Transcript Partial Quotients Division

By Jennifer Adams
 The traditional approach (or algorithm) for large number
division is the most abstract and difficult approach to
division. Yet many adults think it is the only approach. Take
a simple problem like 7,248 divided by 3 and try to explain
the traditional method:
 three goes into seven twice, write down the two over the
seven, multiply two times three and write the answer, six,
under the seven, then subtract six from seven. That leaves
1,248. Since three won't go into one you have to move over a
column and divide three into 12...
 You get the idea. Students often have no idea why they do
what they do in this process. They do it because the
teacher said to, if they can do it at all...
 The partial quotient method of solving large division
problems has two main advantages.
1. It allows elementary school students to see the problem
in a less abstract form. They actually ask concrete
questions like "So, how many nines are there in 2,079?"
**Division becomes an idea instead of a long division
template.
2. It allows the students to work the solution flexibly, using
numbers they're comfortable with, instead of requiring a
rigid mathematical process that the student may not find
comfortable. (How that works will become more obvious
as the method is presented.)
 The first step in the partial
quotient approach is to set
up the problem. This looks
much like a traditional
long division problem
except that a vertical line
gets drawn along the right
side of the problem to
create space for the student
to track "partial quotients.”
 We call the division symbol
the “table” and the vertical
line down the side the
“curtain”
6 72
 The question in the mind of the student is
simple: "How many groups of six are there
in 72?"
 The partial quotient method tries to get the
student to the answer through basic logic.
So the next question the student asks is,
"Well, are there at least blank number of
groups of six in 72?" Fill in the blank with a
number the student is comfortable with let's say 5.
 So the question becomes "Well, are there at
least 5 groups of nine in 72?" The student
does the math and figures that 5 groups of
six (5 x 6) is 30. The student writes 5 in the
partial quotient column and writes 30 under
72 in the problem template; then he does
the subtraction to see how much is left.
6 72
30
42
5 (5*6=30)
 With 42 left in his dividend,
the student should ask this
basic question: "Can I take
that many out again?" If the
answer is "yes" (like in this
case), the student should do
that. If the answer is "no," the
student has to find a smaller
easy multiple to take out. In
this case the student writes 5
in the partial quotient
column again and writes 30
under 42 in the problem
template; then he does the
subtraction again to see how
much is left.
6 72
30
42
30
12
5 (5*6=30)
5 (5*6=30)
 With 12 left in his dividend,
the student should ask that
basic, logical question again:
"Can I take that many out one
more time?" If the answer is
"yes," the student should do
that. But in this case the
answer now is "no," so the
student has to find a smaller
easy multiple to take out.
 Most of our students know
their 2 facts, so they should
all be able to see that there
are two 6’s in 12 and repeat
the steps we have been doing.
6 72
30
42
30
12
12
00
5 (5*6=30)
5 (5*6=30)
2 (2*6=12)
 When the student has taken
this process as far as possible
(the dividend left is less than
the divisor) the final step is
easy: add up the partial
quotients to get the whole
quotient. We like to say that
you add up the numbers in
the “curtain.” The student in
this particular case will add
5+5+2 and get 12.
 There are 12 groups of six in
72. Or, phrased more
traditionally, 72 divided by 6
is 12.
6 72
30
42
30
12
12
00
5 (5*6=30)
5 (5*6=30)
2 (2*6=12)
12
 We like to say that you
put the answer on the
“table” because it’s
DONE! Just like you put
the food on the table
when it’s done!
12
6 72
30
42
30
12
12
00
5 (5*6=30)
5 (5*6=30)
2 (2*6=12)
12
 I hope this really helps you understand what your
students are doing in math. We will also send home
the parent packet that goes with this unit. If you have
any questions, feel free to call or send me a note.
 Please know that this is also an introduction to
division. In future years your child may use the
traditional method for division. However, this is a
great way for them to start learning and it’s a great
transition into the traditional method because they
understand why they do what they do in the
traditional process.