Math Module 3
Multi-Digit Multiplication and Division
Topic E: Division of Tens and Ones with Successive Remainders
Lesson 20: Solve division problems without remainders using the area model.
4.OA.3 4.NBT.6
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Lesson 20
Target
You will solve division
problems without
remainders using the area
model.
Fluency Development
Lesson 20
Divide using the standard algorithm.
67 ÷ 2
(2 x 33) + 1 = 67
67
33
1
Fluency Development
Lesson 20
Divide using the standard algorithm.
60 ÷ 4
(15 x 4) + 0 = 60
60
60
0
Fluency Development
Lesson 20
Divide using the standard algorithm.
29 ÷ 3
(3 x 9) + 2 = 29
29
27
2
Fluency Development
Lesson 19
Divide using the standard algorithm.
77 ÷ 4
(19 x 4) + 1 = 77
77
76
1
Lesso
Fluency Development
Find the Unknown Factor.
15 ÷ 3 = 5
5 x ___ = 15
Lesso
Fluency Development
Find the Unknown Factor.
12 ÷ 4 = 3
4 x ___ = 12
Lesso
Fluency Development
Find the Unknown Factor.
35 ÷ 5 = 7
5 x ___ = 35
Lesso
Fluency Development
Find the Unknown Factor.
36 ÷ 6 = 6
6 x ___ = 36
Lesso
Fluency Development
Find the Unknown Factor.
49 ÷ 7 = 7
7 x ___ = 49
Lesso
Fluency Development
Find the Unknown Factor.
81 ÷ 9 = 9
9 x ___ = 81
Lesso
Fluency Development
Find the Unknown Factor.
48 ÷ 6 = 8
6 x ___ = 48
Lesso
Fluency Development
Find the Unknown Factor.
42 ÷ 7 = 6
7 x ___ = 42
Lesso
Fluency Development
Find the Unknown Factor.
54 ÷ 9 = 6
9 x ___ = 54
Fluency
Mental Multiplication
Say the multiplication
sentence in
in unit
unit form.
form.
sentence
3 tens
tens xx 22 =tens
=6
3
6
tens.
3 ones x 2 = 6 ones.
hundreds.
3 x 2 = ___
30 x 2 = ___ 30 x 20 = ___
Fluency
Mental Multiplication
Say the multiplication
sentence in
in unit
unit form.
form.
sentence
4 tens x 2 tens = 8
4 tens
onesxx22==88tens.
ones.
hundreds.
4 x 2 = ___
40 x 2 = ___ 40 x 20 = ___
Fluency
Mental Multiplication
Say the multiplication
sentence in
in unit
unit form.
form.
sentence
5 tens x 3 tens = 15
5 5tens
x 3x =3 15
tens.
ones
= 15
ones.
hundreds.
5 x 3 = ___
50 x 3 = ___ 50 x 30 = ___
Application Problem
5 Minutes
Write an equation to find the unknown length of
each rectangle. Then find the sum of the two
unknown lengths.
Lesson 20
Application Problem
5 Minutes
Write an equation to find the unknown length of
each rectangle. Then find the sum of the two
unknown lengths.
Lesson 20
Concept Development
Lesson 20
Problem 1: Decompose 48 ÷ 4 from whole to part.
• Draw a rectangle with an area of 48
square units and a width of 4 units.
Draw a rectangle with an area of 48 square units and a width of 4 units.
S: (Draw.)
T: Draw a new rectangle with the same area directly below but partitioned to match the areas of the
rectangles in Part (a) of the Application Problem.
Concept Development
Lesson 20
Problem 1: Decompose 48 ÷ 4 from whole to part.
• Draw a new rectangle with the same area directly below
but partitioned to match the areas of the rectangles in
Part (a) of the Application Problem.
Draw a rectangle with an area of 48 square units and a width of 4 units.
S: (Draw.)
T: Draw a new rectangle with the same area directly below but partitioned to match the areas of the
rectangles in Part (a) of the Application Problem.
Concept Development
Lesson 20
Problem 1: Decompose 48 ÷ 4 from whole to part.
• Draw a number bond to match the whole and parts of
the rectangle.
Draw a rectangle with an area of 48 square units and a width of 4 units.
S: (Draw.)
T: Draw a new rectangle with the same area directly below but partitioned to match the areas of the
rectangles in Part (a) of the Application Problem.
Concept Development
Lesson 20
Problem 1: Decompose 48 ÷ 4 from whole to part.
• Let’s find the unknown side lengths of the smaller
rectangles and add them.
Draw a rectangle with an area of 48 square units and a width of 4 units.
S: (Draw.)
T: Draw a new rectangle with the same area directly below but partitioned to match the areas of the
rectangles in Part (a) of the Application Problem.
Take a moment to
record the number
sentences, reviewing
with your partner their
connection to both the
number bond and the
area model.
What is 10 and 2?
What is 8 ÷ 4?
What
is 48 of
divided
by 4? side?
What is the
length
the unknown
Concept Development
Lesson 20
Problem 1: Decompose 48 ÷ 4 from whole to part.
• Work with your partner to partition the same area of 48
as 2 twenties and 8.
Draw a rectangle with an area of 48 square units and a width of 4 units.
S: (Draw.)
T: Draw a new rectangle with the same area directly below but partitioned to match the areas of the
rectangles in Part (a) of the Application Problem.
Concept Development
Lesson 20
Problem 1: Decompose 48 ÷ 4 from whole to part.
• Try to find another way to partition the area of 48 so it’s
easy to divide. You have 4 minutes – get to work!
Draw a rectangle with an area of 48 square units and a width of 4 units.
S: (Draw.)
30II did
and
18
T: Draw a new rectangle with the same area directly below
but
bydon’t
4to match the areas of the
saiditpartitioned
24
+using
24. work
24
well because
rectangles in Part (a) of the Application Problem.
rectangles,
with
divided
by 4each
is30
6.has
6 + a6
Did anyone find
remainder
when
you
an
area of
12
square
is 12.
another way to
divided
it by 4.
units.
12+12+12+12.
partition the area
of 48 it’s easy to
divide?
Concept Development
Lesson 20
Problem 1: Decompose 48 ÷ 4 from whole to part.
• Explain to your partner why different ways of partitioning
give us the same correct side length.
I use the same break
sumofof4 the
You can take a total,
Drawapart
a rectangle
with an area of 48 square units and aThe
width
units.
and distribute
lengths is the
break it into two parts,
S: (Draw.)
strategy to find the
same as the
andareas
divideofeach
T: Draw
a newto
rectangle
the of
answer
56 ÷ 8. with the same area directly below but partitioned to match the
whole
length
them separately.
rectangles40in÷Part
8 is (a)
5. of the Application Problem.
16 ÷ 8 is 2.
5 and 2 makes 7.
You are starting with
the same amount of
area but just chopping
it up differently.
Repeat the
process we just
Remember
Part B of our
used
to
partition the
Application Problem?
area of 96.
5 Minutes
Find a different
to
Write anway
equation
to find the unknown length of
decompose
each
rectangle. Then find the sum of the two
the problem.
unknown lengths.
Lesson 20
Concept Development
Lesson 20
Problem 2: Decompose 96 ÷4 from whole to part.
• How did you partition
the area of 96?
Did anyone
chop
96square
into units and a width of 4 units.
Draw a•rectangle
with an area
of 48
S: (Draw.) 40 + 40 + 16. It was just
T: Draw a new
likerectangle
48 ÷ 4.with the same area directly below but partitioned to match the areas of the
rectangles in Part (a) of the Application Problem.
Lesson 20
Concept Development
Problem 2: Decompose 96 ÷4 from whole to part.
• Did anyone partition 96 into 4 twenties and 2 eights?
Draw a rectangle with an area of 48 square units and a width of 4 units.
S: (Draw.)
T: Draw a new rectangle with the same area directly below but partitioned to match the areas of the
rectangles in Part (a) of the Application Problem.
4 twenties
2 eights
Concept Development
Lesson 20
Problem 2: Decompose 96 ÷4 from whole to part.
• Who made 96 into 2 forty-eights and used our answer from 48
÷ 4? All you had to do was double it.
Draw a rectangle with an area of 48 square units and a width of 4 units.
S: (Draw.)
T: Draw a new rectangle with the same area directly below but partitioned to match the areas of the
rectangles in Part (a) of the Application Problem.
Concept Development
Lesson 20
Problem 3: Compose 96 ÷4 from part to whole..
96 ÷ 4
• Thinking about area, let’s try a new way to divide. The expression 96 ÷ 4
describe
rectangle
with
anand
area
of 96
Draw acan
rectangle
with anaarea
of 48 square
units
a width
of 4square
units. units. We are trying
S: (Draw.)
to find out the length of the unknown side.
T: Draw a new rectangle with the same area directly below but partitioned to match the areas of the
• What is the known side length?
rectangles in Part (a) of the Application Problem.
• 4.
Concept Development
Lesson 20
Problem 3: Compose 96 ÷4 from part to whole..
96 ÷ 4
• 4 times how many tens gets us as close as possible to an area
of 9 tens?
Draw a rectangle
with an area of 48 square units and a width of 4 units.
• 2 tens.
S: (Draw.)
• Let’s give 2 tens to the
T: Draw a new rectangle with the same area directly below but partitioned to match the areas of the
length.
rectangles in Part
(a) of the Application Problem.
• Let’s record the 2 tens
in the tens place.
• What is 4 times 2 tens?
Concept Development
Lesson 20
Problem 3: Compose 96 ÷4 from part to whole..
96 ÷ 4
Draw a• rectangle
8 tens.with an area of 48 square units and a width of 4 units.
S: (Draw.)
• a How
many square
unitsarea directly below but partitioned to match the areas of the
T: Draw
new rectangle
with the same
rectanglesisinthat?
Part (a) of the Application Problem.
• 80 square units.
• How many tens remain?
• 1 ten.
Concept Development
Lesson 20
Problem 3: Compose 96 ÷4 from part to whole..
96 ÷ 4
Draw •a rectangle
withthe
an area
of 48 square units and a width of 4 units.
Let’s add
remaining
S: (Draw.)
the 6with
ones.
T: Draw aten
new to
rectangle
the What
same area directly below but partitioned to match the areas of the
rectanglesisin1Part
Application Problem.
ten(a)+of6 the
ones?
• 16.
Concept Development
Lesson 20
Problem 3: Compose 96 ÷4 from part to whole..
• We have 16 square units remaining
with a width of 4.
• 4 times how many ones gets us as close
as possible to an area of 16 ones?
Draw a rectangle with an area of 48 square units and a width of 4 units.
• 4 ones.
S: (Draw.)
T: Draw•a new
rectangle
the same
area
directly below but partitioned to match the areas of the
Let’s
give 4with
ones
to the
length.
rectangles in Part (a) of the Application Problem.
• What is 4 times 4?
• 16. We have 16 square units.
• We have no more area to divide.
• Tell me the length of the unknown side.
• 24!
• Our quotient tells us that length.
Concept Development
Lesson 20
Problem 3: Compose 96 ÷4 from part to whole..
• How can we express the length of the unknown side using the
distributive
Draw a rectangle
with an areaproperty?
of 48 square units and a width of 4 units.
S: (Draw.) • (80 ÷ 4) + (16 ÷ 4)
T: Draw a new rectangle with the same area directly below but partitioned to match the areas of the
With
arrows to connect the distributive
rectangles•in Part
(a)your
of the partner,
Applicationdraw
Problem.
property and the area model.
Concept Development
Lesson 20
Problem 3: Compose 96 ÷4 from part to whole..
Draw a rectangle with an area of 48 square units and a width of 4 units.
S: (Draw.)
T: Draw a new rectangle with the same area directly below but partitioned to match the areas of the
rectangles in Part (a) of the Application Problem.
Concept Development
Problem 3: Compose 96 ÷4 from part to whole..
• Review our four drawings and our process with your partner.
Try to reconstruct what we did step by step before we try
another one.
We solved 96 divided by 4 in
two very different ways
using the area model. First,
we started with the whole
rectangle and partitioned it.
The second way was to go
one place value at a time
and make the whole
rectangle from parts.
We’re
ready!
Bring it on!
Lesson 20
Problem Set
10 Minutes
Problem Set
10 Minutes
Problem Set
10 Minutes
• In Problem 2, did you partition the rectangle
the same way as your partner? Why were
we able to go from whole to part?
Problem Set
10 Minutes
• In Problems 2 and 3, explain the connection
between the written method, the number
bond, and the area model.
Problem Set
10 Minutes
Debrief
Lesson Objective:
Solve division
problems without
remainders using
the area model.
• In the last problem, explain the
connection between the algorithm and
the area model.
• Each time we divide, what happens to
the amount of area we still have left to
divide?
• Even though division is messy, I think it is
the most interesting operation of all
because, imagine this, sometimes that
little piece that is left to divide is always
there, even though it gets infinitely
small!
• Talk to your partner about what you
think I might mean by that.
Exit Ticket
Lesson 1