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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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