Division Strategies
Division of Whole Numbers by a Double Digit Divisor
Use models to find quotients of whole numbers (4 digit by 2 digit) including contextual
situations and explain the calculations. (5.NBT.6)
Partial Quotients:
22
Decomposing a Number into Friendly Numbers:
3769
Divide 5892 by 25.
-2200 100
Split 5892 into 2500 + 2500 + 800 + 90 +2
1569
-1100
Use mental math:
50
2500 ÷ 25 = 100
469
-220
10
800 ÷ 25 = 32 (Think: 4 25s = 100)
90 ÷ 25 =
249
-220
2500 ÷ 25 = 100
10
3 w/ 15 left over + 2 = 17
17 is the remainder, so the answer is 235 r17.
29
-22
1
72 ÷ 6 becomes (60 ÷ 6) + (12 ÷ 6) =
7
10
+
2
= 12
The answer is 100 + 50 + 10 + 10 + 1 = 171 r7.
Solving and Easier Problem and Adjusting the Answer:
Instead of dividing by 5, divide by 10 and then double your answer.
Ex. 4400 ÷ 5 becomes 4400 ÷ 10 = 440, and then double your answer to 880.
Ex. 35,000 ÷ 25 becomes 35,000 ÷ 100 = 350, and the quadruple your answer to 1,400.
Solve a More Basic Fact and then Adjust the Place Holder Zeroes:
Ex. 35,000 ÷ 70 becomes 35 ÷ 7 = 5 and then adjust your place holder zeroes = 500.
Ex. 8,800 ÷ 40 becomes 88 ÷ 4 = 22 and then adjust your place holder zeroes = 220.
Dividing Fractions:
Choose, combine and apply strategies for answering multiplication and division
problems involving fractions, mixed numbers and decimals including contextual
situations. (5. NF.3, 5.NF 4, 5 NF.5, 5 NF.6, 5.NF.7, 5. NBT.7)
This is probably the most difficult concept introduced in fifth grade. There are no easy
picture models to use to help students visualize what is happening when you divide a
fraction by a whole number or a whole number by a fraction. The pictures you can
draw are difficult to interpret and lead to more confusion at this age (and with adults
too; I was there last year). Determining what you are solving for is the key. The
algorithm is NOT the focus in fifth grade; rather it is the conceptual understanding of
what you are doing when you divide a fraction by a whole number or a whole number by
a fraction.
(turn over for examples)
A) When you divide a whole number by a fraction, you are finding the count. The answer
gets LARGER because the “new whole” is SMALLER.
(original whole) divided by the (size of the new whole) equals the (count)
example 1
1
1
54 brownies divided into 4 units: There are four 4 units in every whole, so you would
multiply 54 x 4, giving you 216 brownies.
example 2
2
76 brownies divided into 3 units:
wholes
2/3 size
units
(Use a ratio table.)
1 (3/3)
2 (6/3)
6
10
20
60
70
76
1
3
9
15
30
90
105
114
B) When you divide a fraction by a whole number, you are finding the size of the new
whole. The answer (the size of the “new whole”) gets SMALLER because your count
gets LARGER.
(original whole) divided by (count) equals the (size of new whole)
example 1
3
of a pizza is left. 4 people want to share the pizza. How much of the remaining
4
pizza does each person get to eat?
3
÷ 4 Each person is getting ¼ of the pizza that remains. The “whole” is being
4
1
partioned into four evenly sized pieces, each 4 of the original “whole”. In math, of
means to multiply.
3
1
3
x 4 using the models that were introduced earlier would be 16 .
4
example 2
9
Jodi’s relay team ran 11 of the track around the playground. Each of the 5 members
of her team ran the same distance. How fraction of the total distance around the
track did each person run?
9
÷5
11
1
Each person ran 5 of the total distance run altogether. The “whole distance”
1
is being partioned into 5 evenly sized distances, each 5 of the “whole distance”. In
math, of means to multiply.
9
1
9
x using the models that were introduced earlier would be 55 .
11 5