Transcript Long Division Long Division & MathLine Second Problem: ____ 4)259 Long Division For traditional Long Division, teach the algorithm: 1) Divide or D 2) Multiply or M 3) Subtract or S 4)

Long Division
Long Division
&
MathLine
Second Problem:
____
4)259
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
1)
2)
3)
4)
5)
Take the problem
____
4)259
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Long Division
1)
2)
3)
4)
5)
4 into 2?
____
4)259
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Long Division
Put 2 rings to left
____
4)259
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Long Division
4 into 2? No
____
4)259
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Long Division
4 into 25?
____
4)259
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Long Division
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Put 25 rings on MathLine
____
4)259
Long Division
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
For long division on MathLine
ALWAYS
start dividing from the left
Long Division
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
4 into 25?
4
Yes,One
howGroup
manyof
times?
____
4)259
1234
1
Long Division
____
4)259
Two Groups of 4
1234
1
2
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Long Division
____
4)259
1)
2)
3)
4)
5)
Three Groups of 4
1234
1
2
3
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Long Division
____
4)259
1)
2)
3)
4)
5)
Four Groups of 4
1234
1
2
3
4
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Long Division
____
4)259
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Five Groups of 4
12 3 4
1
2
3
4
5
Long Division
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Six Groups of 4
____
4)259
1234
1
2
3
4
5
6
Long Division
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Put a 6 above the 5 of 259
6
____
4)259
Long Division
1)
2)
3)
4)
5)
Now multiply 6 X 4
6
____
4)259
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Long Division
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
sure6 X 4,
OnlyMake
multiply
theorstudents
6 groupsdo
ofnot
4
multiply the remainder
back in!
Long Division
6
____
4)259
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Multiply 6 x 4
Long Division
6
____
4)259
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Multiply 6 x 4
Long Division
6
____
4)259
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Multiply 6 x 4
6 Groups of 4
Long Division
6
____
4)259
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Multiply 6 x 4
6 Groups of 4
Long Division
6
____
4)259
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Multiply 6 x 4
6 Groups of 4
Long Division
6
____
4)259
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Multiply 6 x 4
6 Groups of 4
Long Division
6
____
4)259
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Multiply 6 x 4
6 Groups of 4
Long Division
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
See 6 x 4 on MathLine
_6
___
4)259
Long Division
6
_ ___
4)259
24
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
We multiply 6 x 4
and get 24,
so we put
the 24 below 25
Long Division
6
_ ___
4)259
-24
1
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Subtract 24 from 25,
to get a difference of 1
Long Division
6
_ ___
4)259
-24
1
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Remainder of 1, ‘s
out on MathLine
Long Division
6
_ ___
4)259
9
-24
1
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Bring down
the 9
to get 19
Long Division
Put 19 on MathLine
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Long Division
_ 6_
4)259
-24
19
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Doesmany
4 go
into
19?
How
Yes
times?
Long Division
_ 6_
4)259
-24
19
1 2 3 4
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
One group of 4
Long Division
_ 6_
4)259
-24
19
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Two groups of 4
Long Division
_ 6_
4)259
-24
19
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Three groups of 4
Long Division
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
_ 6_
4)259
-24
19
Four groups of 4
1
3
2
4
Long Division
_ 64_
4)259
-24
19
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Put a 4 above
the 9 of 259
Long Division
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Make sure
the students do not
multiply the remainder
back in!
Long Division
4
_ 6_
4)259
-24
19
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Multiply 4 x 4
Long Division
4
_ 6_
4)259
-24
19
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Multiply 4 x 4
4 Groups of 4
Long Division
4
_ 6_
4)259
-24
19
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Multiply 4 x 4
4 Groups of 4
Long Division
4
_ 6_
4)259
-24
19
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Multiply 4 x 4
4 Groups of 4
Long Division
4 x 4 = 16
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Long Division
__64
4) 259
-24
19
16
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Put 16 below the 19
Long Division
__64
4) 259
-24
19
-16
3
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Subtract 16 from 19,
leaving 3
Long Division
__64
4) 259
-24
19
-16
3
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Remainder of 3,
‘s out
Long Division
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Normally in a curriculum students
must show the remainder…
1. As R.3 or “remainder of 3”
2. As a fraction
3. As a decimal
Long Division
__64
4) 259
-24
19
-16
3
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
So 259 divided by 4
is…
64 r.3
Long Division
__64
4) 259
-24
19
-16
3
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Remainder as a fraction
3
of
or
3/4
4
Long Division
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
64 ¾
_____
4) 259
-24
19
-16
3
Remainder as a
fraction
Long Division
_____
64
4) 259
-24
19
-16
3
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Remainder as a decimal
Long Division
_____
64
4) 259.00
-24
19
-16
3
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Put in zeros to find
remainder as a decimal
Long Division
_____
64
4) 259.00
0
-24
19
-16
3
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Bring down the zero
Long Division
_____
64
4) 259.00
-24
19
-16
30
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Put 30 rings on MathLine
Long Division
_____
64
4) 259.00
-24
19
-16
30
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Does
How 4many
go
Yes
into
times?
30?
Long Division
_____
64
4) 259.00
-24
19
-16
30
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
One group of 4
Long Division
_____
64
4) 259.00
-24
19
-16
30
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Two groups of 4
Long Division
_____
64
4) 259.00
-24
19
-16
30
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Three groups of 4
Long Division
_____
64
4) 259.00
-24
19
-16
30
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Four groups of 4
Long Division
_____
64
4) 259.00
-24
19
-16
30
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Five groups of 4
Long Division
_____
64
4) 259.00
-24
19
-16
30
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Six groups of 4
Long Division
_____
64
4) 259.00
-24
19
-16
30
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
RULE – if we begin a
group on one bar,
it continues on the next.
1
2 34
Long Division
_____
64
4) 259.00
-24
19
-16
30
1
7
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Seven groups of 4!
2
3
4
5
6
Long Division
_______
64. 7
4) 259.00
-24
19
-16
30
28
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Put a 7 after the decimal
above the zero
Long Division
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Make sure
the students do not
multiply the remainder
back in!
Long Division
_______
64. 7
4) 259.00
-24
19
-16
30
1)
2)
3)
4)
5)
Multiply 4 x 7
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Long Division
_______
64. 7
4) 259.00
-24
19
-16
30
1)
2)
3)
4)
5)
Multiply 4 x 7
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Long Division
_______
64. 7
4) 259.00
-24
19
-16
30
1)
2)
3)
4)
5)
Multiply 4 x 7
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Long Division
_______
64. 7
4) 259.00
-24
19
-16
30
1)
2)
3)
4)
5)
Multiply 4 x 7
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Long Division
_______
64. 7
4) 259.00
-24
19
-16
30
1)
2)
3)
4)
5)
Multiply 4 x 7
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Long Division
_______
64. 7
4) 259.00
-24
19
-16
30
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
See the product
4
x
7
=
28
on MathLine
Long Division
_______
64. 7
4) 259.00
-24
19
-16
30
28
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Put 28 under the 30
Long Division
_______
64. 7
4) 259.00
-24
19
-16
30
-28
2
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Subtract 28 from 30
leaving 2
Long Division
_______
64. 7
4) 259.00
-24
19
-16
30
-28
2
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
See the remainder on
MathLine
Long Division
_______
64. 7
4) 259.00
-24
19
-16
30
-28
2
1)
2)
3)
4)
5)
The 2
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
‘s out
Long Division
_______
64. 7
4) 259.00
0
-24
19
-16
30
-28
2
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Bring down the zero
Long Division
_______
64. 7
4) 259.00
-24
19
-16
30
-28
20
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Does
How many
4 Yes!
go into
times?
20?
Long Division
_______
64. 7
4) 259.00
-24
19
-16
30
-28
20
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
First – Put 20 on MathLine
Long Division
_______
64. 7
4) 259.00
-24
19
-16
30
-28
20
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Now divide by 4
Long Division
_______
64. 7
4) 259.00
-24
19
-16
30
-28
20
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
One group of 4
Long Division
_______
64. 7
4) 259.00
-24
19
-16
30
-28
20
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Two groups of 4
Long Division
_______
64. 7
4) 259.00
-24
19
-16
30
-28
20
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Three groups of 4
Long Division
_______
64. 7
4) 259.00
-24
19
-16
30
-28
20
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Four groups of 4
Long Division
_______
64. 7
4) 259.00
-24
19
-16
30
-28
20
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Five groups of 4
Long Division
_______
64. 75
4) 259.00
-24
19
-16
30
-28
20
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Put 5 above 0
Long Division
_______
64. 75
4) 259.00
-24
19
-16
30
-28
20
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Multiply 4 x 5
Long Division
_______
64. 75
4) 259.00
-24
19
-16
30
-28
20
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Multiply 4 x 5 on MathLine
Long Division
_______
64. 75
4) 259.00
-24
19
-16
30
-28
20
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Multiply 4 x 5 on MathLine
Long Division
_______
64. 75
4) 259.00
-24
19
-16
30
-28
20
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Multiply 4 x 5 on MathLine
5 Groups of 4
Long Division
_______
64. 75
4) 259.00
-24
19
-16
30
-28
20
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Multiply 4 x 5 on MathLine
5 Groups of 4
Long Division
_______
64. 75
4) 259.00
-24
19
-16
30
-28
20
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Multiply 4 x 5 on MathLine
5 Groups of 4
Long Division
_______
64. 75
4) 259.00
-24
19
-16
30
-28
20
20
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
4 x 5 = 20
Long Division
_______
64. 75
4) 259.00
-24
19
-16
30
-28
20
20
0
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Subtract 20 from 20
Long Division
_______
64. 75
4) 259.00
-24
19
-16
30
-28
20
20
0
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
On MathLine – no rings
Long Division
_______
64. 75
4) 259.00
-24
19
-16
30
-28
20
20
0
No remainder,
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
‘s out
Long Division
_______
64. 75
4) 259.00
-24
19
-16
30
-28
20
20
0
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Decimal is .75
Long Division
1)
2)
3)
4)
5)
Divide = D
Multiply = M
Subtract = S
Check =
Bring Down = BD
Recap for Remainders
• Remainder
answer is “Reminder of 3”
• Remainder as a fraction is “3 of 4” or 3/4
• Remainder as a decimal is 0.75
Long Division
1)
2)
3)
4)
5)
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
• Remainder can be shown anyway the lesson plan requires
R.3, 3/4 , or .75
• MathLine meets your curriculum where it’s at