Don’t Let Division Get You Down!. Created by Danielle Miller Hawk Ridge Elementary School. What is division?. An operation that tells how many groups there are and how many are in each group Repeated subtraction The inverse of multiplication. 4 6 24. 24 6. = 4.
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6 24
24
6
= 4
What Does Division Look Like?24 ÷ 6 = 4
A division problem can be written as a fraction.
A division problem can be written horizontally.
A division problem can be written with the traditional division sign.
24 ÷ 6 = 4
dividend– the number being divided (total number of items)
divisor – the number by which another number is divided (# of groups)
quotientthe answer to a division problem (# of items in each group)
Identify the divisor (the number of groups) and draw that many circles
Identify the dividend and begin distributing out that number of stars.
Count the number of stars in one circle. This is your quotient.
6
Circles and Stars18÷3=?
18÷3=6
Ducks (÷)
May (x)
Swim ()
Backwards (bring )


0
0
0
“Old School” DivisionThe Standard Algorithm2
4 80
0
8
0
0
2
3 ) 7 4 8
1
3 x 2 = 6
7  6 = 1
2
4
3 ) 7 4 8
1
2
3 x 4 = 12
14  12 = 2
2
4
9
R1
3 ) 7 4 8
1
2
3 x 9 = 27
28  27 = 1
The Partial Quotients Algorithm uses a series of
“at least, but less than”
estimates of how many times the dividend can be divided by the divisor.
There are at least ten 12’s in 158 (10 x 12=120), but fewer than twenty. (20 x 12 = 240)
13 R2
12
158
There are more than three 12’s (3 x 12 = 36), but fewer than four (4 x 12 = 48). Record 3 as the next guess
 120
10 1st guess
Subtract
38
3 2ndguess
 36
Subtract
2
13
Sum of guesses
Since 2 is less than 12, you can stop estimating. The final result is the sum of the guesses (10 + 3 = 13) plus what is left over (remainder of 2 )
36 fewer than twenty. (20 x 12 = 240)
7,891
Did you check your work with
Multiplication?
219 x 36 = 7,884 + 7 = 7,891
Let’s try another one…
219 R7
 3,600
100 – 1st guess
Subtract
4,291
 3,600
100 – 2nd guess
Subtract
691
 360
10 – 3rd guess
331
 324
9 – 4th guess
7
219 R7
Sum of guesses
43 fewer than twenty. (20 x 12 = 240)
8,572
Now do this one on your own…
199 R 15
 4,300
100 – 1st guess
Subtract
4272
3870
90 – 2nd guess
Subtract
402
 301
7 – 3rd guess
101
 86
2 – 4th guess
199 R 15
Sum of guesses
15