DIVISION
÷
HANDBOOK
Desert Willow Family School
Division: Level 1.1 –
Problem
12 276
Build It
Build and Write Answer with No Remainders
Teacher’s Questions
1. What does this mean?
Student’s Answer
1. (Listen to the student’s
answers. They should come
to the conclusion of how
many groups of 12 are
contained in 276.
2. Do you want to start by building 2. I want to start with 276
groups of 12 until you get to 276 or blocks and break them up
do you want to gather 276 blocks into groups of 12.
and break 276 into groups of 12?
3. Get your 276 blocks and move
3. (Student should gather 2
all the other blocks out of the way. hundred blocks, 7 ten
sticks and 6 unit cubes.)
4. Can you build any groups of 12?
4. Yes (most students will
be familiar with building
“groups of” because of
multiplication)
5. Can we make more groups of 12? 5. Yes. (Building a division
(Guide student to use a hundred
problem with the blocks is
block and 2 ten sticks to make a
built groups-of over and
group of ten 12’s)
the answer down because it
is the inverse of multip.)
6. Can you lay your pencil on one
group of 12?
6. (Student should be able
to identify the groups of 12
by laying their pencil on
each row of 12 and counting
down to find out how many
groups of 12 were created.
23
12 276
7. How many 12’s are contained in
7. Twenty three
276? That is your answer….23
8. Can you lay your pencil on the 12 8. (Student should lay pencil
groups of 23?
to count out the 23 groups.)
Division: Level 1.2 –
Problem
11 168
Build It
Build and Write Answer With Remainders
Teacher’s Questions
1. What does this mean?
Student’s Answer
1. (Listen to the student’s
answers. They should come
to the conclusion of how
many groups of 11 are contained in 168.
2. Do you want to start by building 2. I want to start with 168
groups of 11 until you get to 168 or blocks and break them up
do you want to get 168 blocks and into groups of 11.
break 168 into groups of 11?
3. Get your 168 blocks and move
3. (Student should gather 1
all the other blocks out of the way. hundred block, 6 ten sticks
and 8 unit cubes.)
4. Can you build any groups of 11?
4. Yes (students should be
familiar with building
“groups of” from multip.)
5. Can we make more groups of 11? 5. Yes.
(Guide student to use hundred
block and one ten stick to make a
group of ten 11’s)
15 r 3
168
6. Can you lay your pencil on one
group of 11?
6. (Student should be able
to identify the groups of 11
by laying their pencil on
each row of 11 and counting
down to find out how many
groups of 11 were created.
7. How many 11’s are contained in
7. Fifteen
168? That is your answer.
11
8. How many blocks are remaining? 8. Three
9. Can you build anymore groups of 9. No.
11? That is the remainder.
Division: Level 2 – Connect the Blocks to the Long Method Algorithm
Problem
Build It
Teacher’s Questions
Student’s Answer
1. If there is an answer in the hun-
13 168
1300
dreds place, you would be building
1300’s, so we ask…..Could you build
100 groups of 13 which is…..?
1. 1300
x
13 168
1300
2. Are there any groups of 1300
in 168?
….so we place an X in the 100’s
place value.
1300
130
3. If there is an answer in the tens
x
13 168
4. Can you build a 10-group of 13
with 168 blocks?
x1
13 168
1300
130
x1
13
168
-130
38
x1
168
- 130
38
place, you would be building
130’s, so we ask….Could we build
10 groups of 13, which is……?
2. No. We don’t have
enough blocks.
3. 130
4. Yes, you can build
one. (Student uses
blocks to build
10 x 13.)
5. We have used 130 blocks to
1300
130
build our 10-group, so do we have
them to build with anymore?.....
5. No
so we have to subtract them away.
6. Now how many blocks do we have
to build with now?
6. 38
1300
130
13
7.If there is an answer in the ones
place, you would be building 13’s, so
we ask…Could we build any 1 groups
of 13, which is…..?
7. 13
8. How many 1-group of 13’s can
you build?
8. Two
Division: Level 2 – Connect the Blocks to the Long Method Algorithm
(……Continued)
Problem
Build It
Teacher’s Questions
9. Do we have these blocks to
use to build with anymore?
Student’s Answer
9. No
x 12
13 168
-130
38
1300
130
13
10.What should we do to show that
we don’t have them to build with
anymore?
10. Subtract them
away.
- 26
12
11. Now how many blocks are left
to build with?
x1 2
13 168
-130
38
- 26
12
1300
130
13
11. Twelve
12. Can we make any more groups of
13?
12. No….that is the
remainder.
Division: Level 3 – Practicing the Long Method Algorithm WITHOUT Blocks
into the THOUSANDS
Problem
Teacher’s Questions
Student’s Answer
1. If I built a 1000 group of 25, it would be
25 4,234
25,000
25 with how many zeros?
1. Three
which is…..?
2. Do you have any groups of 25,000 in the
number 4,234?
x
25 4,234
…..25,000
2. No.
3. How should we show that on the problem? 3. Place an X over the
25,000
x
thousands place value.
4. Now where do we go in the problem?
4. The next place value
over….the hundreds.
5. What is our next group of 25 to build?
5. 2500
6. Do you have any groups of 2500 in 4234?
6. Yes, 1 group of 2500...
25 4,234
x
25 4,234
25,000
2,500
7. How should we show we have created this
x1
25 4,234
- 2,500
1,734
25,000
2,500
group and don’t have this amount to build
with anymore?
8. Now where do we go in the problem?
7. Subtract 2500 from 4,234
8. To the next place
value…..the tens place.
x 1
25 4,234
- 2,500
1,734
25,000
2,500
9. What is our next group of 25 to build? 9. 10 x 25 = 250
10. Do we have any groups of 250 in our
remaining 1,734?
x16
25 4,234
- 2,500
1,734
25,000
2,500
250
10. Yes, six…..
250 x 6 = 1,500
11. What must we do to show that we have
created these groups of 250 and don’t have
this amount to build with anymore?
11. Subtract 1,500 from
1,734
- 1,500
234
Division: Level 3 – Practicing the Long Method Algorithm WITHOUT Blocks
into the THOUSANDS (continued)
Problem
Teacher’s Questions
Student’s Answer
x16
25 4,234
- 2,500
1,734
- 1,500
234
25,000
2,500
250
25
12. Now where do we go in the problem?
12. To the ones place value
13. What is our next group of 25 to build?
13. 1 x 25 = 25
14. Do we have any groups of 25 in our remaining 234?
14. Yes, 9 x 25 = 225
15. What must we do to show that we have
created these 9 groups of 25 and don’t
have them to build with anymore?
234
x 169
25 4,234
- 2,500
25,000
1,734
2,500
250
- 1,500
25
234
- 225
9
15. Subtract 225 from
16. Can we build any more groups of 25?
16. No, so the remainder
is nine.
Division: Level 4 – Practicing the Long Method Algorithm WITHOUT Blocks
into the TEN THOUSANDS
Problem
Teacher’s Questions
Student’s Answer
1. If I built a 10,000 group of 25, it would be
25 58,147
250,000
25 with how many zeros?
1. Four
which is…..?
2. Do you have any groups of 250,000 in the
number 58,147?
x
25 58,147
…..250,000
2. No.
3. How should we show that on the problem? 3. Place an X over the ten
250,000
x
thousands place value.
4. Now where do we go in the problem?
4. The next place value
over….the thousands.
5. What is our next group of 25 to build?
5. 25,000
6. Do you have any groups of 25,000 in
6. Yes, 2 groups of 25,000
25 58,147
x
25 58,147
250,000
25,000
because 2x25,000= 50,000
7. How should we show we have created these
x2
25 58,147
- 50,000
8,147
58,147?
250,000
25,000
groups and don’t have this amount to build
with anymore?
7. Subtract 50,000 from
58,147
8. Now where do we go in the problem?
8. To the next place value…
the hundreds place.
250,000
25,000
9. What is our next group of 25 to build?
9. 100 x 25 = 2500
2,500
10. Do we have any groups of 2500 in our
remaining 8,147?
x 2
25 58,147
- 50,000
8,147
x23
25 58,147
- 5 0,000
250,000 11. What must we do to show that we have
25,000 created these groups of 2500 and don’t have
10. Yes, three…..
2500 x 3 = 7,500
11. Subtract 7,500 from
8,147
- 7,500
647
2,500
this amount to build with anymore?
8,147
Division: Level 4 – Practicing the Long Method Algorithm WITHOUT Blocks
into the TEN THOUSANDS
Problem
(continued)
Teacher’s Questions
Student’s Answer
250,000 12. Now where do we go in the problem?
25,000
2,500 13. What is our next group of 25 to build?
12. To the tens place value
x23
25 58,147
-
50,000
8,147
- 7,500
647
250
14. Do we have any groups of 250 in our remaining 647?
13. 10 x 25 = 250
14. Yes, 2 x 250 = 500
15. What must we do to show that we have
created these 2 groups of 250 and don’t
have them to build with anymore?
15. Subtract 500 from
647
x 2 32
25 58,147
- 50,000
8,147
- 7,500
647
- 500
147
- 125
22
250,000
25,000
2,500
250
25
16. Now where do we go in the problem?
16. To the ones place value
17. What is our next group of 25 to build?
17. 1 x 25 = 25
18. Do we have any groups of 25 in 147?
18. Yes, five…5 x 25 = 125
19. What must we do to show that we have
created these 5 groups of 25 and don’t
19. Subtract 125 from 147
have them to build with anymore?
20. Can we build any more groups of 25?
20. No, so our remainder is
22
Division: Level 5 – Practicing the Long Method Algorithm WITHOUT Blocks
with ZEROS in the DIVIDEND
Problem
Teacher’s Questions
Student’s Answer
1. If I built a 10,000 group of 25, it would be
25 50,102
250,000
25 with how many zeros?
1. Four
which is…..?
2. Do you have any groups of 250,000 in the
number 50,102?
x
25 50,102
…..250,000
2. No.
3. How should we show that on the problem? 3. Place an X over the ten
250,000
x
thousands place value.
4. Now where do we go in the problem?
4. The next place value
….the thousands.
5. What is our next group of 25 to build?
5. 25,000
6. Do you have any groups of 25,000 in
6. Yes, 2 groups of 25,000
25 50,102
x
25 50,102
250,000
25,000
250,000
25,000
- 50,000
102
25 50,102
- 50,000
with anymore?
8. Now where do we go in the problem?
250,000
25,000
2500
250
x 20
groups and don’t have this amount to build
7. Subtract 50,000 from
50,102
x2
25 50,102
….. 2x25,000= 50,000
7. How should we show we have created these
x2
25 50,102
- 50,000
102
50,102?
8. To the next place value…
the hundreds place.
9. What is our next group of 25 to build?
9. 100 x 25 = 2500
10. Do we have any groups of 2500 in our
remaining 102?
10. No
11. So how do we show on our problem that
we can make ZERO groups?
11. By putting a zero
250,000
25,000 12. Do we have anything to subtract off?
12. No
102
2,500
Division: Level 5 – Practicing the Long Method Algorithm WITHOUT Blocks
with ZEROS in the DIVIDEND
Problem
(continued)
Teacher’s Questions
Student’s Answer
250,000 12. Now where do we go in the problem?
25,000
2,500 13. What is our next group of 25 to build?
12. To the tens place value
x20
25 50,102
-
50,000
102
250
14. Do we have any groups of 250 in our remaining 102?
13. 10 x 25 = 250
14. No
15. What must we do to show that we can
create ZERO groups of 250?
15. Place a zero again.
16. Now where do we go in the problem?
16. To the ones place value
17. What is our next group of 25 to build?
17. 1 x 25 = 25
x 2 00
25 50,102
- 50,000
102
250,000
25,000
2,500
250
25
x 2 004
25 50,102
- 50,000
102
- 100
2
250,000
25,000
2,500
18. Do we have any groups of 25 in 102?
18. Yes, four…4 x 25 = 100
19. What must we do to show that we have
created these 4 groups of 25 and don’t
have them to build with anymore?
19. Subtract 100 from 102
20. Can we build any more groups of 25?
20. No, our remainder is 2
Division: Level 6 – Side
by Side Method to Move Students from
Long Method to Short Method
Long Method Algorithm
Short Method Algorithm
25 8,422
25 8,422
Teacher: Can you build a 1,000-group of 25?
1000 x 25 = 25,000
Teacher: Does 25 go into 8?
Student: No
Teacher: What are you dividing at this step?
Student: 25,000 into 8,000
Teacher: What are you doing on the right?
Student: 25 into 8
Teacher: Let’s place our x and move on….
x
25 8,422
Teacher: Can you build a 100-group of 25?
100 x 25 = 2500
Student: Yes….three times…. 3 x 2500 = 7500
x 3
25 8,422
- 7,5 00
922
25
x
8,422
Teacher: Does 25 go into 84?
Student: Yes, three times…. 3 x 25 = 75
x3
25 8,422
-75
9
Teacher: Can you build a 10-group of 25?
10 x 25 = 250
x3
25 8,422
- 7,5 00
922
Teacher: Bring down the 2
Student: Yes….three times… 3 x 250 = 750
Teacher: Does 25 go into 92?
Student: Yes, three times… 3 x 25 = 75
x33
25 8,422
-75
25
x 33
8,422
- 7,5 00
x 3
25
8,422
-75
92
922
- 750
1 72
Division: Level 6 – Side
92
- 75
17
by Side Method to Move Students from
Long Method to Short Method …..(continued)
Long Method Algorithm
Teacher: Can you build a 10-group of 25?
10 x 25 = 250
x 33
25 8,422
- 7,5 00
922
- 750
1 72
Short Method Algorithm
Teacher: Now you bring down the 2….
x33
25 8,422
-75
92
- 75
17 2
(Notice how both problems now mirror each other when you get to the ones place value.)
Student: Yes….seven times… 7 x 25 = 150
25
x337
8,422
- 7,5 00
922
- 750
1 72
- 1 5 0
22
Student: The final answer is 337 with a remainder
of 22.
Teacher: Does 25 go into 172?
Student: Yes, seven times… 7 x 25 = 150
x33
25 8,422
-75
92
- 75
17 2
- 1 5 0
2 2
Division: Level 7 – Practicing the Short Cut Algorithm
Problem
25
2,605
Teacher’s Questions
Student’s Answer
1. Does 25 go into 2?
1. No
2. What do you do?
2. Put an X
3. Does 25 go into 26?
3. Yes, once….1x25 =25
4. How do we show that in the
problem?
4. Place a 1 over the hundreds
place value and subtract off
25. Now bring down the 0.
5. Does 25 go into 10?
5. No, so I put a zero over the
x
25
2,605
x
25
2,605
x 1
25 2,605
- 25
10
25
x10
2,605
- 25
down the 5.
1 05
25
x104
2,605
6. Does 25 go into 105?
6. Yes, 4x25 = 100.
7. How do we show that in the problem?
7. Place a 4 over the ones place
value and subtract off 100.
- 25
1 05
- 1 0 0
5
tens place value and bring
8. What is the answer?
8. I can make 104 groups of 25 with
a remainder of 5.
Division: Level 8 – The Super Short Cut Algorithm
(when Dividing with a Single-Digit Divisor)
Problem
Teacher’s Questions
4 5936137
1
Student’s Answer
1. Does 4 go into 5?
1. Yes, 1 time with 1 left over.
2. Carry the left over 1 in front of
4 51936137
14
the 9 to make it 19.
3. Does 4 go into 19?
3. Yes, 4 times with 3 left over.
4 519336137
4. Carry the left over 3 in front of
the next number which is the 3.
5. Does 4 go into 33?
5. Yes, 8 times with 1 left over.
1 4 8
4 5193316137
6. Carry the left over 1 in front of
the next number, which is the 6.
7. Does 4 go into 16?
1 4 8 4 0
4 5193316137
4
1 4 8 403
5193316137
1 4 8
4
8.Since there is nothing to carry over,
just ask “Does 4 go into 1?”
9. Now we didn’t use that 1, so we
ask “How many 4’s are in 13?”
8. No, so we put a zero on top.
9. Three because 3x4 = 12
with 1 remaining, so we put
the remainder next to the 7.
403
519331613 17
7. Yes, 4 times with 0 left over.
10. Does 4 go into 17?
10. Yes, 4 times with 1 left over.
4
1 4 8
4 0 3 4 r1
The answer is 1,484,034 r1.
519331613 17
Division: Level 8 – Types of Division Word Problems
Type of Problem
Sample Word Problem
Contained In
Suzie has 200 yards of fabric to make quilts. Each quilt requires
25 yards of fabric to complete. How many quilts will she be able to
make?
Holds
How many nets will the soccer coach need to purchase, if the team
owns 24 soccer balls, and each net can hold 6 balls?
Remainder Matters
If the soccer coach want to carry all of the soccer balls in nets, how
many nets will the soccer coach need to purchase, if the team
owns 26 soccer balls, and each net can hold 6 balls?
Average
For the last three dictations, Sam has scored the following
scores: 70, 70, 90, 50. What is Sam’s average score?
Rate (per)
Between the years 2003 and 2008, 90 students have graduated from
Desert Willow. What is the average yearly rate of graduation?
What is the dollar per mile amount, if a truck driver drives 100 miles
for a fee of $1000.
Division: Level 9 – Timed Tests for Division Facts
Type of Problem
Sample Fact Problem (60 problems in 3 minutes)
Exact
12 ÷ 4 = _____
Student produces exact answer: 3
Non-Exact Fact
13 ÷ 4 = _____
Student produces closest answer: 3
Non-Exact Fact with a
13 ÷ 4 = _____
Student produces answer with the
remainder: 3 r 1
remainder