The Forgiveness Method & Partial Quotients Division The Partial Quotients Algorithm uses a series of...
25
The Forgiveness Method & Partial Quotients Division • The Partial Quotients Algorithm uses a series of “at least, but less than” estimates of how many b’s in a. Students might begin with multiples of 10 – they’re easiest. This method builds towards traditional long division. It removes difficulties and errors associated with simple structure mistakes of long division. Based on EM resources
-
Upload
thomas-walsh -
Category
Documents
-
view
220 -
download
1
Transcript of The Forgiveness Method & Partial Quotients Division The Partial Quotients Algorithm uses a series of...
The Forgiveness Method &Partial Quotients Division
• The Partial Quotients Algorithm uses a series of “at least, but less than” estimates of how many b’s in a. Students might begin with multiples of 10 – they’re easiest.This method builds towards traditional long division. It removes difficulties and errors associated with simple structure mistakes of long division.
Based on EM resources
Partial Quotients Division
• Easy step by step directions to help with long division…..look at the picture below. What game does it
• remind you of?Answer: HANGMAN!!!
1778Start by setting up the problem like this. It looks just like the traditional long division method, except for the long line that is drawn to the right of the divisor. (Just like in the Hangman Game.)
Discuss benchmark numbers…
X 1
X 10
X 100
Partial Quotients Division
Ask - How many [8s] are in 177? There are at least 10, so that will be the first partial quotient..1778
10
Write on the side
8 x 1 = 8
8 x 10 = 80
8 x 100 = 800
Multiply 10 * 8, write the produce under the dividend in the problem. Then subtract!
80
1778
Subtract 177 minus 80.
Now check, is 97 less than your divisor, 8? If yes, then you have finished dividing. If not…..
10 80 97
-
8 x 1 = 8
8 x 10 = 80
8 x 100 = 800
1778
Start the process over again. Ask - how many [8s] are in 97?
Again, there are at least 10.
10 80 97
-
108 x 1 = 8
8 x 10 = 80
8 x 100 = 800
80
1778
Subtract 97 minus 80.
10 80 97 80
17
-
10-
8 x 1 = 8
8 x 10 = 80
8 x 100 = 800
Now check, is 17 less than your divisor, 8? If yes, then you have finished dividing. If not…..
1778
Start the process again. Ask - how many [8s] are in 17. There are at least 2.
10 80 97 80
17
-
10-
28 x 1 = 8
8 x 10 = 80
8 x 100 = 800
16 1
-Subtract 17 minus 16.
1778
Since the 1 is less than 8, you are finished dividing.
Now add up the partial quotients - 10 plus 10 plus 2.
10 80 97 80
17 16 1
-
10-
2-
22
8 x 1 = 8
8 x 10 = 80
8 x 100 = 800 Write the answer above with the remainder.
You are finished.
22 R1
1778Start by setting up the problem like this. It looks just like the traditional long division method, except for the long line that is drawn to the right of the divisor. (Just like in the Hangman Game.)
Now, let’s try to same problem using basic multiplication facts!
Partial Quotients Division
Ask - How many [8s] are in 17? There are at least 2, so 2 will be the first partial quotient..
177820 Multiply 2 * 8, write the
product under the dividend in the problem.
Now, you will notice that there is an empty space under the last 7 in the dividend. We will place a “0” to occupy the empty space and add a “0” to the 2 in the partial quotient column. Then subtract!
160
Now, let’s try to same problem using basic multiplication facts!
1778
Start the process over again. Ask - how many [8s] are in 17?
Again, there are at least 2.
17
-
28 x 1 = 8
8 x 10 = 80
8 x 100 = 800
16
20 160
1778
Subtract 17 minus 16.
20160 17
1
-
-
8 x 1 = 8
8 x 10 = 80
8 x 100 = 800
Now check, is 1 less than your divisor, 8? If yes, then you have finished dividing. If not…..keep going.
2 16
1778
20160 17
1
-
-
8 x 1 = 8
8 x 10 = 80
8 x 100 = 800
1 is less than your divisor, 8, so you are finished dividing.
Now, add up the partial quotients, 20 and 2 and write their sum with the remainder at the top of the problem.
2 16
22
22 R. 1
1778
Since the 1 is less than 8, you are finished dividing.
Now add up the partial quotients - 10 plus 10 plus 2.
10 80 97 80
17 16 1
-
10-
2-
22
8 x 1 = 8
8 x 10 = 80
8 x 100 = 800 Write the answer above with the remainder.
You are finished.
22 R1
Let’s try another one…..
843 ÷ 4
Set up the problem
8434
Write on the side
4 x 1 = 4
4 x 10 = 40
4 x 100 = 400
Ask - How many [4s] are in 843? There are at least 100, so that will be the first partial quotient..
8434
4 x 1 = 4
4 x 10 = 40
4 x 100 = 400
100- 400
443
Start the process over again. Ask - how many [4s] are in 443?
There are at least 100 more.
100- 400
43
8434
4 x 1 = 4
4 x 10 = 40
4 x 100 = 400
100- 400
443
Start the process over again. Ask - how many [4s] are in 43?
There are at least 10 more.
100- 400
4310- 40
3
8434
4 x 1 = 4
4 x 10 = 40
4 x 100 = 400
100- 400
443100- 400
4310- 40
3Since the 3 is less than 4, you are finished. Now add up the partial quotients:
100 +100 + 10 = 210.
210 r 3
8434
Write on the side
4 x 1 = 4
4 x 10 = 40
4 x 100 = 400
First, underline the 8 in the dividend. Then ask yourself- How many [4s] are in 8? There are at least 2. Now, for the empty spaces under the 43, add a 0 in the empty spaces in both the problem and the partial quotients comlumn. So 200 will be the first partial quotient..
Let’s look at solving the same problem in a different way!!!!
8434
4 x 1 = 4
4 x 10 = 40
4 x 100 = 400
200- 800
43
Now ask yourself, is 43 less than 4? If not, start the process over again. Ask - how many [4s] are in 40?
There are at least 10 more.
8434
4 x 1 = 4
4 x 10 = 40
4 x 100 = 400
200-800
43
Start the process over again. Ask - how many [4s] are in 43?
There are at least 10 more.
Is 3 less than 4? If so, then you are done dividing.
10 - 40
3
8434
4 x 1 = 4
4 x 10 = 40
4 x 100 = 400
200- 800
4310 - 40
3
Since the 3 is less than 4, you are finished. Now add up the partial quotients:
200 + 10 = 210.
210 r 3
Hangman Division(Partial Quotient)
See, dividing with The Forgiveness Method or Partial Quotients Method is EASY!!!
