Download Multiply Tens, Hundreds, and Thousands

LESSON
2.3
Multiply Tens, Hundreds,
and Thousands
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
MP4 Model with mathematics. MP5 Use appropriate tools strategically. MP7 Look for and make
use of structure. MP8 Look for and express regularity in repeated reasoning.
F C R Coherence:
Standards Across the Grades
Before
Grade 4 After
3.OA.A.3 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
Multiply tens, hundreds, and thousands by
whole numbers through 10.
Language Objective
Students complete the sentence frame, Place
value helps you to multiply tens, hundreds,
and thousands by __________.
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 61J.
About the Math
Professional Development
Teaching for Depth
In this lesson, students are shown different ways to
multiply tens, hundreds, and thousands by a whole
number through 10.
The first strategy involves students’ understanding of
place value. In One Way, students draw a quick picture
of the problem using a square for one hundred and a
square with a T inside for one thousand. Students regroup
as needed to find the answer. In Another Way, students
rewrite the problem using place value. For example,
8 × 200 can be rewritten as 8 × 2 hundreds. Then
students use the basic fact, 8 × 2, to write the answer as
16 hundreds, or 1,600.
In the second strategy, students use patterns to find
products. Students visualize patterns using number lines
and patterns in multiplication problems. As the number
of zeros in a factor increases, the number of zeros in the
product increases.
Professional Development Videos
75A
Chapter 2
Interactive Student Edition
Personal Math Trainer
Math on the Spot
Animated Math Models
iTools: Base-Ten Blocks
iTools: Number Charts
iTools: Number Lines
Daily Routines
Common Core
Problem of the Day 2.3
1 ENGAGE
with the Interactive Student Edition
Essential Question
For Field Day, the students were grouped
into 20 teams of 10 students each. How
many is 20 tens? 200
How does understanding place value help you multiply
tens, hundreds, and thousands?
Vocabulary
Invite students to tell you what they know about place value.
™Interactive Student Edition
™Multimedia eGlossary
Making Connections
What happens to place value as you move from tens to hundreds?
The value is 10 times larger. What happens to place value as you move
from hundreds to thousands? The value is 10 times larger.
Learning Activity
Connect the story to the problem.
Fluency Builder
Materials Digit Cards 0-9 (see eTeacher Resource)
Mental Math Have pairs practice their
multiplication facts. Give partners two sets
of digit cards (0-9). Have students shuffle
the cards and place them facedown in a
single pile on the table. One student turns
over two cards and makes a 2-digit number
with them. The other student states a
multiplication fact with the 2-digit number
as the product or states that it is not
possible. Partners switch roles and continue
until all cards have been played.
• What are you trying to find? how much money the gas station owner
collects in one day
• How much does one gallon of gas cost? $4
• How many gallons of gas were sold? 200
• What does the 2 represent in 200? hundreds
• What expression will you use? 200 × 4
Literacy and Mathematics
Choose one or more of the following activities.
• Ask students to identify the full word that gas is an abbreviation
for. gasoline Have them think of other words that use
abbreviations in that way. bike/bicycle; mic/microphone; phone/
telephone
• Have students work in pairs and explain how they might solve the
problem if only 6 gallons of gas were sold that day, at $4 a gallon.
How does understanding
place value help you
multiply tens, hundreds,
and thousands?
Lesson 2.3
75B
LESSON
2.3
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
NOT
EDIT--Changes
made
"File info"
using
strategies
based onmust
placebevalue
andthrough
the properties
of operations. Illustrate and explain the calculation by using equations,
CorrectionKey=B
rectangular arrays, and/or area models.
Lesson 2.3
Name
Unlock the Problem
Multiply Tens, Hundreds, and Thousands
Number and Operations in Base
Ten—4.NBT.B.5 Also 4.NBT.A.1
MATHEMATICAL PRACTICES
MP2, MP5, MP7
Essential Question How does understanding place value help you multiply tens,
hundreds, and thousands?
MATHEMATICAL PRACTICES
Read and discuss the problem. Make sure
students understand that a “car” is one
section of a train.
• How many cars long is the train? 8 cars
• How many seats are in each car? 200 seats
Unlock
Unlock the
the Problem
Problem
Each car on a train has 200 seats. How many
seats are on a train with 8 cars?
Find 8 × 200.
One Way
One Way Draw a quick picture.
MP4 Model with mathematics. Point out
that drawing quick pictures can help students
represent a problem.
• What does each square on the left
represent? Each square represents 1 hundred.
• How do the squares on the left show
8 × 200? Possible answer: there are 8 rows of
T
Think: 10 hundreds = 1,000
2 squares. This shows 8 groups of 200 or 8 × 200.
• What does the picture to the right show?
Possible answer: it shows a group of 10 hundreds
regrouped as 1 thousand plus 6 hundreds.
Explain that students can use place value as
another way to solve the problem.
• How can you rename 200 using place
value? 2 hundreds
• What basic fact can you use to help you
solve this problem? 8 × 2 = 16
• How can you rename 16 hundreds in
standard form? Write 2 zeros after 16 to get 1,600.
Think: 6 hundreds = 600
© Houghton Mifflin Harcourt Publishing Company • Image Credits: (t) ©Corbis
Another Way
1,600
1,000 + 600 = _
Another Way Use place value.
2
hundreds
8 × 200 = 8 × _
Possible explanation: I can solve the
basic fact 8 × 2 and then write the number
of zeros in the greater factor, 200.
16
hundreds
=_
1,600 Think: 16 hundreds is 1 thousand, 6 hundreds.
=_
Math
Talk
1,600 seats on a train with 8 cars.
So, there are _
MATHEMATICAL PRACTICES 7
Look for a Pattern How
can finding 8 × 2 help you
find 8 × 200?
Chapter 2 75
Math
Talk
Use Math Talk to focus on students’
understanding of how to use place
value and the basic fact to solve the problem.
ELL Strategy:
Scaffold Language
Draw a picture of a multiplication problem
with tens, hundreds, and thousands by a
whole number through 10.
•Have students describe the picture.
•Next prompt them to say it using place value
and write a multiplication sentence to
match.
•Use leveled questions to help students use
math language:
Beginning: Yes/no–Is this 2 × 400?
Intermediate: How many hundreds are
there?
Advanced: Explain how your model works.
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Reteach 2.3
2
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1
Lesson 2.3
Reteach
Name Multiplication Inequalities
Write ,, ., or 5 for each
You can use a pattern to multiply with tens, hundreds, and thousands.
Count the number of zeros in the factors.
← basic fact
4 3 60 5 240
← When you multiply by tens, the last digit in the
product is 0.
4 3 600 5 2,400
← When you multiply by hundreds, the last two
digits in the product are 0.
Lesson 2.3
Enrich
Name
Multiply Tens, Hundreds, and Thousands
4 3 6 5 24
Differentiated
Instruction
Enrich 2.3
3
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4 × 6,000 = 24,000 ← When you multiply by thousands, the last three
digits in the product are 0.
When the basic fact has a zero in the product, there will be an extra zero
in the final product:
.
1.
7 3 60 . 400
2.
700 , 90 3 8
3.
3 3 800 , 2,500
4.
2,000 5 400 3 5
5.
8 3 6,000 . 40,000
6.
3 3 9,000 , 39,000
7.
6 3 900 , 700 3 8
8.
8 3 3,000 5 6,000 3 4
9.
9 3 4,000 5 6,000 3 6
5 3 4 5 20, so 5 3 4,000 5 20,000
Complete the pattern.
1. 9
3 2 5 18
2. 8
3 4 5 32
3 20 5
8
3 40 5
8
3 400 5
180
1,800
9 3 200 5
18,000
9 3 2,000 5
9
3. 6
3 6 5 36
360
6 3 60 5
3,600
6 3 600 5
36,000
6 3 6,000 5
Find the product.
5. 7
3 300 5 7 3
5
5
© Houghton Mifflin Harcourt Publishing Company
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4. 4
3 7 5 28
3 70 5
800 3 9 , 3,000 3 3
Explain how you found the answer in Exercise 10.
11.
280
2,800
4 3 700 5
28,000
4 3 7,000 5
4
10.
Possible answer: I used the basic fact 8 3 9 5 72 and a pattern to find 800
3 9 5 7,200. I used the basic fact 3 3 3 5 9 and a pattern to find 3,000 3 3 5
9,000. Then I compared 7,200 and 9,000. Since 9,000 has the greater digit
in the thousands place, 7,200 is less than 9,000.
3
21
2,100
Chapter Resources
320
3,200
32,000
8 3 4,000 5
hundreds
hundreds
6. 5
3 8,000 5 5 3
5
5
2-9
8
thousands
40 thousands
40,000
Reteach
Chapter Resources
© Houghton Mifflin Harcourt Publishing Company
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2-10
Enrich
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Other Ways
A Use a number line.
Example A
Lead a discussion with students about why
they would use multiplication to solve this
problem. I am combining the number of sleds rented
Bob’s Sled Shop rents 4,000 sleds each month.
How many sleds does the store rent in 6 months?
each month. When I combine equal groups, I can multiply
to find the total.
Other Ways
• How do the numbers on the number lines
change from one number line to the next?
Find 6 × 4,000.
Multiplication can be thought of as repeated addition.
Draw jumps to show the product.
14
14
14
14
14
Possible answer: each number line is 10 times greater
than the number line above it.
14
6 × 4 = 24
0
4
8
12
16
20
24
0
40
80
120
160
200
240
0
400
800
1,200
1,600
2,000
2,400
← basic fact
• How do the products 24, 240, 2,400, and
24,000 change from one product to the
next? Possible answer: each product is 10 times
6 × 40 = 240
0
4,000
8,000
12,000
16,000
20,000
greater than the product before it.
24,000
• How does the last number line show
6 × 4,000? Possible answer: the number line shows
6 × 400 = 2,400
6 jumps of 4,000.
6 × 4,000 = 24,000
Example B
• Explain the pattern that you see. Possible
B Use patterns.
Basic fact with a zero:
Basic fact:
3 × 7 = 21
← basic fact
3 × 70 = 210
← basic fact
8 × 5 = 40
8 × 50 = 400
2,100
3 × 700 = ___
4,000
8 × 500 = ___
21,000
3 × 7,000 = ___
40,000
8 × 5,000 = ___
t How does the number of zeros in the product of 8 and 5,000
compare to the number of zeros in the factors? Explain.
Possible explanation: there are 4 zeros in the product and only 3 zeros in the factors
because there is a zero in the basic fact, 8 × 5 = 40.
Possible description: as the number of
zeros in a factor increases, the number
of zeros in the product increases.
Math
Talk
MATHEMATICAL PRACTICES 5
Use Patterns to tell how the
number of zeros in the factors
and products changes in
Example B.
76
Advanced Learners
Logical
Individual
© Houghton Mifflin Harcourt Publishing Companyt*NBHF$SFEJUTUS
ª"SJFM4LFMMFZ#MFOE*NBHFT$PSCJT
24,000
So, Bob’s Sled Shop rents __
sleds in 6 months.
explanation: when you increase the number of zeros
in one of the factors, there will be an equal increase
in the number of zeros in the product.
Math
Talk
Use Math Talk to help students
recognize patterns in the number
of zeros in factors and products.
• As the number of zeros in a factor changes
each time, how does the size of the factor
change? Possible answer: It becomes 10 times
greater.
MP8 Look for and express regularity in
repeated reasoning.
• When a tens, hundreds, or thousands
number is multiplied by a one-digit
number, how does the number of zeros
in the product compare to the number of
zeros in the tens, hundreds, or thousands
number? Possible answer: There will be as many
zeros in the product as in the tens, hundreds, or
thousands number. There will be an additional zero if
the basic fact has a zero.
• What is the Associative Property of Multiplication? The
property that says you may group factors anyway you like and the
product will remain the same.
Show students this problem: 9 × 80.
• How can you write 80 as a product of a number and
10? 80 = 8 × 10 This means we can rewrite the problem
as 9 × (8 × 10) or, using the Associative Property of
Multiplication, (9 × 8) × 10.
• Which expression shows a basic fact? (9 × 8)
• Rewrite the expression using the product from the
basic fact. 72 × 10
• So, what is the product of 9 × 80? the same as the product
COMMON ERRORS
Error Students may not include the correct
number of zeros in the product.
Example
8 × 5,000 = 4,000
Springboard to Learning Have the
students write the basic fact first and
then circle it before they write the zeros.
8 × 5,000 = 40,000
of 72 × 10, or 720
Lesson 2.3
76
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CorrectionKey=A
Name
3 EXPLAIN
Share
Share and
and Show
Show
MATH
BOARD
Math
Talk
1. Use the drawing to find 2 × 500.
Share and Show
MATH
T
Hands
On
BOARD
Math
Talk
Complete the pattern.
2. 3 × 8 = 24
• How can you restate 2 ∙ 500 using place
value? 2 × 5 hundreds
• How can you use place value to write the
product of 2 ∙ 5 hundreds in standard
form? 10 hundreds can be renamed as 1 thousand,
240
3 × 80 = __
120
6 × 20 = __
200
4 × 50 = __
2,400
3 × 800 = __
1,200
6 × 200 = __
2,000
4 × 500 = __
24,000
3 × 8,000 = __
12,000
6 × 2,000 = __
20,000
4 × 5,000 = __
5
5. 6 × 500 = 6 × __
hundreds
Then
a student misses the checked
exercises
Differentiate Instruction with
• Reteach 2.3
• 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.
• How can you use inverse operations to find
the missing factor for Exercise 11? I can think
56 divided by 7 equals what number? Since 7 × 8 = 56,
then 56 ÷ 7 = 8. So, 7 × 8,000 = 56,000.
MP5 Use appropriate tools
strategically. Exercise 13 provides students
an opportunity to communicate verbally, not
just demonstrate, how the product of a basic
fact that ends in zero affects the number of
zeros in a product.
77 Chapter 2
5
6. 9 × 5,000 = 9 × __
thousands
30
= __
hundreds
45
= __
thousands
3,000
= __
45,000
= __
On
On Your
Your Own
Own
Find the product.
42,000
7. 7 × 6,000 = __
MATHEMATICAL
PRACTICE
© Houghton Mifflin Harcourt Publishing Company
If
If
Rt II
Rt
© Houghton Mifflin Harcourt Publishing Company • Image Credits: (tr) ©Ariel Skelley/Blend Images/Corbis
Use the checked exercises for Quick Check.
3
3
2
2
1
1
20
4. 4 × 5 = __
3. 6 × 2 = 12
Find the product.
which can be written in standard form.
Quick Check
Check
Quick
Possible explanation: I can think
of 2 × 500 as 2 times 5 hundreds,
which equals 10 hundreds. 10
hundreds equal 1,000.
1,000
2 × 500 = ___
Use Math Talk to focus on students’
understanding of how to use place
value to find the product.
MATHEMATICAL PRACTICES 7
Look for Structure to tell
how you would use place
value to find 2 × 500.
2
320
8. 4 × 80 = __
1,500
9. 3 × 500 = __
Use Reasoning Algebra Find the missing factor.
10.
7 × 9,000 = 63,000
_
8,000 = 56,000
11. 7 × _
400 = 3,200
12. 8 × _
13.
MATHEMATICAL
5 Communicate How does the number of zeros in the product
PRACTICE
of 8 and 5,000 compare to the number of zeros in the factors? Explain.
Possible explanation: there are 4 zeros in the product and only 3 zeros in the factors
because there is a zero in the basic fact, 8 × 5 = 40.
Chapter 2 • Lesson 3
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MATHEMATICAL PRACTICES
ANALYZEt-00,'034536$563&t13&$*4*0/
4 ELABORATE
Unlock
Unlock the
the Problem
Problem
14.
SMARTER
Joe’s Fun and Sun rents beach chairs. The store
rented 300 beach chairs each month in April and in May. The
store rented 600 beach chairs each month from June through
September. How many beach chairs did the store rent during
the 6 months?
Unlock the Problem
MATHEMATICAL PRACTICES
a. What do you need to know? the total number of beach chairs rented during
SMARTER
the 6 months
Have students read Exercise 14 and discuss
the important information. Students can
make a list of the steps necessary to solve
this multistep problem.
b. How will you find the number of beach chairs? I will multiply 2 times 300 and 4
times 600. Then I will add the products.
c. Show the steps you use to solve
the problem.
d. Complete the sentences.
600
For April and May, a total of __
beach chairs were rented.
2 × 300 = 600
4 × 600 = 2,400
600 + 2,400 = 3,000
Math on the Spot
Video Tutor
For June through September, a total of
Use this video to help students model and
solve this type of Think Smarter problem.
2,400 WRITE
Math twere
Showrented.
Your Work
__
beach chairs
3,000
Joe’s Fun and Sun rented __
beach chairs during the 6 months.
DEEPER
Mariah makes bead necklaces. Beads are
packaged in bags of 50 and bags of 200. Mariah bought
4 bags of 50 beads and 3 bags of 200 beads. How many
beads did Mariah buy?
16.
SMARTER
800 beads
SMARTER
Carmen has three books of 20 stamps
and five books of 10 stamps. How many stamps does
Carmen have? Complete the equation using the numbers
on the tiles.
3
5
110
50
60
100
© Houghton Mifflin Harcourt Publishing Company
15.
Math on the Spot videos are in the Interactive
Student Edition and at www.thinkcentral.com.
3
5
110
_
× 20 + _
× 10 = _
78
Exercise 16 assesses students' ability to use
place value as well as their knowledge of
the order of operations. If students choose
the correct numbers as "3" and "5" but get
an answer of "650," they are working out
the problem from left to right. Students will
need to review the order of operations.
5 EVALUATE Formative
Assessment
Essential Question
DIFFERENTIATED INSTRUCTION
D
INDEPENDENT ACTIVITIES
Differentiated Centers Kit
Literature
Putting the World on
a Page
Students read
about how
Julia uses
multiplication
to decide how
to arrange the
stamps in a collection.
Games
Triangle Products
(BNFT
gameboard.
Students
practice
multiplying
by tens to
win spaces
on the
Using the Language Objective
Reflect Have students complete the
sentence frame, Place value helps you to
multiply tens, hundreds, and thousands
by __________, to answer the Essential
Question.
How does understanding place value help
you multiply tens, hundreds, and thousands?
Possible answer: I can rewrite the problem using place
value. For example, to find 4 × 300, I can rewrite it
as 4 × 3 hundreds. Then I can solve 4 × 3 hundreds
= 12 hundreds, using the basic fact 4 × 3. Then I
rename 12 hundreds as 1,200 by writing 2 zeros after
the basic fact.
Math Journal
WRITE
Math
Explain how finding 7 × 20 is similar to
finding 7 × 2,000. Then find each product.
Lesson 2.3
78
Practice and Homework
Name
Multiply Tens, Hundreds, and Thousands
Lesson 2.3
COMMON CORE STANDARD—4.NBT.B.5
Use place value understanding and properties of
operations to perform multi-digit arithmetic.
Find the product.
Practice and Homework
28,000
1. 4 × 7,000 = ___
540
2. 9 × 60 = ___
Think: 4 × 7 = 28
So, 4 × 7,000 = 28,000
Use the Practice and Homework pages to
provide students with more practice of the
concepts and skills presented in this lesson.
Students 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 student’s understanding of content
for this lesson. Encourage students to use their
Math Journals to record their answers.
1,600
3. 8 × 200 = ___
30,000
4. 5 × 6,000 = ___
5,600
5. 7 × 800 = ___
720
6. 8 × 90 = ___
18,000
7. 6 × 3,000 = ___
24,000
8. 3 × 8,000 = ___
2,500
9. 5 × 500 = ___
36,000
10. 9 × 4,000 = ___
Problem
Problem Solving
Solving
11. A bank teller has 7 rolls of coins. Each roll
has 40 coins. How many coins does the
bank teller have?
12. Theo buys 5 packages of paper. There are
500 sheets of paper in each package. How
many sheets of paper does Theo buy?
© Houghton Mifflin Harcourt Publishing Company
280 coins
13.
2,500 sheets
Math Explain how finding 7 × 20 is similar to
WRITE
finding 7 × 2,000. Then find each product.
Check students’ work.
Chapter 2
79
COMMON
COMM
ON CORE
CORE
PROFESSIONAL
DEVELOPMENT
79
Math Talk in Action
Teacher:
Explain how you found the answer to Exercise 10.
Mattie:
I found the answer a different way. I thought of
9 3 4,000 as 9 3 4 thousands. Then I found
4 3 9 5 36, so the answer is 36 thousands,
or 36,000.
Eli:
I made a quick picture of the problem. I drew
9 rows of 4 thousands blocks. That was 36
thousands blocks, or 36,000.
Teacher:
How did you know what to draw?
Teacher:
Did anyone use a number line to find the product?
Eli:
9 3 4,000 means 9 groups of 4,000.
Roland:
Teacher:
Did anyone use a different strategy?
Jessika:
I looked for a pattern. I knew 4 3 9 5 36, so
4 3 90 5 360, 4 3 900 5 3,600, and 4 3 9,000 5
36,000.
I did. I thought of the problem as repeated
addition. So, I made a number line that started
at 0. I marked 4,000; 8,000; 12,000; and so on. It
increased by 4,000 each time. Then I made 9
jumps of 4,000 and ended on 36,000.
Teacher:
You all used good strategies to find the product!
Well done.
Teacher:
Explain the pattern you used.
Jessika:
Each time I wrote a zero in a factor, I wrote a zero
in the product.
Chapter 2
DO NOT EDIT--Changes must be made through “File info”
CorrectionKey=B
Lesson Check (4.NBT.B.5)
1. A plane is traveling at a speed of
400 miles per hour. How far will the
plane travel in 5 hours?
2,000 miles
2. One week, a clothing factory made
2,000 shirts in each of 6 different colors.
How many shirts did the factory make
in all?
Continue concepts and skills practice with
Lesson Check. Use Spiral Review to engage
students in previously taught concepts and
to promote content retention. Common Core
standards are correlated to each section.
12,000 shirts
Spiral Review (4.OA.A.1, 4.OA.A.2, 4.OA.A.3, 4.NBT.A.2)
3. Write a comparison sentence to represent
this equation.
6 × 7 = 42
Possible answer: 42 is 6 times as
4. The population of Middleton is six
thousand, fifty-four people. Write this
number in standard form.
6,054
many as 7.
voted for Carl Green and 67,952 people
voted for Maria Lewis. By how many votes
did Carl Green win the election?
17,082 votes
6. Meredith picked 4 times as many green
peppers as red peppers. If she picked a total
of 20 peppers, how many green peppers did
she pick?
16 green peppers
© Houghton Mifflin Harcourt Publishing Company
5. In an election for mayor, 85,034 people
FOR MORE PRACTICE
GO TO THE
80
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Personal Math Trainer
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Lesson 2.3 80