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**Long Division & MathLine**

____ 6)192 First Problem:

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**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

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**____ 6)192 Take the problem Long Division Divide = D Multiply = M**

Subtract = S Check = Bring Down = BD Take the problem ____ 6)192 3

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**____ 6)192 6 into 1? Long Division Divide = D Multiply = M**

Subtract = S Check = Bring Down = BD 6 into 1? ____ 6)192 4

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**____ 6)192 Put 1 on MathLine Long Division Divide = D Multiply = M**

Subtract = S Check = Bring Down = BD Put 1 on MathLine ____ 6)192 5

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**____ 6)192 6 into 1? No Long Division Divide = D Multiply = M**

Subtract = S Check = Bring Down = BD Long Division 6 into 1? No ____ 6)192 6

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**____ 6)192 6 into 19? Long Division Divide = D Multiply = M**

Subtract = S Check = Bring Down = BD 6 into 19? ____ 6)192 7

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**____ 6)192 Put 19 on MathLine Long Division Divide = D Multiply = M**

Subtract = S Check = Bring Down = BD Put 19 on MathLine ____ 6)192 8

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**For long division on MathLine start dividing from the left**

Divide = D Multiply = M Subtract = S Check = Bring Down = BD For long division on MathLine ALWAYS start dividing from the left

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**____ 6)192 6 into 19? One Group of 6 Yes, how many times?**

Long Division Divide = D Multiply = M Subtract = S Check = Bring Down = BD ____ 6)192 6 into 19? Yes, how many times? One Group of 6 1 2 3 4 5 6 1 10

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**____ 6)192 Two Groups of 6 Long Division 1 2 3 4 5 6 1 1 2 Divide = D**

Multiply = M Subtract = S Check = Bring Down = BD ____ 6)192 Two Groups of 6 1 2 3 4 5 6 1 1 2 11

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**____ 6)192 Three Groups of 6 Long Division 1 2 3 4 5 6 1 1 2 3**

Divide = D Multiply = M Subtract = S Check = Bring Down = BD ____ 6)192 Three Groups of 6 1 2 3 4 5 6 1 1 2 3 12

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**____ 3 6)192 Put a 3 above the 19 of 192 Long Division Divide = D**

Multiply = M Subtract = S Check = Bring Down = BD Put a 3 above the 19 of 192 3 ____ 6)192 13 13

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**____ 3 6)192 Now multiply 3 X 6 Long Division Divide = D Multiply = M**

Subtract = S Check = Bring Down = BD Now multiply 3 X 6 3 ____ 6)192 14 14

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**multiply the remainder**

Long Division Divide = D Multiply = M Subtract = S Check = Bring Down = BD Make sure the students do not multiply the remainder back in! Only multiply 3 X 6, or 3 groups of 6 15 15

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**____ 3 6)192 Multiply 3 x 6 Long Division 3 Groups of 6 Divide = D**

Multiply = M Subtract = S Check = Bring Down = BD 3 Multiply 3 x 6 ____ 6)192 3 Groups of 6 16 16

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**____ 3 6)192 Multiply 3 x 6 Long Division 3 Groups of 6 Divide = D**

Multiply = M Subtract = S Check = Bring Down = BD 3 Multiply 3 x 6 ____ 6)192 3 Groups of 6 17 17

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**3 _ ___ 6)192 18 We multiply 3 x 6 and get 18, so we put**

Long Division Divide = D Multiply = M Subtract = S Check = Bring Down = BD 3 _ ___ 6)192 We multiply 3 x 6 and get 18, so we put the 18 below 19 18 18 18

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**3 _ ___ 6)192 -18 1 Long Division Subtract 18 from 19,**

Divide = D Multiply = M Subtract = S Check = Bring Down = BD 3 _ ___ 6)192 -18 Subtract 18 from 19, to get a difference of 1 1 19 19

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**Remainder of 1, ‘s out on MathLine**

Long Division Divide = D Multiply = M Subtract = S Check = Bring Down = BD 3 _ ___ 6)192 -18 Remainder of 1, ‘s out on MathLine 1 20

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**3 _ ___ 6)192 -18 2 1 Bring down the 2 to get 12 Long Division**

Divide = D Multiply = M Subtract = S Check = Bring Down = BD 3 _ ___ 6)192 -18 Bring down the 2 to get 12 2 1 21

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**Put 12 on MathLine Long Division Divide = D Multiply = M Subtract = S**

Check = Bring Down = BD Put 12 on MathLine 22 22

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**_ 3_ 6)192 -18 12 How many times? Does 6 go into 12? Yes Long Division**

Divide = D Multiply = M Subtract = S Check = Bring Down = BD _ 3_ 6) 12 How many times? Does 6 go into 12? Yes 23

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**_ 3_ 6)192 -18 12 One group of 6 Long Division 1 2 3 4 5 6 Divide = D**

Multiply = M Subtract = S Check = Bring Down = BD _ 3_ 6) 12 One group of 6 1 2 3 4 5 6 24

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**_ 3_ 6)192 -18 12 Two groups of 6 Long Division 1 2 3 4 5 6 Divide = D**

Multiply = M Subtract = S Check = Bring Down = BD _ 3_ 6) 12 Two groups of 6 1 2 3 4 5 6 25

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**2 _ 3 _ 6)192 -18 12 Put a 2 above the 2 of 192 Long Division**

Divide = D Multiply = M Subtract = S Check = Bring Down = BD 2 _ 3 _ 6) 12 Put a 2 above the 2 of 192 26

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**2 _ 3 _ 6)192 -18 12 Now multiply 2 x 6 Long Division Divide = D**

Multiply = M Subtract = S Check = Bring Down = BD 2 _ 3 _ 6) 12 Now multiply 2 x 6 27

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**2 x 6 = 12 Long Division 2 Groups of 6 Divide = D Multiply = M**

Subtract = S Check = Bring Down = BD Long Division 2 x 6 = 12 2 Groups of 6 28 28

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**__32 6) 192 -18 12 Put 12 below the 12 12 Long Division Divide = D**

Multiply = M Subtract = S Check = Bring Down = BD __32 6) 192 Put 12 below the 12 12 29 29

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**__32 6) 192 -18 12 Subtract 12 from 12 -12 Long Division Divide = D**

Multiply = M Subtract = S Check = Bring Down = BD __32 6) 192 Subtract 12 from 12 -12 30 30

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**Remainder of 0, ‘s out on MathLine**

Long Division Divide = D Multiply = M Subtract = S Check = Bring Down = BD __32 6) 192 Remainder of 0, ‘s out on MathLine -12 31 31

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**Recap for Long Division**

Divide = D Multiply = M Subtract = S Check = Bring Down = BD Recap for Long Division MathLine makes the algorithm concrete, steps are organized Multiplication problem is set up Check step is built in Makes long division FUN for students

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