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Don’t Let DivisionDon’t Let DivisionGet YouGet YouDown!Down!

Created by Danielle MillerHawk Ridge Elementary School

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What is division?What is division?• An operation that tells how many groups there are

and how many are in each group

• Repeated subtraction

• The inverse of multiplication

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What Does Division What Does Division Look Like?Look Like?

24 ÷ 6 = 4

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6 24

24

6= 4

A division problem can be written horizontally.

A division problem can be written as a fraction.

A division problem can be written with the traditional division sign.

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Division VocabularyDivision Vocabulary2424 ÷ 66 = 44

dividenddividend – the number being divided – the number being divided

(total number of items)(total number of items)

divisor divisor – the number by which another – the number by which another

number is divided (# of groups)number is divided (# of groups)

quotientquotient-- the answer to a division the answer to a division

problem (# of items in problem (# of items in eacheach group) group)

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dividenddividend

divisordivisor

quotientquotient

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6 24

24 is the…24 is the…

6 is the…6 is the…

4 is the…4 is the…

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Division MethodsDivision Methods• Draw a Picture

–Circles and Stars

• “Old School”–The Standard Algorithm

• “New School”–Short Hand Division

–Partial Quotients

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Circles and StarsCircles and Stars• Read the problem• Identify the divisor (the

number of groups) and draw that many circles

• Identify the dividend and begin distributing out that number of stars.

• Count the number of stars in one circle. This is your quotient.

1818 ÷÷ 33 == ??

66

1818 ÷÷ 33 == 66

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““Old School” DivisionOld School” DivisionThe Standard AlgorithmThe Standard Algorithm

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4 80DDucks (ucks (÷)÷)

MMay (x) ay (x)

SSwim (-)wim (-)

BBackwards (bring )ackwards (bring )

8-00

0

0-00

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““New School” DivisionNew School” DivisionShort Hand DivisionShort Hand Division

• Short division is similar to long division only you do the multiplication and subtraction in your head.

• Knowing your basic facts is a must!

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Steps in Short DivisionSteps in Short Division

3 ) 7 4 82

3 x 2 = 6

7 - 6 = 1

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•Divide into the number.

•Place answer above # divided

into

•Multiply this answer & divisor

together in your head.

•Subtract product from 7.

•Put your answer, 1, in front of

the 4 in the dividend.

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• Divide 3 into 14.

• Place answer above #

divided into.

• Multiply the new number &

divisor together in your

head.

• Subtract product from 14.

• Put your answer, 2, in front

of the 8 in the dividend.

3 ) 7 4 82

3 x 4 = 1214 - 12 = 2

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42

Steps in Short DivisionSteps in Short Division

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• Divide 3 into 28.

• Place answer above #

divided into.

• Multiply that answer and

divisor together in your

head.• Subtract product from 28.• Put your answer, 1, as the

remainder.

3 ) 7 4 82

3 x 9 = 2728 - 27 = 1

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42

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Steps in Short DivisionSteps in Short Division

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3 ) 7 4 8

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Hooray! I did it!

4 9 R1

Steps in Short DivisionSteps in Short Division

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““New School” DivisionNew School” DivisionPartial Quotients AlgorithmPartial Quotients Algorithm

The Partial Quotients Algorithm

uses a series of

“at least, but less than”

estimates of how many times the

dividend can be divided by the

divisor.

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12 158

There are at least ten 12’s in 158 (10 x 12=120), but fewer than twenty. (20 x 12 = 240) 10 1st

guess- 120

38Subtract

There are more than three 12’s (3 x 12 = 36), but fewer than four (4 x 12 = 48). Record 3 as the next guess

3 2ndguess

- 36

2 13

Sum of guesses

Subtract

Since 2 is less than 12, you can stop estimating. The final result is the sum of the guesses (10 + 3 = 13) plus what is left over (remainder of 2 )

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Let’s try another one…Let’s try another one…

36 7,891100 – 1st guess

- 3,6004,291

Subtract

100 – 2nd guess

- 3,600

7 219 R7

Sum of guesses

Subtract

69110 – 3rd guess

- 360 331

9 – 4th guess

- 324Did you check your

work withMultiplication?

219 x 36 = 7,884 + 7 = 7,891

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Now do this one on your Now do this one on your own…own…

43 8,572100 – 1st guess

- 4,3004272

Subtract

90 – 2nd guess

-3870

15199 R 15

Sum of guesses

Subtract

4027 – 3rd guess- 301

1012 – 4th guess

- 86

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Choose the Method That Choose the Method That Works For You!Works For You!

• Read the problem that you have to solve carefully and choose the best method for the problem!

• Select the method of division that you are most comfortable with to help you.

• Don’t forget to always check you work with multiplication.

• If you have access to a calculator – use it – that’s what it is there for!

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Don’t forget…Don’t forget…• There is no substitution for lacking There is no substitution for lacking

fluency with your math facts!fluency with your math facts!

• To use any of these strategies – To use any of these strategies – you need to have memorized your you need to have memorized your basic addition, subtraction, basic addition, subtraction, multiplication and division facts.multiplication and division facts.

• Quick recall is required for Quick recall is required for success in math!success in math!

• Keep studying! Keep practicing!Keep studying! Keep practicing!