Partial Quotients
Division
Algorithm
Quick Slate Review
Solve the following problems.
……. Ready………
…………..Set…………..
………Go!
7x3 =
6x5 =
4x5 =
2x8 =
3x9 =
5x10 =
Check your work
7x3 = 21
6x5 = 30
4x5 = 20
2x8 = 16
3x9 = 27
5x10 = 50
Slate Review of
Extended Multiplication Facts
……. Ready………
…………..Set…………..
………Go!
7 x 10 = 70
7 x 100 = 700
7 x 1,000 = 7,000
5 x 10 = 50
5 x 100 = 500
5 x 1,000 = 5,000
Check your
answers!
Let’s Learn the
Partial Quotients Algorithm
for Dividing!
Today we are only going to learn
how to divide a 3 digit number
by a 1 digit number.
Let’s try 244 ÷ 7
We are going to
set it up like this:
7
244
To help us, lets make
a math box of 7’s
multiplication facts!
7x1= 7
7 x 2 = 14
7 x 5 = 35
7 x 10 = 70
7 x 20 = 140
7 x 50 = 350
7 x 100 = 700
We are going to look at our I see a math fact that
entire dividend and our
is close to 244
math box to find a product without going over!
close to our dividend:
7
244
-140 20
104
7x1= 7
7 x 2 = 14
7 x 5 = 35
7 x 10 = 70
7 x 20 = 140
7 x 50 = 350
7 x 100 = 700
Now, we look at our new
dividend of 104 and our
math box to find a product
close to our dividend:
7 244
-140 20
104
-70 10
34
I see a math fact that
is close to 104
without going over!
7x1= 7
7 x 2 = 14
7 x 5 = 35
7 x 10 = 70
7 x 20 = 140
7 x 50 = 350
7 x 100 = 700
Again, we look at our new
dividend of 34 and our
math box to find a product
close to our dividend:
7
244
-140
104
-70
34
-28
6
I see a math fact that is
close to 34 without going
over! However, 14 is quite
a bit smaller so we are
going to double it (7 x 4 =
28).
7x1= 7
20
10
4
7 x 2 = 14
7 x 5 = 35
7 x 10 = 70
7 x 20 = 140
7 x 50 = 350
7 x 100 = 700
Once our dividend is
smaller than our divisor we
stop!
34 r 6
7
244
-140
104
-70
34
-28
6
20
10
4
Now we are
ready to add our
partial quotients
and report our
remainder.
We add all three!
Then report our
quotient with
remainder.
7
244
-140 20
104
7x1= 7
7 x 2 = 14
7 x 5 = 35
7 x 10 = 70
7 x 20 = 140
7 x 50 = 350
7 x 100 = 700
Let’s review our steps:
1. Set up the problem.
2. Make a math box of simple
multiplication facts with the
divisor.
3. Find the math fact with a
product closest to the
dividend without going
over.
4. Write your quotient to
the right of the vertical
line. Then subtract.
Let’s Model Another One!
Set up the problem & make your math box.
5
322
-250 50
75
Find the product closest to the
dividend without going over.
Subtract to find the difference.
5x1= 5
5 x 2 = 10
5 x 5 = 25
5 x 10 = 50
5 x 20 = 100
5 x 50 = 250
5 x 100 = 500
Continue until the dividend is smaller
than
the
divisor!
65 r 0
5
322
-250 50
75
-50
25
-25
0
10
Find the product closest to the
dividend without going over.
Subtract to find the difference.
5
5x1= 5
5 x 2 = 10
5 x 5 = 25
5 x 10 = 50
5 x 20 = 100
5 x 50 = 250
5 x 100 = 500
Try this one using your slate.
Use the blank worksheet to help guide you.
Follow these steps:
1. Set up the problem.
2. Make a math box of simple
multiplication facts with the
divisor.
3. Find the math fact with a
product closest to the
dividend without going over.
4. Write your quotient to the
right of the vertical line. Then
subtract.
4
443
The teacher will be around
to assist you.
Help Button ~>
110 r 3
4 443
-400 100
43
-40 10
3
4x1= 4
4x2= 8
4 x 5 = 20
4 x 10 = 40
4 x 20 = 80
4 x 50 = 200
4 x 100 = 400
Let’s try one more!
Use the blank worksheet to help guide you.
Follow these steps:
1. Set up the problem.
2. Make a math box of simple
multiplication facts with the
divisor.
3. Find the math fact with a
product closest to the
dividend without going over.
4. Write your quotient to the
right of the vertical line. Then
subtract.
8
982
The teacher will be around
to assist you.
Help Button ~>
122 r 6
8 982
-800 100
182
-160 20
22
-16
2
6
8x1= 8
8 x 2 = 16
8 x 5 = 40
8 x 10 = 80
8 x 20 = 160
8 x 50 = 400
8 x 100 = 800
Homework
* You will complete a worksheet
with 6 division problems which
you will use Partial Quotients
to solve.
You did a wonderful job today!
We will practice more with partial
quotients tomorrow by reviewing
first, and then learning how to
divide 3 digit and 4 digit numbers
by a 2 digit number.