Math Module 3
Multi-Digit Multiplication and Division
Topic F: Reasoning with Divisibility
Lesson 24: Determine whether a whole number is a multiple of another number.
4.OA.4
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Lesson 24
Target
Determine whether a
whole number is a
multiple of another
number.
•3
•6
•9
• 12
•9
•6
•9
• 12
• 15
• 18
• 15
• 12
• 15
• 18
• 21
• 24
• 21
• 18
• 15
• 12
• 15
• 18
• 21
• 24
• 27
• 24
• 21
• 24
• 27
• 30
Group
Counting
(5 minutes)
• Count by threes to
30 and change
directions when
you see the arrow.
You
did it!
Fluency
Lesson 24
•5
• 10
• 15
• 20
• 15
• 10
• 15
• 20
• 25
• 30
• 25
• 20
• 25
• 30
• 35
• 40
• 35
• 30
• 25
• 20
• 25
• 30
• 35
• 40
• 45
• 40
• 35
• 40
• 45
• 50
Group
Counting
(5 minutes)
• Count by fives to
50 and change
directions when
you see the arrow.
You
did it!
Fluency
Lesson 24
•2
•4
•6
•8
•6
•4
•6
•8
• 10
• 12
• 10
•8
• 10
• 12
• 14
• 16
• 14
• 12
• 10
•8
• 10
• 12
• 14
• 16
• 18
• 16
• 14
• 16
• 18
• 20
Group
Counting
(5 minutes)
• Count by twos to
20 and change
directions when
you see the arrow.
You
did it!
Fluency
Lesson 24
• 10
• 20
• 30
• 40
• 30
• 20
• 30
• 40
• 50
• 60
• 50
• 40
• 50
• 60
• 70
• 80
• 70
• 60
• 50
• 40
• 50
• 60
• 70
• 80
• 90
• 80
• 70
• 80
• 90
• 100
Group
Counting
(5 minutes)
• Count by tens to
100 and change
directions when
you see the arrow.
You
did it!
Fluency
Lesson 24
•4
•8
• 12
• 16
• 12
•8
• 12
• 16
• 20
• 24
• 20
• 16
• 20
• 24
• 28
• 32
• 28
• 24
• 20
• 16
• 20
• 24
• 28
• 32
• 36
• 32
• 28
• 32
• 36
• 40
Group
Counting
(5 minutes)
• Count by fours to
40 and change
directions when
you see the arrow.
You
did it!
Fluency
Lesson 24
•6
• 12
• 18
• 24
• 18
• 12
• 18
• 24
• 30
• 36
• 30
• 24
• 30
• 36
• 42
• 48
• 42
• 36
• 30
• 24
• 30
• 36
• 42
• 48
• 54
• 48
• 42
• 48
• 54
• 60
Group
Counting
(5 minutes)
• Count by sixes to
60 and change
directions when
you see the arrow.
You
did it!
Fluency
Lesson 24
Fluency
Lesson 24
Prime or Composite?
Prime
or
5
Composite
Write the factor pair.
Fluency
Lesson 24
Prime or Composite?
Prime
or
15
Composite
Write the factor pairs.
Fluency
Lesson 24
Prime or Composite?
Prime
or
12
Composite
Write the factor pairs.
Fluency
Lesson 24
Prime or Composite?
Prime
or
19
Composite
Write the factor pair.
Fluency
Lesson 24
Prime or Composite?
Prime
or
24
Composite
Write the factor pairs.
Fluency
Test for Factors
30 45 48 56
• Write down the
numbers that have
10 as a factor.
Lesson 24
Fluency
Test for Factors
Lesson 24
• Write the division
equations that prove
both 5 and 6 are
factors of 30.
5=6
Fluency
Test for Factors
30 45 48 56
• Write down the
numbers that have 6
as a factor.
Lesson 24
Fluency
Test for Factors
30 = 3 x 10
= 3 x (2 x 5)
= (3 x 2) 5
Lesson 24
• Prove that both 3
and 2 are factors of
30 using the
associative property.
Fluency
Test for Factors
48 = 24 x 2
= (8 x 3) x 2
= 8 x (3 x 2)
Lesson 24
• Prove that both 3
and 2 are factors of
48 using the
associative property.
Fluency
Test for Factors
56 45 48 30
• Write down the
numbers that have 8
as a factor.
Lesson 24
Fluency
Test for Factors
48 = 24 x 2
= (6 x 4) x 2
= 6 x (4 x 2)
Lesson 24
• Prove that both 4
and 2 are factors of
48 using the
associative property.
Fluency
Test for Factors
56 = 28 x 2
= (7 x 4) x 2
= 7 x (4 x 2)
Lesson 24
• Prove that both 4
and 2 are factors of
56 using the
associative property.
Application Problem
5 minutes
8 cm × 12 cm = 96 square centimeters. Imagine a rectangle with an
area of 96 square centimeters and a side length of 4 centimeters.
What is the length of its unknown side? How will it look when
compared to the 8 by 12 rectangle? Draw and label both rectangles.
Lesson 24
Concept Development
Lesson 24
Problem 1: Determine the meaning of the word multiple.
• Turn to your partner and count by fours, taking turns
with each new number. So, for example, you start by
saying 0, your partner says 4, then you say 8. You have
Stop!
What
Your
one minute. Ready? Begin.
Tell me some
number did
things
you
turn!
you count up
noticed!
to?
Go!
80
24
16
412
20
28
Concept Development
We started by
saying the 4
times table,
then kept
adding on 4.
When we
got to 100,
the
counting
started over
again.
Lesson 24
Problem 1: Determine the meaning of the word multiple.
Just like we started with
0, 4, 8, 12, after 100 it
was 104, 108, 112, and
so on.
There was a
pattern with
how the
numbers
ended.
Concept Development
Problem 1: Determine the meaning of the word multiple.
When we skip-count
by aThose
whole
arenumber,
nice
observations.
Let’s
try that
the numbers
that
we
again,
where
saybeginning
are called
you leftmultiples.
off. This time, as
you count, think about
Talk patterns
to yourthere
partner
what
are.
about what you
Ready?
Begin.
noticed.
Lesson 24
Lesson 24
Concept Development
All of the
multiples of 4
were even
numbers.
No matter
how high
we counted
we kept
adding on 4
more.
Problem 1: Determine the meaning of the word multiple.
The digit in the
ones place of
every number
followed its
own pattern. It
went 0, 4, 8, 2,6
over and over
again.
Concept Development
Lesson 24
Problem 1: Determine the meaning of the word multiple.
• Study this visually. This pattern in the ones
place continues forever! Why?
• Because it is always 4 more. If that’s what
has been happening, then the same things
will keep happening. It worked up to 1
hundred, and the ones and tens place will
continue with the same pattern, so it will
even work in the two hundreds and three
hundreds. 4 times 25 is 100, so then in every
hundred it repeats, and so it just keeps going
in cycle!
• How is a multiple different from a factor?
• When we found the factors of a number, we
listed them and then we were done. With
multiples, we could keep going forever and
ever!
Concept Development
Lesson 24
Problem 2: Determine if one number is a multiple of another number and list multiples of given numbers.
When we count
that! Use the
by
we get
No,fours
because
we Try We
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a
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to
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Application
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of
24.
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divided
by
5
that
8
times
12
and
4
And
3 is
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24.
Well,
8
divisible by
3.
We
might
can
we
find
out
if
Problem,
since
4
Is
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a
times
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are
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the
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is a factor
of 24,
96times
is a multiple
24 is 96.of
use the
associative
Application
Problem.
multiple
of
4?
3? 5?
associative
so remainder.
24
must
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What
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Also,
5 is of
a not
of
to figure
that
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multiple
8. 12 and
that
8 times
4 8?
out?
a factor of 24.
times 24 are 96 from the
Application Problem.
Lesson 24
Since zero times
any
number
is
Concept Development
Problem 2: Determine if one number is a multiple of another number and list multiples of given numbers.
zero, zero is a multiple of every
number. So we could consider it
There
was
no
the first multiple of every number.
No.
It’s
less.
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remainder
so
30isa
However, when
we skip-count,
we
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times
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count
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32
factor
of
96.
Yes!
32!
3.
number
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of
five
we’re counting
So,
we
usually
12,by.
15.
you
factor
pair
3?
three
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maybe?
96
a
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get
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32?
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case 3, as the
first
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multiple 0of
3.
to
first?
96?
instead of 0. That way, the first
multiple is 1 × 3, the second is 2 ×
3, and so on.
Concept Development (Optional)
Lesson 24
Problem 3: Use the associative property to see that any multiple of 6 is also a multiple of 3 and 2.
•
•
•
•
•
•
Shout out a multiple of 6.
Is any multiple of 6 also a multiple of 2 and 3?
Let’s use the associative property (and commutative property) to find out.
60 = 10 × 6
= 10 × (2 × 3)
= (10 × 2) × 3= 20 × 3 Yes, 60 is a multiple of 3. If we count by 3 twenty times, we
get to 60.
• = (10 × 3) × 2= 30 × 2 Yes, 60 is a multiple of 2. If we count by 2 thirty times, we
get to 60.
• Let’s use a letter to represent the number of sixes to see if this is true for all sixes.
Concept Development (Optional)
Lesson 24
Problem 3: Use the associative property to see that any multiple of 6 is also a multiple of 3 and 2.
• n × 6 = n × (2 × 3)
• n × 6 = (n × 2) × 3
• n × 6 = (n × 3 ) × 2
• Discuss with your partner why these equations are true. You might try plugging in
4 or 5 as the number of sixes, n, to help you understand.
• It takes twice as many threes to get to the multiple as sixes. It’s double the
number of multiples of six, 2 × n. And it’s three times as many twos to get
there! It’s because twos are smaller units so it takes more.
• So maybe the multiples of a number are also the multiples of its factors.
Problem Set
10 Minutes
Problem
Set
• In Problem 1, which
multiples
were the
10 Minutes
easiest to write, the fives, fours, or sixes?
Why?
What
strategy
did you
use in
Problem
2?
Problem Set
10 Minutes
Problem Set
10 Minutes
In Problem 5 (c) and
(d), what patterns did
you discover about
multiples of 5 and 10?
Debrief
Lesson Objective:
Determine whether a
whole number is a
multiple of another
number.
• Explain the difference between factors and
multiples.
• Which number is a multiple of EVERY
number?
• How can the associative property help you
to know if a number is a multiple of
another number?
• Did anybody answer “no” on Problem 4?
What about 1? Are prime numbers
multiples of 1?
• In the lesson we found that when counting
by fours, the multiples followed a pattern
of having 0, 4, 8, 2, and 6 in the ones digit.
Does that mean any even number is a
multiple of 4?
Exit Ticket
Lesson 1