Transcript Long Division

Long Division
chunking
Leftovers
 1st stage
 It might be helpful to start the kids on the game of Leftovers from About
Teaching Mathematics. Here’s the basic game:
 Give each pair of kids 15 color tiles, 6 paper plates or squares of
paper, and 1 die.
 The first child rolls the dice and lays out the same number of paper
plates as the number on the die. The child then distributes the color
tiles evenly one at a time onto the paper plates. Each plate must have
the same number of tiles. Leftovers go into that child’s pot and the
child then records the number sentence. Example: 15 tiles and the
child rolls a 4 – 3 tiles on each plate and there are 3 left over. The child
keeps the 3 leftovers and writes 15 divided by 4 =3 remainder 3.
He/she passes the 12 remaining tiles to the next child and that child
does the same thing but with 12 tiles. Play continues until the number
rolled is larger than the number of tiles and that becomes that players
leftovers. The child with the most leftovers at the end, wins.
Circle Division
347 divided by 4
First draw 4 circles
List friendly
numbers on the
side
100
50
20
10
5
2
1

Instead of putting tiles in the circles one at a time, let’s try putting them in chunks. How about 100, it’s our first friendly
number? If I have 347, can I put 100 tiles on each plate? No, because I know 100x4=400 and that’s too big. How
about 50? 50x4 =200 and that will work.
50
50
100
50
20
10
5
2
1
347
-200
147
50
50
50 x 4 = 200

Okay, we have 147 tiles left. Can I put 50 more on each plate? No, because that would be 200 and we don’t have 200
left. How about 20? 20 x 4 = 80, yes that will work
100
50
20
10
5
2
1
50
50
20
147
- 80
20
- 67
50
50
20
20
50 x 4 = 200
20 x 4 = 80

We have 67 tiles left now. Can I put 20 more on each plate? No, because 67 is smaller than 80. So the next friendly
number is 10. 10 x 4 = 40 and I can subtract 40 from 67
50
50
10
10
20
100
50
20
10
5
2
1
67
- 40
20
27
50
20
10
50
20
10
50 x 4 = 200
20 x 4 = 80
10 x 4 =
40

Now we have 27 tiles left. Can I put 10 on each plate again? No, because that would need 40 tiles and I only have 27.
Our next friendly number is 5. Will that work? Yes, 5 x 4 = 20, and I have enough tiles to get rid of 20.
50
50
20
50
20
10
20
10
5
5
27
- 20
5
10
100
50
20
10
5
2
1
7
50
20
10
5
50 x 4 = 200
20 x 4 = 80
10 x 4 =
40
5 x4=
20

7 tiles left. Can I put 5 more on each plate? No, then how about 2 on each plate? 2 x 4 = 8 and I don’t have 8 tiles
left. So how about 1 tile on each plate?
50
20
10
50 10
7
5
20 5
1
- 4
1
100
50
20
10
5
2
1
3
50 x 4 = 200
50
10
20
5
1
50
10
20
5
1
20 x 4 = 80
10 x 4 =
40
5 x4=
20
1 x4=
4

Can I put 1 more on each plate? No, so I have 3 tiles left over. How many tiles are now on each plate? 86 with 3
remaining. I can check my work by adding. Don’t forget to add in the remainder.
50
20
10
50 10
7
5
20 5
1
- 4
1
100
50
20
10
5
2
1
3
50 x 4 = 200
50
10
20
5
1
50
10
20
5
1
20 x 4 = 80
10 x 4 =
40
5 x4=
20
1 x4=
4
344+3 = 347
Long Division

Let’s look at the same problem in a different way: How many equal groups of 4 can I
make with 347? I can’t make 100 equal groups because that would be 400. Let’s try 50
4
347
We can still
use friendly
numbers:
100
50
20
10
5
2
1
Long Division

Let’s look at the same problem in a different way: How many equal groups of 4 can I
make with 347? I can’t make 100 equal groups because that would be 400. Let’s try 50
4
347
200
147
We can still
use friendly
numbers:
50
100
50
We multiply 50 x
4 and get 200
then subtract the
200 from 347 and
we get 147.
20
10
5
2
1
Long Division

We have 147 left and I still have to ask myself how many groups of 4 are in 147. The
next friendly number is 20
4
347
200
147
-80
67
We can still
use friendly
numbers:
50
20
100
50
We multiply 20 x
4 and get 80 then
subtract the 80
from 147 and we
get 67.
20
10
5
2
1
Long Division

I still have 67 left. How many groups of 4 in 67? Let’s try 10
4
347
200
147
-80
67
-40
27
20
We can still
use friendly
numbers:
10
100
50
50
We multiply 10 x
4 and get 40 then
subtract the 40
from 67 and we
get 27.
20
10
5
2
1
Long Division

Now we have 27. I can use my friendly numbers and go to 5 next or, if I’m pretty good
with multiplication and division I know that 6 x4 =24 and that’s faster
4
347
200
147
-80
67
-40
27
-24
3
20
We can still
use friendly
numbers:
10
100
50
50
6
We multiply 6 x 4
and get 24 then
subtract the 24
from 27 and we
get 3. 3 is
smaller than 4, so
I’m finished. Add
up the numbers
on the right side
20
10
5
2
1
Long Division
4
347
200
147
-80
67
-40
27
-24
3
20
We can still
use friendly
numbers:
10
100
50
50
6
_____
86
After we add the
numbers on the
right, we find our
answer is 86 with
3 remaining.
20
10
5
2
1