Van de Walle and Fosnot/Dolk
Division Problem Types
and Strategies
The student will be able to explain multi-digit computations
fluently and accurately.
(This is a year long goal to develop fluency)
4
In addition to level
3.0 and above and
beyond what was
taught in class, the
student may:



3
The student will be able to
explain multi-digit
computations fluently and
accurately.
 Explain the standard
division algorithm,
Make connection
referencing place value
with other
 Determine when to use
concepts in math
paper pencil algorithms,
Make connection
mental math, or a
with other
computing tool when
content areas.
dividing multi-digit
Applications
numbers
with other
 Interpret remainders as
concepts in
fractions and in context
math.
of the problem
 Represent the
relationship between the
numbers in the division
problem as a numerical
statement
2
The student will be able
to use the standard
algorithm to compute
multi-digit numbers.
 Understand the
standard division
algorithm, using
place value
 Write remainders
as fractions.
1
With help from
the
teacher, the
student has
partial success
with levels 2
and 3.
0
Even with help,
the student has
no success with
computing
multi-digit
numbers.
The jar has 783 jelly beans and Aidan
and her four friends want to share
them equally. How many jelly beans
will Aidan and each of her friends get?
1. Write the division and
multiplication equations
that match the story.
2. Solve and be prepared
to explain and defend
your strategy with a
partner.
• Were the groups missing or the amount inside
the groups?
• Is there a remainder in this problem and if so,
what does it represent? Can it be split into a
decimal or fraction? Which would represent
the remainder better, based on the context? A
decimal or fraction?
783 ÷ 5 = _ and 5 x _ = 783
Jumbo the elephant loves peanuts. His
trainer has 625 peanuts. If he gives
Jumbo 20 peanuts each day, how many
days will the peanuts last?
1. Write the division and
multiplication equations that
match the story.
2. Solve and be prepared
to explain and defend your
strategy with a partner.
• Were the groups missing or the amount
inside the groups?
• Is there a remainder in this problem and if
so, what does it represent? Can it be split
into a decimal or fraction? Which would
represent the remainder better, based on
the context? A decimal or fraction?
625 ÷ 20 = _ and 20 x _ = 625
Missing Factor Strategy
1. Write the division and
multiplication equations
that match the story.
2. Solve and be prepared
to explain and defend
your strategy with a
partner.
• Were the groups missing or the amount
inside the groups?
• Is there a remainder in this problem and if
so, what does it represent? Can it be split
into a decimal or fraction? Which would
represent the remainder better, based on
the context? A decimal or fraction?
143 ÷ 11 = _ and _ x 11 = 143
There are 11 mini busses to take all of 6th
grade to the Science Center. If there are
372 students, how many children will ride
in each mini bus. Explain your answer
1. Write the division and
multiplication equations that
match the story.
2. Solve and be prepared
to explain and defend your
strategy with a partner.
• Were the groups missing or the amount inside
the groups?
• Is there a remainder in this problem and if so,
what does it represent? Can it be split into a
decimal or fraction? Which would represent
the remainder better, based on the context? A
decimal or fraction?
372 ÷ 11 = _ and 11 x _ = 372
It takes 2 yards of cotton to make a tshirt. How many t-shirts can be made
with 247 yards of material?
1. Write the division and
multiplication equations
that match the story.
2. Solve and be prepared to
explain and defend your
strategy with a partner.
• Were the groups missing or the amount inside
the groups?
• Is there a remainder in this problem and if so,
what does it represent? Can it be split into a
decimal or fraction? Which would represent
the remainder better, based on the context? A
decimal or fraction?
247 ÷ 2 = _ and _ x 2 = 247
Write a partitive (looking for what’s inside the
groups) and a measurement (looking for the
groups) word problem for
514 ÷ 8
and solve it.
Write the division equation
and multiplication equation
for both questions.
Discuss what is different about both
problems with a partner.
Connecting Multiplication and Division
• We’ve used open arrays for multiplication:
(42 x 7) Distributive Property
(37 x 84) Associative Property
7
84
80
4
30
2400
120
7
560
28
40
280
42
37
2
14
Connecting Multiplication and Division
Now, let’s use an open array for division (it’s
working backwards from multiplication):
15
5
?
5 x 15 = _
?
5
75
75 ÷ 5 = _
Connecting Multiplication and Division
180 ÷ 15
180 ÷ 15 = (150 ÷ 15) + (30 ÷ 15)
(10
+
2) = 12
15
10
150
2
30
12
Making Friendly Numbers to Solve
270 ÷ 6
• Explain what is happening in this array? Is the
divisor or dividend being broken into parts?
Where did 300 come from and why are we
subtracting?
50
45
5
6
270
30
270 ÷ 6 = (300 ÷ 6) – (30 ÷ 6) = 45
270 ÷ 6 = (50
–
5) = 45