Math Module 3
Multi-Digit Multiplication and Division
Topic F: Reasoning with Divisibility
Lesson 22: Find factor pairs for numbers to 100 and use understanding of factors to
define prime and composite.
4.OA.4
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Lesson 22
Target
You will find factor pairs
for numbers to 100 and
use understanding of
factors to define prime and
composite.
Fluency
Write a division expression for
this area model.
Divide Using the Area Model
68 ÷2
68
60
Lesson 22
Label the length of each
rectangle in the area model.
8
Solve using the standard
algorithm or the
distributive property with
a number bond.
(60÷2) + (8÷2)
= 30 + 4
34
2
30
4
60
8
Fluency
Write a division expression for
this area model.
Divide Using the Area Model
96 ÷3
96
90
Lesson 22
Label the length of each
rectangle in the area model.
6
Solve using the standard
algorithm or the
distributive property with
a number bond.
(90÷3) + (6÷3)
= 30 + 2
32
3
30
2
90
6
Fluency
Write a division expression for
this area model.
Divide Using the Area Model
72 ÷3
72
69
Lesson 22
Label the length of each
rectangle in the area model.
3
Solve using the standard
algorithm or the
distributive property with
a number bond.
(69÷3) + (3÷3)
= 23 + 1
24
3
23
1
69
3
Fluency
Write a division expression for
this area model.
Divide Using the Area Model
72 ÷4
72
68
Lesson 22
Label the length of each
rectangle in the area model.
4
Solve using the standard
algorithm or the
distributive property with
a number bond.
(68÷3) + (4÷4)
= 17 + 1
18
4
17
1
68
4
Lesso
Fluency Development
Find the Unknown Factor.
9÷3=3
3 x ___ = 9
Lesso
Fluency Development
Find the Unknown Factor.
16 ÷ 4 = 4
4 x ___ = 16
Lesso
Fluency Development
Find the Unknown Factor.
45 ÷ 5 = 9
5 x ___ = 45
Lesso
Fluency Development
Find the Unknown Factor.
42 ÷ 6 = 7
6 x ___ = 42
Lesso
Fluency Development
Find the Unknown Factor.
56 ÷ 7 = 8
7 x ___ = 56
Lesso
Fluency Development
Find the Unknown Factor.
72 ÷ 9 = 8
9 x ___ = 72
Lesso
Fluency Development
Find the Unknown Factor.
54 ÷ 6 = 9
6 x ___ = 54
Lesso
Fluency Development
Find the Unknown Factor.
63 ÷ 7 = 9
7 x ___ = 63
Lesso
Fluency Development
Find the Unknown Factor.
54 ÷ 9 = 6
9 x ___ = 54
Lesson 22
Fluency
Mental Multiplication
4 × 20 = ____.
4 × 2 = ____.
2 × 40 = ____.
20 x 40 =____
Fluency
Mental Multiplication
3 × 30 = ____.
3 × 3 = ____.
30 × 30 = ____.
Lesson 22
Fluency
Mental Multiplication
3 × 40 = ____.
3 × 4= ____.
30 × 40 = ____.
Lesson 22
Application Problem
Divide Using the Area Model
8 × ____ = 96.
Find the unknown side length, or
factor. Use an area model to solve
the problem.
Lesson 22
Lesson 22
Concept Development
Problem 1: Identify the factors and product represented in an array.
========
1x8=8
factors
product
====
====
2x4=8
factors
• Tell your partner the multiplication sentences that are represented by these
arrays.
• Both arrays show a product of 8. The factors 1 and 8, and 2 and 4, are
multiplied to give a product of 8.
• 1, 2, 4, and 8 are all factors of 8.
product
Concept Development
Lesson 22
Problem 1: Identify the factors and product represented in an array.
==================
1 x 18 = 18
=========
=========
2 x 9 = 18
(1, 2, 9, 18)
• What product is represented in both arrays?
• Record the multiplication sentences for each array.
• Circle the factors.
• Write the factors of 18 that are represented in
order from least to greatest.
• With your partner, draw an array to represent
another pair of factors with the product of 18.
Concept Development
Lesson 22
Problem 1: Identify the factors and product represented in an array.
==================
======
1 x 18 = 18
======
======
=========
3 x 6 = 18
========= • What new factors of 18 did you find?
2 x 9 = 18
(1,(1,
2,2,
3,9,
6,18)
9, 18)
• 3 and 6.
• Revise your list of factors of 18.
• How can we make sure we found all
of the factors of 18?
Concept Development
Problem 1: Identify the factors and product represented in an array.
•But what if the
number
is really
How can we make sure we found all of the factors of 18?
I canbig,
think
like 92?
I don’t
I could
draw
arrays
through
my
know
all the
factors
to find
all the
multiplication
of factors,
92.
making
Ifacts.
can use
myof 3, then 4,
rows
multiplication
then 5 and all the
That will take a long
chart. way to 92.
time!
Lesson 22
Concept
Development
Notice that 3 and 6 are the middle pairs. We’ve checked everything up to 3, and
Lesson 22
Problem 1: Identify the factors and product represented in an array.
the counting numbers between 3 and 6 are not factors of 18, so we found all the
pairs. Try that with the factors of 8.
Look at the list of factors for 18. Draw an arrow from 1 to 18.
1, 2, 3, 6, 9, 18
These are factor pairs because 1 x 18 = 18. With your partner,
draw the rest of the arrows to connect the factor pairs.
Concept Development
Problem 1: Identify the factors and product represented in an array.
1, 2, 4, 8
Lesson 22
Concept Development
Lesson 22
Problem 2: Identify factors to define prime and composite numbers.
2 x 8 = 16
• What are the factors?
• 2 and 8.
• What other multiplication sentences can you write, using different factors, that will give
us the same product?
• 1 × 16 = 16. 4 × 4 = 16.
• So, what are all of the factors of 16?
• 1, 2, 4, 8, and 16.
• How do you know those are all of the factors of 16?
I stopped at 8, too,
because it was half of
16. There isn’t a factor
between 1 and 2, so I
guess we never need
to go beyond the
halfway point.
Lesson
22
I
listed
them
Concept Development
Problem 1: Identify the factors and product represented in an array.
in order.
When I got to
How do you know those are all of the factors of 16?
8, I noticed I
already had
its factor pair.
Two times 8
is 16, so I
didn’t have
to go any
further
Concept Development
Problem 2: Identify factors to define prime and composite numbers.
1, 2, 4, 8, 16
Lesson 22
If we drew
Concept Development
arrays to Problem 2: Identify factors to define prime and composite numbers.
represent
factors of 7,
• What are the factors in this equation?
the array for• 1 and 7.
Two,pair
3,for4,7.5, and 6
1 × 7 and 7 •× Find another factor
don’t work. I can’t find
1 would look
7 × 1?
Those
another pair.
the same.
are the same
factors.
There
can’t
1x7=7
be another
pair.
Lesson 22
Concept Development
Lesson 22
Problem 2: Identify factors to define prime and composite numbers.
1x7=7
There are more factor pairs for
8, 10, 16, and 18 than there
are for 7.
Seven has only one pair of
factors, but the other numbers
we looked at had more than
one pair.
I hear you saying that
1 and 7 are the only
factors. Talk to your
partner. How is that
different from the
factors of 8, 10, 16,
and 18?
Concept Development
Problem 2: Identify factors to define prime and composite numbers.
1x7=7
5…
That’s right! Now
think about the
number 5. Name a
pair of factors that
will give us a product
of 5.
1 and 5.
Lesson 22
Concept Development
Problem 2: Identify factors to define prime and composite numbers.
1x7=7
Nope. One times
5 makes 5 just like
1 times 7 is seven.
They both only
have only one set
of factors.
Are there any other
factor pairs?
Lesson 22
Concept Development
Problem 2: Identify factors to define prime and composite numbers.
Numbers like 5 and
7 that have exactly
Lesson 22
Concept Development
Lesson 22
Problem 2: Identify factors to define prime and composite numbers.
11
17
With your
partner, list at
least two more
prime numbers.
13
Concept Development
Lesson 22
Problem 2: Identify factors to define prime and composite numbers.
11
17
If these are prime
numbers, can you
name a number
that is not prime?
13
Concept Development
Problem 2: Identify factors to define prime and composite numbers.
The numbers you
Lesson 22
Lesson 22
Concept Development
Problem 2: Identify factors to define prime and composite numbers.
Let’s use 6 as an example.
======
===
===
==
==
==
• Does 6 have more than two factors?
• Yes! One and 6 are factors, but 2 and 3 are also
factors.
• So, what can we say about the number 6?
• It is composite. It has more than two arrays to
represent it.
=
=
=
=
=
=
Lesson 22
Concept Development
Problem 3: Identify factors of numbers and determine if they are prime or composite.
35
• Let’s use a table to record the factor pairs for 35. Tell me the first factor
pair.
• Is 35 a prime or composite number?
Why?
• Composite, because it has more
than one factor pair.
• With your partner, use a table to list
factors of 23 and 48 and tell if each
one is prime or composite.
Factor Pairs
for 35
1
5
35
7
Lesson 22
Concept Development
Problem 3: Identify factors of numbers and determine if they are prime or composite.
23
• Are any of these numbers prime numbers? How do you know?
• Twenty-three is prime because we
thought about all the possible
factors up to 11 and none worked.
• Why can we stop at the number 11?
• Eleven is the closest whole number
to half of 23. Once I get halfway, I
have found all of the factor pairs.
After that, they just keep repeating.
Factor Pairs
for 23
1
?
23
?
Concept Development
Lesson 22
Problem 3: Identify factors of numbers and determine if they are prime or composite.
48
• Why is 48 composite? Let’s
fill in the factor chart.
• There are more than two
factors.
• It has 6 and 8 as factors.
• It also has 4 and 12.
• I found 10 factors! It sure
isn’t prime!
Factor Pairs for 48
1
48
2
24
3
16
4
12
6
8
Problem Set
10 Minutes
Problem Set
In Problem 1, what numbers have an odd number of factors? Why is that so?
10 Minutes
Compare the factors in Problem 1(e) and 1(l). Twenty-four is double 12. What do you
notice about their factors? Compare the factors in Problem 1(d) and 1(i).
Problem Set
10 Minutes
Problem Set
10 Minutes
Are all prime numbers odd?
Explain what you would tell
Bryan in Problem 3. Problem Set
10 Minutes
Debrief
Lesson Objective: Find
factor pairs for
numbers to 100 and
use understanding of
factors to define
prime and composite.
• Eighteen is double 9. What do you
notice about their factors?
• Explain your answer to Problem 3(b).
Are all even numbers composite?
How many even numbers are not
composite?
• We talked a lot about the number 1
today as being a factor of other
numbers, but we have not classified
it as prime or composite. Can 1 be
composite? (No.) It turns out that it’s
not considered prime either!
Exit Ticket
Lesson 1