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Long Division. Long Division & MathLine. ____ 4)259. Second Problem:. Long Division. For traditional Long Division, teach the algorithm: 1) Divide or D 2) Multiply or M 3) Subtract or S 4) Check or 5) Bring Down or BD. Long Division. Divide = D Multiply = M - PowerPoint PPT Presentation
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Long Division Long Division &&
MathLineMathLine
Long Division
____ ____ 4)2594)259
Second Problem:Second Problem:
For traditional Long Division,For traditional Long Division, teach the algorithm:teach the algorithm:
1) Divide or D1) Divide or D2) Multiply or M2) Multiply or M3) Subtract or S3) Subtract or S4) Check or 4) Check or 5) Bring Down or 5) Bring Down or
BDBD
Long Division
Take the problemTake the problem
Long Division
____ ____ 4)2594)259
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
________ 44))225959
4 into 2?4 into 2?
Long Division
________ 44))225959
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
Put 2 rings to lefPut 2 rings to leftt
Long Division
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
4 into 2? No4 into 2? No
Long Division
________ 44))225959
4 into 25? 4 into 25?
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
________ 44))252599
Long Division
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
Put 25 rings on MathLinePut 25 rings on MathLine ________ 44))252599
Long Division
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
For long division on MathLine For long division on MathLine
ALWAYSALWAYS start dividing from thestart dividing from the leftleft
Long Division
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
________ 44))252599
4 4 intointo 25? 25? Yes, how many times?Yes, how many times?One One GroupGroup of 4 of 4
Long Division
2211 4433
1
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
________ 44))252599
Two Groups of 4Two Groups of 4
Long Division
21
2211 4433
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
________ 44))252599
Three Groups of 4Three Groups of 4
Long Division
21
2211 4433
3
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
________ 44))252599
Four Groups of 4Four Groups of 4
Long Division
3 41 2
2211 4433
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
________ 44))252599
Five Groups of 4Five Groups of 4
Long Division
4 51 2 3
2211 4433
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
________ 44))252599
Six Groups of 4Six Groups of 4
Long Division
6
2211 4433
4 51 2 3
________ 4)2594)259
Put a 6 above the 5 of 259Put a 6 above the 5 of 259
6 6
Long Division 1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
________ 44)259)259
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
Now multiply 6 X 4Now multiply 6 X 4
6 6
Long Division
Make sureMake sure the students the students do notdo not
multiply the remainder multiply the remainder back in!back in!
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
Long Division
Only multiply 6 X 4, Only multiply 6 X 4, or 6 groups of 4or 6 groups of 4
____ ____ 4)2594)259
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
6 6
Multiply 6 x 4Multiply 6 x 4
Long Division
____ ____ 4)2594)259
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
6 6
Multiply 6 x 4Multiply 6 x 4
Long Division
________ 44)259)259
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
6 6
Long Division
Multiply 6 x 4Multiply 6 x 4
6 Groups of 4
________ 44)259)259
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
6 6
Long Division
Multiply 6 x 4Multiply 6 x 4
6 Groups of 4
________ 44)259)259
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
6 6
Long Division
Multiply 6 x 4Multiply 6 x 4
6 Groups of 4
________ 44)259)259
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
6 6
Long Division
Multiply 6 x 4Multiply 6 x 4
6 Groups of 4
____ ____ 44)259)259
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
6 6
Long Division
Multiply 6 x 4Multiply 6 x 4
6 Groups of 4
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
See 6 x 4 on MathLineSee 6 x 4 on MathLine
_ ____ ___ 44)259)259
66
Long Division
We multiply 6 x 4 We multiply 6 x 4 and get 24, and get 24, so we put so we put
the 24 below 25 the 24 below 25
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
_ ____ ___ 4)2594)259
66
Long Division
2424
Subtract 24 from 25, Subtract 24 from 25, to get a difference of 1 to get a difference of 1
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
_ ____ ___ 4)4)252599 --2424
66
Long Division
11
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
Remainder of 1, ‘s Remainder of 1, ‘s out on MathLineout on MathLine
Long Division
_ ____ ___ 4)2594)259 --2424
66
11
Bring downBring down the 9the 9
to get 19to get 19
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
_ ____ ___ 4)2594)259 --2424
66
11
Long Division
99
Put 19 on MathLine Put 19 on MathLine
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
Long Division
Does 4 go into 19? Does 4 go into 19?
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
_ _ 6_6_ 44)259)259 - -2424 1919
Long Division
How many times?How many times?YesYes
One group of 4One group of 4
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
_ _ 6_6_ 44)259)259 - -2424 1919
Long Division
11 22 33 44
Two groups of 4 Two groups of 4
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
_ _ 6_6_ 44)259)259 - -2424 1919
Long Division
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
_ _ 6_6_ 44)259)259 - -2424 1919
Long Division
Three groups of 4Three groups of 4
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
_ _ 6_6_ 44)259)259 - -2424 1919
Long Division
Four groups of 4 Four groups of 4
11 22 33 44
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
_ _ 6 _6 _ 4)2594)259 - -2424 1919
Put a 4 abovePut a 4 above the 9 of 259the 9 of 259
Long Division
44
Make sureMake sure the students the students do notdo not
multiply the remainder multiply the remainder back in!back in!
Long Division 1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
Multiply 4 x 4 Multiply 4 x 4
_ _ 6_6_ 44)259)259 - -2424 1919
44
Long Division
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
Multiply 4 x 4 Multiply 4 x 4
_ _ 6_6_ 44)259)259 - -2424 1919
44
Long Division
4 Groups of 4
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
Multiply 4 x 4 Multiply 4 x 4
_ _ 6_6_ 44)259)259 - -2424 1919
44
Long Division
4 Groups of 4
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
_ _ 6_6_ 44)259)259 - -2424 1919
44Multiply 4 x 4 Multiply 4 x 4
Long Division
4 Groups of 4
4 x 4 = 164 x 4 = 16
Long Division1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
Put 16 below the 19Put 16 below the 19
____64 64 44) 259 ) 259 --2424 1919
Long Division 1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
1616
Subtract 16 from 19, Subtract 16 from 19,
____64 64 4) 259 4) 259 --2424 1919 --1616
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
Long Division
33
leaving 3leaving 3
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check =Check = 5)5) Bring Down = BDBring Down = BD
Remainder of Remainder of 33, , ‘ ‘s outs out
____64 64 4) 259 4) 259 --2424 1919 --1616 33
Long Division
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
Normally in a curriculum students Normally in a curriculum students must show the remainder…must show the remainder…
1. As R.3 or “remainder of 3”As R.3 or “remainder of 3”2. As a fractionAs a fraction 3. As a decimal. As a decimal
Long Division
So 259 divided by 4 So 259 divided by 4 is…is…
64 64 r.3r.3
Long Division
____64 64 4) 259 4) 259 --2424 1919 --1616 33
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
Remainder as a fractionRemainder as a fraction
____64 64 4) 259 4) 259 --2424 1919 --1616 33
Long Division
33 ofof 44oror3/43/4
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
_____ _____
4) 259 4) 259 --2424 19 19 --1616 33
Remainder as a Remainder as a fractionfraction
64 64 ¾¾
Long Division 1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
__________4) 259 4) 259 --2424 19 19 --1616 33
Remainder as a decimalRemainder as a decimal
6464
Long Division 1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
__________4) 259.4) 259.0000 --2424 19 19 --1616 33
6464
Long Division
Put in zeros to find Put in zeros to find remainder as a decimalremainder as a decimal
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
__________4) 259.4) 259.0000 --2424 19 19 --1616 33
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
6464
Long Division
Bring down the zeroBring down the zero
0
__________4) 259.00 4) 259.00 --2424 19 19 --1616 33
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
6464
Long Division
0
Put 30 rings on MathLinePut 30 rings on MathLine
__________44) 259.00 ) 259.00 --2424 19 19 --1616 33
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
6464
Long Division
0
Does 4 go into 30?Does 4 go into 30?YesYesHow many times?How many times?
__________44) 259.00 ) 259.00 --2424 19 19 --1616 33
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
6464
Long Division
0
One group of 4One group of 4
__________44) 259.00 ) 259.00 --2424 19 19 --1616 33
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
6464
Long Division
0
Two groups of 4Two groups of 4
__________44) 259.00 ) 259.00 --2424 19 19 --1616 33
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
6464
Long Division
0
Three groups of 4Three groups of 4
__________44) 259.00 ) 259.00 --2424 19 19 --1616 33
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
6464
Long Division
0
Four groups of 4Four groups of 4
__________44) 259.00 ) 259.00 --2424 19 19 --1616 33
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
6464
Long Division
0
Five groups of 4Five groups of 4
__________44) 259.00 ) 259.00 --2424 19 19 --1616 33
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
6464
Long Division
0
Six groups of 4Six groups of 4
__________44) 259.00 ) 259.00 --2424 19 19 --1616 33
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
6464
Long Division
0
RULE – if we begin a RULE – if we begin a group on one bar, group on one bar,
it continues on the next.it continues on the next.
11
334422
__________44) 259.00 ) 259.00 --2424 19 19 --1616 33
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
6464
Long Division
0
Seven groups of 4!Seven groups of 4!
11 33 44 665522
77
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
Long Division
______________4) 259.00 4) 259.00 --2424 19 19 --1616 3 03 0
64.64.7
Put a 7 after the decimal Put a 7 after the decimal above the zeroabove the zero
2 82 8
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
Make sureMake sure the students the students do notdo not
multiply the remainder multiply the remainder back in!back in!
Long Division
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
Long Division
Multiply 4 x 7 Multiply 4 x 7
______________44) 259.00 ) 259.00 --2424 19 19 --1616 3 03 0
64.64.7
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
Long Division
Multiply 4 x 7 Multiply 4 x 7
______________44) 259.00 ) 259.00 --2424 19 19 --1616 3 03 0
64.64.7
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
Long Division
Multiply 4 x 7 Multiply 4 x 7
______________44) 259.00 ) 259.00 --2424 19 19 --1616 3 03 0
64.64.7
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
Long Division
Multiply 4 x 7 Multiply 4 x 7
______________44) 259.00 ) 259.00 --2424 19 19 --1616 3 03 0
64.64.7
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
Long Division
Multiply 4 x 7 Multiply 4 x 7
______________44) 259.00 ) 259.00 --2424 19 19 --1616 3 03 0
64.64.7
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
Long Division
See the product See the product on MathLineon MathLine
______________44) 259.00 ) 259.00 --2424 19 19 --1616 3 03 0
64.64.7
4 x 7 = 28 4 x 7 = 28
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
Long Division
______________44) 259.00 ) 259.00 --2424 19 19 --1616 3 03 0
64.64.7
Put 28 under the 30Put 28 under the 30
2 82 8
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
Long Division
______________4) 259.00 4) 259.00 --2424 19 19 --1616 3 03 0
64.64.7
Subtract 28 from 30 Subtract 28 from 30 leaving 2leaving 2
- 2 8- 2 82 2
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
Long Division
______________4) 259.00 4) 259.00 --2424 19 19 --1616 3 03 0
64.64.7
- 2 8- 2 82 2
See the remainder on See the remainder on MathLineMathLine
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
Long Division
______________4) 259.00 4) 259.00 --2424 19 19 --1616 3 03 0
64.64.7
- 2 8- 2 82 2
The 2The 2 ‘s out‘s out
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
Long Division
______________4) 259.00 4) 259.00 --2424 19 19 --1616 3 03 0
64.64.7
- 2 8- 2 822
00
Bring down the zero Bring down the zero
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
Long Division
______________44) 259.00 ) 259.00 --2424 19 19 --1616 3 03 0
64.64.7
- 2 8- 2 82 0 2 0
Does 4 go into 20?Does 4 go into 20?Yes!Yes!How many times?How many times?
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
Long Division
______________44) 259.00 ) 259.00 --2424 19 19 --1616 3 03 0
64.64.7
- 2 8- 2 82 0 2 0
First – Put 20 on MathLineFirst – Put 20 on MathLine
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
Long Division
______________44) 259.00 ) 259.00 --2424 19 19 --1616 3 03 0
64.64.7
- 2 8- 2 82 0 2 0
Now divide by 4Now divide by 4
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
Long Division
______________44) 259.00 ) 259.00 --2424 19 19 --1616 3 03 0
64.64.7
- 2 8- 2 82 0 2 0
One group of 4One group of 4
Long Division
______________44) 259.00 ) 259.00 --2424 19 19 --1616 3 03 0
64.64.7
- 2 8- 2 82 0 2 0
Two groups of 4Two groups of 4
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
Long Division
______________44) 259.00 ) 259.00 --2424 19 19 --1616 3 03 0
64.64.7
- 2 8- 2 82 0 2 0
Three groups of 4Three groups of 4
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
Long Division
______________44) 259.00 ) 259.00 --2424 19 19 --1616 3 03 0
64.64.7
- 2 8- 2 82 0 2 0
Four groups of 4Four groups of 4
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
Long Division
______________44) 259.00 ) 259.00 --2424 19 19 --1616 3 03 0
64.64.7
- 2 8- 2 82 0 2 0
Five groups of 4Five groups of 4
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
Long Division
______________4) 259.00 4) 259.00 --2424 19 19 --1616 3 03 0
64.64.75
- 2 8- 2 8
Put 5 above 0Put 5 above 0
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
2 0 2 0
Long Division
______________44) 259.00 ) 259.00 --2424 19 19 --1616 3 03 0
64.64.75
- 2 8- 2 8
Multiply 4 x 5 Multiply 4 x 5
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
2 0 2 0
Long Division
Multiply 4 x 5 on MathLineMultiply 4 x 5 on MathLine
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD ______________
44) 259.00 ) 259.00 --2424 19 19 --1616 3 03 0
64.64.75
- 2 8- 2 82 0 2 0
Long Division 1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
Multiply 4 x 5 on MathLinMultiply 4 x 5 on MathLinee
______________44) 259.00 ) 259.00 --2424 19 19 --1616 3 03 0
64.64.75
2 0 2 0 - 2 8- 2 8
Long Division 1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
Multiply 4 x 5 on MathLineMultiply 4 x 5 on MathLine
______________44) 259.00 ) 259.00 --2424 19 19 --1616 3 03 0
64.64.75
2 0 2 0 - 2 8- 2 8
5 Groups of 4
Long Division 1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
Multiply 4 x 5 on MathLineMultiply 4 x 5 on MathLine
______________44) 259.00 ) 259.00 --2424 19 19 --1616 3 03 0
64.64.75
2 0 2 0 - 2 8- 2 8
5 Groups of 4
Long Division 1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
Multiply 4 x 5 on MathLineMultiply 4 x 5 on MathLine
______________44) 259.00 ) 259.00 --2424 19 19 --1616 3 03 0
64.64.75
2 0 2 0 - 2 8- 2 8
5 Groups of 4
Long Division 1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
4 x 5 =4 x 5 =
______________44) 259.00 ) 259.00 --2424 19 19 --1616 3 03 0
64.64.75
2 0 2 0 - 2 8- 2 8
2 0 2 0
2020
Long Division 1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
Subtract 20 from 20Subtract 20 from 20
______________4) 259.00 4) 259.00 --2424 19 19 --1616 3 03 0
64.64.75
2 0 2 0 2 02 0 0 0
- 2 8- 2 8
Long Division 1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD ______________
44) 259.00 ) 259.00 --2424 19 19 --1616 3 03 0
64.64.75
2 0 2 0 2 02 0 0 0
- 2 8- 2 8
On MathLine – no rings On MathLine – no rings
Long Division 1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD ______________
44) 259.00 ) 259.00 --2424 19 19 --1616 3 03 0
64.64.75
2 0 2 0 2 02 0 0 0
- 2 8- 2 8
No remainder, ‘s outNo remainder, ‘s out
Long Division 1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD ______________
4) 259.00 4) 259.00 --2424 19 19 --1616 3 03 0
64.64.75
2 0 2 0 2 02 0 0 0
- 2 8- 2 8
Decimal is Decimal is .75.75
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
Recap for RemaindersRecap for Remainders
• Remainder answer is “Reminder of 3”Remainder answer is “Reminder of 3”
• Remainder as a fraction is “3 of 4” or 3/4 Remainder as a fraction is “3 of 4” or 3/4
• Remainder as a decimal is 0.75Remainder as a decimal is 0.75
Long Division
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
Recap for Long DivisionRecap for Long Division • MathLine makes the algorithm concrete, MathLine makes the algorithm concrete,
steps are organizedsteps are organized
• Multiplication problem is set upMultiplication problem is set up
• Check step is built inCheck step is built in
• Remainder can be shown anyway the lesson plan requiresRemainder can be shown anyway the lesson plan requires
R.3, 3/4 , or .75R.3, 3/4 , or .75
• MathLine meets your curriculum where it’s atMathLine meets your curriculum where it’s at
Long Division
