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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.

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slide1

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

slide2

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!!!

slide3

8

177

Partial Quotients Division

Start 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

slide4

Ask - How many [8s] are in 177? There are at least 10, so that will be the first partial quotient..

8

177

80

10

Multiply 10 * 8, write the product under the dividend in the problem. Then subtract!

Write on the side

8 x 1 = 8

8 x 10 = 80

8 x 100 = 800

slide5

Subtract 177 minus 80.

Now check, is 97 less than your divisor, 8? If yes, then you have finished dividing. If not…..

8

177

-

80

10

97

8 x 1 = 8

8 x 10 = 80

8 x 100 = 800

slide6

Start the process over again. Ask - how many [8s] are in 97?

Again, there are at least 10.

8

177

-

80

10

97

80

10

8 x 1 = 8

8 x 10 = 80

8 x 100 = 800

slide7

Subtract 97 minus 80.

8

177

-

80

10

Now check, is 17 less than your divisor, 8? If yes, then you have finished dividing. If not…..

97

-

80

10

8 x 1 = 8

8 x 10 = 80

8 x 100 = 800

17

slide8

Start the process again. Ask - how many [8s] are in 17. There are at least 2.

8

177

-

80

10

97

-

80

10

8 x 1 = 8

8 x 10 = 80

8 x 100 = 800

Subtract 17 minus 16.

17

-

16

2

1

slide9

Since the 1 is less than 8, you are finished dividing.

Now add up the partial quotients - 10 plus 10 plus 2.

22 R1

8

177

-

80

10

97

-

80

10

8 x 1 = 8

8 x 10 = 80

8 x 100 = 800

17

-

16

2

Write the answer above with the remainder.

You are finished.

1

22

slide10

8

177

Partial Quotients Division

Start 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!

slide11

Ask - How many [8s] are in 17? There are at least 2, so 2 will be the first partial quotient..

Now, let’s try to same problem using basic multiplication facts!

8

177

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

20

slide12

Start the process over again. Ask - how many [8s] are in 17?

Again, there are at least 2.

8

177

-

160

20

17

16

2

8 x 1 = 8

8 x 10 = 80

8 x 100 = 800

slide13

Subtract 17 minus 16.

8

177

-

160

20

Now check, is 1 less than your divisor, 8? If yes, then you have finished dividing. If not…..keep going.

17

-

16

2

8 x 1 = 8

8 x 10 = 80

8 x 100 = 800

1

slide14

22 R. 1

8

177

-

160

20

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.

17

-

16

2

8 x 1 = 8

8 x 10 = 80

8 x 100 = 800

1

22

slide15

Since the 1 is less than 8, you are finished dividing.

Now add up the partial quotients - 10 plus 10 plus 2.

22 R1

8

177

-

80

10

97

-

80

10

8 x 1 = 8

8 x 10 = 80

8 x 100 = 800

17

-

16

2

Write the answer above with the remainder.

You are finished.

1

22

slide16

Let’s try another one…..

843 ÷ 4

Set up the problem

slide17

4

843

Ask - How many [4s] are in 843? There are at least 100, so that will be the first partial quotient..

Write on the side

4 x 1 = 4

4 x 10 = 40

4 x 100 = 400

slide18

4

843

- 400

100

4 x 1 = 4

4 x 10 = 40

4 x 100 = 400

443

100

- 400

43

Start the process over again. Ask - how many [4s] are in 443?

There are at least 100 more.

slide19

4

843

- 400

100

4 x 1 = 4

4 x 10 = 40

4 x 100 = 400

443

100

- 400

43

10

- 40

3

Start the process over again. Ask - how many [4s] are in 43?

There are at least 10 more.

slide20

4

843

210 r 3

- 400

100

4 x 1 = 4

4 x 10 = 40

4 x 100 = 400

443

100

- 400

43

10

- 40

3

Since the 3 is less than 4, you are finished. Now add up the partial quotients:

100 +100 + 10 = 210.

slide21

4

843

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!!!!

Write on the side

4 x 1 = 4

4 x 10 = 40

4 x 100 = 400

slide22

4

843

- 800

200

4 x 1 = 4

4 x 10 = 40

4 x 100 = 400

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.

slide23

4

843

-800

200

4 x 1 = 4

4 x 10 = 40

4 x 100 = 400

43

10

- 40

3

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.

slide24

4

843

210 r 3

- 800

200

4 x 1 = 4

4 x 10 = 40

4 x 100 = 400

43

10

- 40

3

Since the 3 is less than 4, you are finished. Now add up the partial quotients:

200 + 10 = 210.

slide25

Hangman Division(Partial Quotient)

See, dividing with The Forgiveness Method or

Partial Quotients Method is EASY!!!