Long Division &MathLine ____ ____ 6)192 6)192 First Problem:
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Long Division Long Division & & MathLine MathLine Long Division ____ ____ First Problem: First Problem:
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Transcript of Long Division &MathLine ____ ____ 6)192 6)192 First Problem:
Long Division Long Division &&
MathLineMathLine
Long Division
____ ____ 6)1926)192
First Problem:First 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
____ ____ 6)1926)192
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
________ 66))119292
6 into 1?6 into 1?
Long Division
________ 66))119292
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
Put 1 on MathLinePut 1 on MathLine
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 into 1? No6 into 1? No
Long Division
________ 66))119292
6 into 19? 6 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
________ 66))191922
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 19 on MathLinePut 19 on MathLine ________ 66))191922
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
ALWAYS ALWAYS start dividing from thestart dividing from the leftleft
Long Division
Yes, how many times?Yes, 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
________ 66))191922
6 into 19? 6 into 19? One Group of 6One Group of 6
Long Division
2211 4433
1
55 66
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
________ 66))191922
Two Groups of 6Two Groups of 6
Long Division
2
2211 4433 55 66
11
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
________ 66))191922
Three Groups of 6Three Groups of 6
Long Division
2211 4433 55 66
11 2 3
________ 6)1926)192
Put a 3 above the 19 of 192Put a 3 above the 19 of 192
3 3
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
________ 66)192)192
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 3 X 6Now multiply 3 X 6
3 3
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 3 X 6, Only multiply 3 X 6, or 3 groups of 6or 3 groups of 6
____ ____ 66)192)192
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
3 3
Multiply 3 x 6Multiply 3 x 6
3 Groups of 6
Long Division
____ ____ 66)192)192
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
3 3
Multiply 3 x 6Multiply 3 x 6
3 Groups of 6
Long Division
We multiply 3 x 6 We multiply 3 x 6 and get 18, and get 18, so we put so we put
the 18 below 19 the 18 below 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)1926)192
33
Long Division
1818
Subtract 18 from 19, Subtract 18 from 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)191922 --1818
33
Long Division
11
to get a difference of 1to 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
Remainder of 1, ‘s Remainder of 1, ‘s out on MathLineout on MathLine
Long Division
_ ____ ___ 6)1926)192 --1818
33
11
Bring downBring down the 2the 2
to get 12to get 12
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
_ ____ ___ 6)1926)192 --1818
33
11
Long Division
22
Put 12 on MathLine Put 12 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 6 go into 12? Does 6 go into 12?
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
_ _ 3_3_ 66)192)192 - -1818 1212
Long Division
How many times?How many times?YesYes
One group of 6One group of 6
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
_ _ 3_3_ 66)192)192 - -1818 1212
Long Division
2211 4433 55 66
Two groups of 6Two groups of 6
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
_ _ 3_3_ 66)192)192 - -1818 1212
Long Division
2211 4433 55 66
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
_ _ 3 _3 _ 6)1926)192 - -1818 1212
Put a 2 abovePut a 2 above the 2 of 192the 2 of 192
Long Division
22
1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
_ _ 3 _3 _ 66)192)192 - -1818 1212
Now multiply 2 x 6 Now multiply 2 x 6
Long Division
22
2 x 6 =2 x 6 =
Long Division1)1) Divide = DDivide = D2)2) Multiply = MMultiply = M3)3) Subtract = SSubtract = S4)4) Check = Check = 5)5) Bring Down = BDBring Down = BD
2 Groups of 6
1212
Put 12 below the 12Put 12 below the 12
____32 32 66) 192 ) 192 --1818 1212
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
1212
Subtract 12 from 12Subtract 12 from 12
____32 32 66) 192 ) 192 --1818 1212
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
-12-1200
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 0, Remainder of 0, ‘s out on MathLine‘s out on MathLine
Long Division
____32 32 66) 192 ) 192 --1818 1212
-12-1200
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
• Makes long division FUN for studentsMakes long division FUN for students
Long Division
