÷ 14
Generic Rectangle
350 ÷ 14
20
100
100
50
10
+
5
200
50
80
20
+
4
40
40
20
25
25
Solve the following multiplication problems using one of the Array
methods.
156 ÷ 12
264 ÷ 24
Page 2 of 4
1476 ÷ 123
Alternate Division Algorithms
SCMP September 2008
Scaffolding Method
Study the algorithm below and answer the following questions:
1. How does it work?
2. How does this method support student’s conceptual
understanding of division?
3. How can the teacher support students using this algorithm?
4. What difficulties might students have with this method?
6
20
100
600
6 4356
The answer is 726
!3600
756
!600
156
!120
36
!36
0
Solve the following division problems using the Scaffolding method.
156 ÷ 12
264 ÷ 24
Page 3 of 4
1476 ÷ 123
Alternate Division Algorithms
SCMP September 2008
Column Division
Study the algorithm below and answer the following questions:
1. How does it work?
2. How does this method support student’s conceptual
understanding of multiplication?
3. How can the teacher support students using this algorithm?
4. What difficulties might students have with this method?
017 4
The answer is 174 R 2
7 12 2 0
0
1
12
!7
5
52
!49
3
30
!28
2
Solve the following division problems using Column Division.
156 ÷ 12
264 ÷ 24
Page 4 of 4
1476 ÷ 123