ALGEBRA
Lesson 2.1
Name
Multiplication Comparisons
Essential Question How can you model multiplication comparisons?
You can use multiplication to compare amounts. For example,
you can think of 15 = 3 × 5 as a comparison in two ways:
15 is 3 times as many as 5.
15 is 5 times as many as 3.
15
15
5
5
3
5
Operations and Algebraic
Thinking—4.OA.A.1
MATHEMATICAL PRACTICES
MP1, MP4, MP7
3
3
3
3
The Commutative Property
states that you can multiply
two factors in any order and
get the same product.
3
5
Unlock
Unlock the
the Problem
Problem
Carly has 9 pennies. Jack has 4 times as many
pennies as Carly. How many pennies does
Jack have?
• What do you need to compare?
Draw a model and write an equation
to solve.
RECORD
MODEL
Carly
Use the model to write an equation and solve.
n=_×_
n=_
Jack
The value of n is 36.
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Think: n is how many pennies Jack has.
So, Jack has _ pennies.
•
SMARTER
Explain how the equation for 4 is 2 more than
2 is different from the equation for 4 is 2 times as many as 2.
Math
Talk
MATHEMATICAL PRACTICES 1
Describe what is being
compared and explain
how the comparison
model relates to the
equation.
Chapter 2
63
Example Draw a model and write an
equation to solve.
• How many rabbits does Miguel have? _
• How many rabbits does Sara have?
Miguel has 3 times as many rabbits as Sara. Miguel
has 6 rabbits. How many rabbits does Sara have?
MODEL
RECORD
Think: You don’t know how many rabbits Sara has.
Use n for Sara’s rabbits.
Use the model to write an equation and solve.
6=_×_
6=3×_
Think: 3 times what
number equals 6?
The value of n is 2.
Think: n is how many rabbits Sara has.
So, Sara has 2 rabbits.
Try This! Write an equation or a comparison sentence.
A Write an equation.
B Write a comparison sentence.
21 is 7 times as many as 3.
8 × 5 = 40
_=_×_
_ times as many as _ is _ .
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B
1. There are 8 students in the art club. There are 3 times as many
students in chorus. How many students are in chorus?
n=_×_
n=_
The value of
n is _ .
So, there are _ students in chorus.
64
Math
Talk
MATHEMATICAL PRACTICES 6
Explain how you could write
the equation a different way.
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Write an equation and solve.
Name
Draw a model and write an equation.
2. 6 times as many as 2 is 12.
3. 20 is 4 times as many as 5.
Write a comparison sentence.
4. 18 = 9 × 2
5. 8 × 4 = 32
_ is _ times as many as _ .
_ times as many as _ is _ .
On
On Your
Your Own
Own
Write a comparison sentence.
6. 5 × 7 = 35
7. 54 = 6 × 9
_ times as many as _ is _ .
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8.
9.
_ is _ times as many as _ .
DEEPER
One week, Jake and Sally collected canned goods for a
food drive. On Monday, Jake collected 4 boxes and Sally collected
2 boxes. At the end of the week, Jake had 3 times as many boxes as
he had on Monday. Sally had 4 times as many boxes as she had on
Monday. Together, how many boxes of canned goods did they have
at the end of the week?
DEEPER
Nando has 4 goldfish. Jill has
3 goldfish. Cooper has 2 times as many
goldfish as Nando and Jill combined. Write
an equation that compares the number of
goldfish Cooper has with the number of
goldfish that Nando and Jill have.
10.
MATHEMATICAL
PRACTICE
2
Represent a Problem Write
a comparison sentence about pet food that
could be represented using the equation
12 = 4 × 3.
______
______
______
______
Chapter 2 • Lesson 1 65
MATHEMATICAL PRACTICES .0%&-t3&"40/tM",&4&/4&
Unlock
Unlock the
the Problem
Problem
11.
SMARTER
Luca has 72 baseball cards.
This is 8 times as many cards as Han has.
How many baseball cards does Han have?
a. What do you need to find?
____
b. How can you use a model to find the number of cards
Han has?
d. Write an equation and solve.
_=_×_
_=_
So, Han has _ baseball cards.
SMARTER
12.
Complete the statements to describe each model.
24
24
4
4
4
4
4
6
4
66
6
6
6
4
24 is
6
times as many as
.
24 is
times as many as
.
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c. Draw the model.
Practice and Homework
Lesson 2.1
Name
Multiplication Comparisons
COMMON CORE STANDARD—4.OA.A.1
Use the four operations with whole numbers to
solve problems.
Write a comparison sentence.
1. 6 × 3 = 18
2. 63 = 7 × 9
6 times as many as _
3 is _
18 .
_
3. 5 × 4 = 20
_ is _ times as many as _.
4. 48 = 8 × 6
_ times as many as _ is _.
_ is _ times as many as _.
Write an equation.
5. 2 times as many as 8 is 16.
6. 42 is 6 times as many as 7.
7. 3 times as many as 5 is 15.
8. 36 is 9 times as many as 4.
Problem
Problem Solving
Solving
9. Alan is 14 years old. This is twice as old as his
10. There are 27 campers. This is nine times as
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brother James is. How old is James?
11.
many as the number of counselors. How
many counselors are there?
Math Draw a model, and write an
equation to represent “4 times as many as 3 is 12.”
Explain your work.
WRITE
Chapter 2
67
Lesson Check (4.OA.A.1)
1. Write an equation that represents this
comparison sentence.
24 is 4 times as many as 6.
2. Write a comparison sentence that
represents this equation.
5 × 9 = 45
Spiral Review (4.OA.A.3, 4.NBT.A.2, 4.NBT.A.3)
3. Which symbol makes the following
200,000 + 80,000 + 700 + 6?
statement true?
574,908
5. Sean and Leah are playing a computer
game. Sean scored 72,491 points.
Leah scored 19,326 points more
than Sean. How many points did Leah
score?
6. A baseball stadium has 38,496 seats.
Rounded to the nearest thousand, how
many seats is this?
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4. What is the standard form for