LESSON
3.1
Multiply by Tens
FOCUS
COHERENCE
RIGOR
LESSON AT A GLANCE
F C R Focus:
Common Core State Standards
4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit
whole number, and multiply two two-digit numbers, using strategies
based on place value and the properties of operations. Illustrate and
explain the calculation by using equations, rectangular arrays, and/or area models.
Mathematical Practices
MP1 Make sense of problems and persevere in solving them. MP4 Model with mathematics.
MP7 Look for and make use of structure.
F C R Coherence:
Standards Across the Grades
Before
Grade 4 After
3.OA.B.5 4.NBT.B.5 5.NBT.B.5
F C R Rigor:
Level 1: Understand Concepts....................Share and Show ( Checked Items)
Level 2: Procedural Skills and Fluency.......On Your Own
Level 3: Applications..................................Think Smarter and Go Deeper
Learning Objective
Use place value and multiplication properties to
multiply by tens.
Language Objective
Student pairs list the strategies you can use to
multiply by tens.
Materials
MathBoard
F C R For more about how GO Math! fosters Coherence
within the Content Standards and Mathematical Progressions
for this chapter, see page 143J.
About the Math
Professional Development
Number Line Models
A number line is a graphic organizer that helps students
visualize the relative magnitude of numbers.
About the Math
Professional
Development
Students often confuse
left and
right. Consistently
emphasize that numbers are greater moving to the right.
Numbers are lesser moving to the left. In this lesson,
students use number lines to represent multiplication.
25 26 27 28 29 30
greater
It is important for students to understand a number line
because this visual model is used from the earliest primary
grades when students learn to count, well into high school
when students represent and graph situations that involve
integers and rational numbers.
25 30 35 40 45 50
Professional Development Videos
145A Chapter 3
lesser
–3 –2 –1 0 +1 +2 +3
1 ENGAGE
Daily Routines
Common Core
Problem of the Day 3.1
The table shows the heights of some of the
tallest mountains in the world.
Name of Mountain
Height in Feet
Abi Gamin
24,131
Himalchuli
25,896
Lhotse
27,940
Trivor
24,859
How many more feet high is Lhotse than
Himalchuli? 2,044 ft
Vocabulary
with the Interactive Student Edition
Essential Question
What strategies can you use to multiply by tens?
Making Connections
Invite students to tell you what they know about multiplying a
one-digit by a two-digit number.
What methods have you used to multiply numbers? Possible answer:
Repeated addition, mental math How did you determine which method
to use? Possible answer: It depends on the value of the numbers, whether
they end in zero.
Learning Activity
• What are you trying to find in the problem? the number of gallons
of water the fire hose will pump out in 30 minutes
• How many gallons of water can the fire hose pump in one
minute? 95 gallons
™Interactive Student Edition
™Multimedia eGlossary
• How many minutes are they going to pump the hose? 30 min
• What operation can you use to find the answer? multiplication
Fluency Builder
Common Core Fluency
Standard 3.OA.C.7
Multiplication Facts Write the following
examples on the board. Have students
practice multiplication facts by finding the
products. Have students check answers with
a partner.
2×3=6
7 × 3 = 21
9 × 2 = 18
7 × 5 = 35
3 × 6 = 18
6 × 4 = 24
Have students think about how they might use multiplication to
solve the problem.
Literacy and Mathematics
Choose one or more of the following activities.
• Have students find information about fire hoses and write a short
story about how they might find the number of gallons pumped
after 30 minutes.
• Have students write a short story about how they might find the
number of gallons pumped after 30 minutes.
What strategies can
you use to multiply by
tens?
Lesson 3.1
145B
LESSON
3.1
2 EXPLORE
4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers,
DO
NOTstrategies
EDIT--Changes
be made
info” of operations. Illustrate and explain the calculation by using using
based must
on place
valuethrough
and the“File
properties
CorrectionKey=B
equations, rectangular arrays, and/or area models.
Lesson 3.1
Name
Unlock the Problem
Multiply by Tens
Number and Operations in
Base Ten—4.NBT.B.5 Also 4.NBT.A.1
MATHEMATICAL PRACTICES
MP2, MP4, MP7
Essential Question What strategies can you use to multiply by tens?
MATHEMATICAL PRACTICES
MP2 Reason abstractly and
quantitatively. In this problem, various
methods will be introduced to multiply a
2-digit number by a 2-digit number with a
zero in the ones place.
Unlock
Unlock the
the Problem
Problem
Animation for a computer-drawn cartoon
requires about 20 frames per second.
How many frames would need to be
drawn for a 30-second cartoon?
• The phrase “20 frames per second” means
20 frames are needed for each second of
animation. How does this help you know
what operation to use?
One Way
30 groups of 20 frames are
One method is to use place value.
• Why is 2 tens easier to use than 20? Possible
needed, so multiply.
One Way Use place value.
answer: you can just multiply the 2 instead of 20.
Multiply. 30 × 20
Work through the steps with students. Make
sure students understand that they need to
retain the tens, and then express the product
in standard form.
• How do you change 60 tens to a number in
standard form? Possible answer: think of base-ten
You can think of 20 as 2 tens.
60 tens
=_
= 600
Another Way Use the Associative Property.
blocks. 10 tens is equal to 1 hundred. 60 tens is equal
to 6 hundreds. So, the number in standard form is 600.
You can think of 20 as 2 × 10.
= (30 × 2) × 10
Review the Associative Property.
• How is the factor 20 changed? The 20 is
me because I think it is easier to multiply 60 by 10.
Math
Talk
Use Math Talk to focus on
students’ understanding of using
place value to multiply.
• What is the value of the digit 6 in 60? 6 tens
• What place is 10 times greater than the
tens place? hundreds
• What is 10 times greater than 6 tens?
6 hundreds
60 × _
10
=_
600
=_
© Houghton Mifflin Harcourt Publishing Company
Discuss how the factors can be grouped as
(30 × 2) × 10 using both the Commutative
Property and the Associative Property. Help students multiply 60 × 10 = 600. Explain
that multiplying 6 tens by 10 is the same as
multiplying the place value by 10. The place
value of the digit 6 in the product will be in
the hundreds place.
• Which grouping makes the multiplication
easier? Possible answer: (30 × 2) × 10 is easier for
Math
Talk
30 × 20 = 30 × (2 × 10)
Another Way
changed to 2 × 10.
The Associative Property
states that you can group
factors in different ways and
get the same product. Use
parentheses to group the
factors you multiply first.
2
tens
30 × 20 = 30 × _
MATHEMATICAL PRACTICES 7
Look for Structure How
can you use place value to
tell why 60 × 10 = 600?
Possible answer: the value of the
digit 6 in 600 is ten times the value
of the digit 6 in 60.
600 frames would need to be drawn.
So, _
• Compare the number of zeros in each factor to the number
of zeros in the product. What do you notice?
Possible answer: there is one zero in each factor, and there are two zeros in the
product; one from each factor.
Chapter 3
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3
Reteach 3.1
Enrich 3.1
2
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DO NOT EDIT--Changes must be made through "File info"
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1
Lesson 3.1
Reteach
Name Differentiated
Instruction
Lesson 3.1
Enrich
Name
Multiply by Tens
Multiplying with Tens
Solve each problem.
One section of seating at an arena has 30 rows. Each row has 40 seats.
How many seats in all are in that section?
1.
Juice boxes come in cases of 24.
A school ordered 480 juice boxes.
How many cases of juice boxes did
the school order?
3.
A bank received a supply of
2,000 quarters. Each roll of quarters
has 40 quarters in it. How many rolls
of quarters did the bank receive?
Multiply. 30 3 40
Step 1 Think of each factor as a multiple
of 10 and as a repeated addition.
2.
John has 630 baseball cards. He sorts
the cards into stacks of 30 cards. How
many stacks can he make?
4.
There are 10 tickets in each strip of
carnival tickets. A total of 3,850 tickets
were sold in one day. How many strips
of tickets were sold that day?
30 5 3 3 10 or 10 1 10 1 10
40 5 4 3 10 or 10 1 10 1 10 1 10
40
Step 2 Draw a diagram to show
the multiplication.
Step 3 Each small square in the diagram
shows 10 3 10, or 100 . Count the
squares.
There are 12 squares of 100 .
Step 4 Use patterns and mental math to
find 12 3 100.
30
10
10
10
10
10
100
100
100
100
10
100
100
100
100
10
100
100
100
100
12 3 1 5
20 cases
12
21 stacks
385 strips of tickets
50 rolls
12 3 10 5 120
12 3 100 5 1,200
There are 1,200 seats in that section.
Explain what strategy you used to solve Problem 3.
5.
1. 20
3 90 5
Methods will vary.
1,800 2. 40 3 40 5 1,600 3. 60 3 70 5 4,200
4. 50
3 30 5
1,500
Choose a method. Then find the product.
145 Chapter 3
Chapter Resources
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4_MNLEAN343085_C03R01.indd 5
5. 80
3 60 5
3-5
4,800
6. 90
3 40 5
3,600
Reteach
Possible explanation: I wrote the equation
40 3 n 5 2,000, and worked backward to find 50.
I used 4 3 n 5 20. I know 4 3 5 is 20, so 40 3 50 5
2,000.
Chapter Resources
© Houghton Mifflin Harcourt Publishing Company
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4_MNLEAN343085_C03E01.indd 6
3-6
Enrich
2/12/14 2:22 PM
Other Ways
Example A shows a number line as another
method used to multiply 2-digit numbers.
• Why do you think the second number line
shows intervals of 20? Possible answer: I need to
Other Ways
A Use a number line and a pattern to multiply 15 × 20.
skip count by 20, 15 times.
Draw jumps to show the product.
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
0
20
40
60
80 100 120 140 160 180 200 220 240 260 280 300
• How is the number line helpful in finding
the product? Possible answer: it shows the numbers
30
15 × 2 = __
30
in order, and you can make sure that the product
makes sense because of the order of the numbers.
Example B shows how to use mental math to
multiply 2-digit numbers.
• Why is the number 14 divided by 2? so that
300
15 × 20 = __
B Use mental math to find 14 × 30.
we can use an easier number, 7, to multiply with
Use the halving-and-doubling strategy.
STEP 1 Find half of 14 to make
STEP 2 Multiply.
STEP 3 Double 210.
• Why do you use doubling in Step 3? I divided
Think: To double a
number, multiply by 2.
Try This!
by 2 in Step 1, so now I need to multiply by 2.
the problem simpler.
Think: To find half of
a number, divide by 2.
7
14 ÷ 2 = __
210
7 × 30 = __
Have students use the two methods: mental
math and place value to find 12 × 40.
MP3 Construct viable arguments and
critique the reasoning of others.
• How would you choose mental math or
place value, to multiply a 2-digit number by
a tens number? Possible answer: if I could multiply
420
2 × 210 = __
So, 14 × 30 = 420.
Multiply.
Use mental math to find 12 × 40.
Possible answer:
Think half of 12 is 6.
6 × 40 = 240
2 × 240 = 480
Share
Share and
and Show
Sh
Use place value to find 12 × 40.
12 × 40 = 12 × 4 tens
= 48 tens
= 480
MATH
BOARD
1. Find 20 × 27. Tell which method you chose. Explain what happens
in each step.
540; possible answer: mental math; since 2 × 27 = 54, then 20 × 27 is 540.
the 2-digit number by the nonzero digit in the tens
number without regrouping, I would use mental math.
Otherwise, I would use place value to break apart the
2-digit number.
ELL Strategy:
Model Concepts
Form teams of students of mixed English
proficiency levels.
• Review the definition of the Associative
Property of Multiplication. Have students
role play the parts of an equation, holding
signs to represent their part.
146
Advanced Learners
© Houghton Mifflin Harcourt Publishing Company
Try This!
Logical / Mathematical
Partners
• Students rephrase key terms in words or
with numbers and quick drawings.
• Have students make up a problem similar to the
following:
The product of my number and twice my number
is 200. What is half my number? 5
• Students should make sure that both factors (their
number and twice their number) are 2-digit numbers.
• Have students trade problems with a partner
to solve.
The product of my number
and twice my number is
800. What is half my
number?
The product of my number
and twice my number is
1,800. What is half my
number?
3 EXPLAIN
Share and Show
MATH
M
A
TH
ATH
TH
BOARD
B
Hands
On
The first problem connects to the learning
model.
Lesson 3.1
146
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CorrectionKey=A
Name
Use the checked exercises for Quick Check.
Students should show their answers for the
Quick Check on the MathBoard.
Choose a method. Then find the product.
2. 10 × 12
3. 20 × 20
120
Methods will vary.
4. 40 × 24
400
5. 11 × 60
960
660
Math
Talk
Use Math Talk to focus on students’
understanding of using place value
to multiply.
Possible explanation: think of 12 as
10 + 2. So 10 × 30 is 300 and 2 × 30 is
60. 300 + 60 = 360
• How can you use place value to break apart
12? 12 = 10 + 2
• How does thinking of 12 as 10 ∙ 2 help you
multiply 30 ∙ 12? Possible answer: I can find the
Choose a method. Then find the product.
6. 70 × 55 3,850
7. 17 × 30 510
8. 30 × 60
9. 12 × 90
1,800
1,080
Rt I
Differentiate Instruction with
• Reteach 3.1
• Personal Math Trainer 4.NBT.B.5
• RtI Tier 1 Activity (online)
On Your Own If students complete the checked exercises
correctly, they may continue with the
remaining exercises.
MP2 Reason abstractly and quantitatively. Exercises 10–12 require students to use higher
order thinking skills as they find the unknown
digit in each product. Encourage students to
use place value to reason about the result of
the factors being multiplied.
COMMON ERRORS
Error Students may make errors in placing
zeros in the product when using place value.
Example 12 ∙ 40 ∙ 12 ∙ 4 tens ∙ 48
tens ∙ 4,800
Springboard to Learning Have students
use base-ten blocks to check their product.
Remind students of how to trade 10 tens for 1 hundred. Have them trade the tens for hundreds and record the number of hundreds and tens they have now: 4 hundreds 8 tens. Have students write the value of the base-ten blocks: 480.
© Houghton Mifflin Harcourt Publishing Company
Then
2
Reason Quantitatively Algebra Find the unknown digit in the number.
10. 64 × 40 = 2,56■
© Houghton Mifflin Harcourt Publishing Company
If
If
a student misses the checked
exercises
11. 29 × 50 = 1,
0
■=_
13.
50
4
=_
DEEPER
Caroline packs 12 jars of jam in
a box. She has 40 boxes. She has 542 jars of
jam. How many jars of jam will she have left
when all the boxes are full?
62 jars
12. 3
■
MATHEMATICAL
PRACTICE
147 Chapter 3
Methods will vary.
■
3
3
2
2
1
1
MATHEMATICAL PRACTICES 7
Identify Relationships
How can you use
30 × 10 = 300 to
find 30 × 12?
On
On Your
Your Own
Own
partial products of 30 × 10 and 30 × 2 and add them
together. I already know that 30 × 10 = 300, and
30 × 2 = 60. 300 + 60 = 360
Quick Check
Math
Talk
14.
× 47 = 1,410
0
=_
DEEPER
Alison is preparing for a
math contest. Each day, she works on
multiplication problems for 20 minutes and
division problems for 10 minutes. How many
minutes does Alison practice multiplication
and division problems in 15 days?
450 minutes
Chapter 3 • Lesson 1 147
4_MNLESE342200_C03L01.indd 147
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MATHEMATICAL PRACTICES .0%&-t3&"40/tM",&4&/4&
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4 ELABORATE
Use the table for 15–16.
15.
MATHEMATICAL
PRACTICE
4
Use Graphs How many frames
did it take to produce 50 seconds of Pinocchio?
Animated Productions
950 frames
16.
Date
Released
Frames
per
Second
The Enchanted Drawing
1900
20
©
1911
16
1937
24
1940
19
1960–1966
24
Title
DEEPER
Are there fewer frames in
10 seconds of The Flintstones or in 14 seconds
of The Enchanted Drawing? What is the
difference in the number of frames?
The Flintstones; 40 frames
©
Little Nemo
Snow White and the Seven Dwarfs
©
Pinocchio
The Flintstones™
17.
©
Problem Solving • Applications
MATHEMATICAL PRACTICES
MP4 Model with mathematics.
For Exercises 15 and 16, students need to
use the information in the table to solve the
problems.
SMARTER
The product of my number
and twice my number is 128. What is half my
number? Explain how you solved the problem.
SMARTER
For Exercise 17, students may find it helpful
to test numbers and record their results
in a table to find the number. Then they
are ready to find half of the number.
4; possible explanation: I made a table to
test numbers less than 10 since 10 × 20 =
200. 2 × 8 = 16; 8 × 16 = 128; 8 ÷ 2 = 4
18.
SMARTER
Tanya says that the product of a
multiple of ten and a multiple of ten will always
have only one zero. Is she correct? Explain.
WRITE
Math t Show Your Work
Math on the Spot
Video Tutor
No. The product of two multiples of ten will
Use this video to help students model and
solve this type of Think Smarter problem.
always have at least 2 zeros.
Math on the Spot videos are in the Interactive
Student Edition and at www.thinkcentral.com.
SMARTER
For numbers 19a–19e, select
Yes or No to tell whether the answer is correct.
19a.
28 × 10 = 280
Yes
No
19b.
15 × 20 = 300
Yes
No
19c.
17 × 10 = 17
Yes
No
19d.
80 × 10 = 800
Yes
No
19e.
16 × 30 = 1,800
Yes
No
© Houghton Mifflin Harcourt Publishing Company
19.
148
DIFFERENTIATED INSTRUCTION
D
INDEPENDENT ACTIVITIES
SMARTER
In Exercise 18, students analyze a statement
to decide if there is an error.
SMARTER
Exercise 19 assesses students' ability to find
products when one factor is a multiple of 10.
Students who answer Yes for 19c may only be
looking at the factor 17 and not focusing on
the number of zeros in the answer.
5 EVALUATE Formative
Assessment
Essential Question
Differentiated Centers Kit
Activities
Roomy Dimensions
Students
complete
blue
Activity
Card 3 by
finding the perimeter
and area of a room
Games
Triangle Products
Students
practice
multiplying
by tens to win
(BNFT
spaces on the
gameboard.
Using the Language Objective
Reflect Have student partners make a list to
answer the Essential Question.
What strategies can you use to multiply
by tens? Possible answer: I can use place value, the
Associative Property, a number line, and mental math.
Math Journal
WRITE
Math
Write the steps for how to use a number line
to multiply a 2-digit number by 20. Give an
example.
Lesson 3.1
148
DO NOT EDIT--Changes must be made through “File info”
CorrectionKey=B
Practice and Homework
Name
Lesson 3.1
Multiply by Tens
COMMON CORE STANDARD—4.NBT.B.5
Use place value understanding and properties
of operations to perform multi-digit arithmetic.
Practice and Homework
Choose a method. Then find the product.
Methods will vary.
Use the halving-and-doubling strategy.
1. 16 × 60
Use the Practice and Homework pages to
provide children with more practice of the
concepts and skills presented in this lesson.
Children master their understanding as they
complete practice items and then challenge
their critical thinking skills with Problem
Solving. Use the Write Math section to
determine children’s understanding of content
for this lesson. Encourage children to use their
Math Journals to record their answers.
Find half of 16: 16 ÷ 2 = 8.
Multiply 60 by this number: 8 × 60 = 480
Double this result: 2 × 480 = 960
960
__
2. 80 × 22
3. 30 × 52
1,760
__
4. 60 × 20
1,560
__
1,200
__
Problem
Problem Solving
Solving
5. Kenny bought 20 packs of baseball cards.
6. The Hart family drove 10 hours to their
There are 12 cards in each pack. How many
cards did Kenny buy?
© Houghton Mifflin Harcourt Publishing Company
240 cards
PROFESSIONAL
DEVELOPMENT
7.
vacation spot. They drove an average of
48 miles each hour. How many miles did
they drive?
480 miles
Math Write the steps for how to use a
WRITE
number line to multiply a 2-digit number by 20.
Give an example.
Check students’ work.
Mathematical Practices in Your Classroom
Chapter 3
4_MNLESE342200_C03P01.indd 149
PROFESSIONAL
DEVELOPMENT
07/10/14 7:26 PM
Mathematical Practices in Your Classroom
CCSS.Math.Practice.MP8 Look for and express
regularity in repeated reasoning.
In this lesson, students have opportunities to use various methods and
to look for shortcuts to multiply 2-digit numbers by tens. They see
that they can use their knowledge of place value to multiply by 3 tens
instead of 30, for example. Students see that they can rename numbers
and group factors in different ways to multiply.
Example: To find 20 3 30, students can think of 30 as 3 3 10. Then they
can group the factors, 20, 3, and 10, different ways to multiply.
Provide opportunities for students to look for shortcuts to multiply
2-digit numbers by tens:
• Is there a way to find 70 3 55 mentally? Possible answer:
I thought of 55 as 50 1 5. Then I multiplied 70 3 50 and 70 3 5,
and added the products.
• So you used easier numbers to multiply with. That is a good way
to use the mental math method. Did anyone else find a quick way to multiply 70 3 55? Possible answer: I wrote 70 as 7
tens.
• So you used place value. How did that help you? Possible
answer: instead of multiplying by 70, I multiplied by 7 tens.
50 3 7 tens and 5 3 7 tens. Then I added the products.
149 Chapter 3
149
Lesson Check (4.NBT.B.5)
1. For the school play, 40 rows of chairs are
set up. There are 22 chairs in each row.
How many chairs are there?
880 chairs
2. At West School, there are 20 classrooms.
Each classroom has 20 students. How
many students are at West School?
Continue concepts and skills practice with
Lesson Check. Use Spiral Review to engage
children in previously taught concepts and to
promote content retention. Common Core
standards are correlated to each section.
400 students
Spiral Review (4.OA.A.1, 4.OA.A.2, 4.OA.A.3, 4.NBT.B.4)
number of stickers Max has. How many
stickers does Max have?
8 stickers
5. Allison has 3 containers with 25 crayons
in each. She also has 4 boxes of markers
with 12 markers in each box. She gives
10 crayons to a friend. How many crayons
and markers does Allison have now?
113 crayons and markers
4. Ali’s dog weighs 8 times as much as her cat.
Together, the two pets weigh 54 pounds.
How much does Ali’s dog weigh?
48 pounds
6. The state of Utah covers 82,144 square
miles. The state of Montana covers
145,552 square miles. What is the total
area of the two states?
227,696 square miles
© Houghton Mifflin Harcourt Publishing Company
3. Alex has 48 stickers. This is 6 times the
FOR MORE PRACTICE
GO TO THE
150
Personal Math Trainer
Lesson 3.1
150