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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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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!