1 Don’t Let Division Get You Down! Created by Danielle Miller Hawk Ridge Elementary School.

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

Created by Danielle MillerHawk Ridge Elementary School

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

46 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.

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 – the number by which another number is divided (# of groups)another 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)

dividenddividend

divisordivisor

quotientquotient

46 24

24 is the…24 is the…

6 is the…6 is the…

4 is the…4 is the…

Division MethodsDivision Methods• Draw a Picture

–Circles and Stars• “Old School”

–The Standard Algorithm• “New School”

–Short Hand Division–Partial Quotients

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

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

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4 80DDucks (÷)ucks (÷)

MMay (x) ay (x)

SSwim (-)wim (-)

BBackwards ackwards (bring )(bring )

8-00

0

0-00

““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 8

2

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 8

2

3 x 9 = 2728 - 27 = 1

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42

9R1

Steps in Short DivisionSteps in Short Division

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3 ) 7 4 8

2

Hooray! I did it!

4 9R1

Steps in Short DivisionSteps in Short Division

““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

- 12038

SubtractThere 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 )

13 R2

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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

219 R7

69110 – 3rd guess

- 360 331 9 – 4th

guess - 324

Did you check your work with

Multiplication?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

199 R 15

4027 – 3rd guess- 301

101 2 – 4th

guess - 86

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

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