LESSON
3.5
Multiply with Regrouping
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
MP2 Reason abstractly and quantitatively. 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.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 regrouping to multiply 2-digit numbers.
Language Objective
Student partners describe how you can use
regrouping to multiply 2-digit numbers.
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
MP8 Look for and express regularity
in repeated reasoning.
In this lesson, students are introduced to using regrouping
to multiply two 2-digit numbers. As they learn to multiply
with regrouping, they use repeated reasoning when they
notice that they are repeating the steps of regrouping
that they use on the ones, again on the tens.
While students learn to use the regrouping method in
multiplication, they also use the
4
1
partial-products method. The
25
partial-products method helps students
× 93
to understand the numbers they are
3 × 25
75
multiplying at each step. This helps
2,250
__
90
× 25
them to understand the process
2,325
applied in the regrouping method.
Professional Development Videos
171A
Chapter 3
Interactive Student Edition
Personal Math Trainer
Math on the Spot
Animated Math Models
iTools: Base-Ten Blocks
iTools: Number Charts
HMH Mega Math
1 ENGAGE
Daily Routines
Common Core
Problem of the Day 3.5
Use rounding to estimate the product of 42
and 29. 1,200
Vocabulary
with the Interactive Student Edition
Essential Question
How can you use regrouping to multiply 2-digit numbers?
Making Connections
Invite students to tell you what they know about multiplying a
two-digit number and a one-digit number.
How would you find 25 × 3? Possible answer: draw a model of three
groups of 25. Count the total number of items to get 75.
™Interactive Student Edition
™Multimedia eGlossary
Learning Activity
Fluency Builder
Common Core Fluency
Standard 4.NBT.B.4
Subtract 3-Digit or More Whole Numbers
Write the following examples on the board.
Have students practice subtracting 3-digit
numbers. Have students check answers with
a partner.
268 – 135 = 133
3,752 – 1,214 = 2,538
379 – 84 = 295
6,120 – 2,167 = 3,953
• What are you trying to find in this problem? the number of gallons
of gas the neighbor used on the trip
• How many gallons of gas does the gas tank hold? 18 gallons
• How many times did the neighbor fill the gas tank? 14 times
• What mathematical operation could you use to solve the
problem? multiplication
Have students think about how to use multiplication to find the
solution to the problem.
Literacy and Mathematics
Choose one or more of the following activities.
• Have students research the number of gallons of gas trucks and
cars can hold. Have students summarize their findings.
• Have students write a short story about the problem. Have
students discuss the role of multiplication in the short story.
2,709 – 920 = 1,789
39,869 – 27,038 = 12,831
4,820 – 1,911 = 2,909
57,094 – 31,849 = 25,245
Literature Connection
From the Grab-and-Go™
Differentiated Centers Kit
Students read about how
Julia uses multiplication
to decide how to arrange
the stamps in a collection.
How can you use
regrouping to multiply
2-digit numbers?
Putting the World on a Page
Lesson 3.5
171B
LESSON
3.5
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,
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.
Unlock the Problem
Multiply with Regrouping
Tell students that they will learn how to use
regrouping to multiply 2-digit numbers.
MP7 Look for and make use of structure.
Remind students how they regrouped in
addition. They add the ones. If the number of
ones is more than 9, they regroup as 1 ten and
some more ones. Tell them that regrouping in
multiplication is similar.
• How do you think regrouping to add
is similar to regrouping to multiply? Possible
Unlock
Unlock the
the Problem
Problem
By 1914, Henry Ford had streamlined his
assembly line to make a Model T Ford car in
93 minutes. How many minutes did it take to
make 25 Model Ts?
Use place value and regrouping.
THINK
4
STEP 2
1
25
×
93
_
75
• Multiply 25 by 9 tens.
2,250 ← 90 × 25
© Houghton Mifflin Harcourt Publishing Company • Image Credits: (tr) ©Bettmann/CORBIS
multiply with the tens.
Work through Steps 2 and 3 with students.
Multiply 5 by 9 tens to get 45 tens, or 4
hundreds 5 tens. Record the 5 tens in the
product and record the regrouped 4 hundreds
in the tens column above the digit 1. Then
multiply 20 by 9 tens to get 180 tens, or 18
hundreds, and add the regrouped 4 hundreds
to get 22 hundreds. Record 22 hundreds in the
product. Then add the partial products to get
the final product.
STEP 3
Possible explanation: the
Commutative Property of
Multiplication says that
when the order of two
factors is changed, the
product is the same.
4
1
25
×
93
_
75
2,250
__
• Add the partial products.
2,325
Math
Talk
2,325
So, 93 × 25 is 2,325. Since __
is close
2,700
to the estimate of __
, the answer is reasonable.
MATHEMATICAL PRACTICES 8
Use Repeated Reasoning
Why do you get the same
answer whether you
multiply 93 × 25
or 25 × 93?
Chapter 3
Math
Talk
answer: the order of the factors does not change the
product.
25
× 93
__
75 ← 3 × 25
• Multiply 25 by 3 ones.
• What do you do with the regrouped
1 ten? Add it to the product you get when you
▲ The first production Model T Ford
was assembled on October 1, 1908.
1
• Think of 93 as 9 tens and 3
ones.
product is 15, or 1 ten 5 ones. Record the 5 ones in the
product. Record the 1 ten above the tens column.
• What does the Commutative Property state
about factors in a different order? Possible
RECORD
STEP 1
Discuss regrouping in Step 1.
• How do you regroup and record when
you multiply 5 by 3 ones? Possible answer: the
factors are in different orders.
2,700
Estimate. 90 × 30 = _
Multiply. 93 × 25
answer: first multiply by the ones. Then multiply by the
tens. Regroup when there are more than 9 ones or 9
tens.
• How are 93 × 25 and 25 × 93 different? The
Number and Operations in Base
Ten—4.NBT.B.5 Also 4.OA.A.3
MATHEMATICAL PRACTICES
MP2, MP7, MP8
Essential Question How can you use regrouping to multiply 2-digit
numbers?
MATHEMATICAL PRACTICES
Use Math Talk to focus on students’
understanding of the Commutative
Property of Multiplication.
Lesson 3.5
Name
3
Reteach 3.5
Differentiated
Instruction
Enrich 3.5
2
1
Lesson 3.5
Reteach
Name
Multiplication Mystery
Write the multiplication problem represented by the partial
products. Then write the product.
Estimate. Then use regrouping to find 28 3 43.
30 3 40 5 1,200
Step 1 Round to estimate the product.
Step 2 Think: 28 5 2 tens 8 ones.
Multiply 43 by 8 ones.
8 3 3 5 24. Record the 4. Write the
regrouped 2 above the tens place.
8 3 40 5 320. Add the regrouped
tens: 320 1 20 5 340.
Step 3 Multiply 43 by 2 tens.
20 3 3 5 60 and 20 3 40 5 800.
Record 860 below 344.
So, 28 3 43 5
1.
Estimate:
1.
2.
2.
600 1 40 1 180 1 12
8 3 43
26 3 32 5 832
43 3 27 5 1,161
43
3 28
344
860
20 3 43
1,204
344 1 860
3.
2,000 1 280 1 300 1 42
4.
46 3 57 5 2,622
1,204 . 1,204 is close to 1,200. The answer is reasonable.
400
800 1 280 1 60 1 21
2
43
3 28
344
2
Step 4 Add the partial products.
Estimate. Then find the product.
Lesson 3.5
Enrich
Name
Multiply with Regrouping
171
3,600 1 300 1 300 1 25
65 3 65 5 4,225
Possible estimates are given.
Estimate:
1,200
3.
Estimate:
36
3
12
_
43
3
29
_
51
3
47
_
432
1,247
2,397
5.
2,500
2,100 1 560 1 0 1 0
6.
70 3 38 5 2,660
7.
7,200 1 270 1 320 1 12
94 3 83 5 7,802
Which exercise did you find the most difficult
to solve? Explain.
Possible explanation: Exercise 6, because the ones
digits could have been 6 and 2 or 4 and 3.
171 Chapter 3
Chapter Resources
© Houghton Mifflin Harcourt Publishing Company
3-13
Reteach
Chapter Resources
© Houghton Mifflin Harcourt Publishing Company
3-14
Enrich
Different Ways to Multiply
The first way shows how Shawn used place
value and mental math to multiply.
• Where did the 60 that Shawn multiplied by
come from? Possible answer: he broke apart the
Different Ways to Multiply You can use different ways to
multiply and still get the correct answer. Shawn and Patty both
solved 67 × 40 correctly, but they used different ways.
factor 67 into 6 tens 7 ones, or 60 and 7
Look at Shawn’s paper.
60
7
2,400
x
x
+
40
40
280
=
=
=
The second way shows how Patty used place
value and regrouping to multiply. Discuss
the steps to make sure students understand
Patty’s work.
The first partial product is found by
multiplying 0 ones by 67, which is 0. To find
the second partial product, Patty multiplied
40 × 7 ones and 40 × 6 tens. 40 × 7 ones
= 280 ones. Discuss how Patty regrouped
and recorded.
MP3 Construct viable arguments and
critique the reasoning of others.
• How are Shawn's and Patty's strategies
related? Possible answer: Patty's first partial product
2,400
280
2,680
So, Shawn’s answer is 67 × 40 = 2,680.
Look at Patty’s paper.
2
67
x 40
00
+ 2,680
2,680
So, Patty also found 67 × 40 = 2,680.
has a value of zero, but her second partial product has
the same value as the sum of Shawn's partial products.
Shawn multiplied 40 × 60 and 40 × 7 to get his partial
products. Patty multiplied 40 × 7 and 40 × 60 and
regrouped to get her second partial product.
1. What method did Shawn use to solve the problem?
Shawn used place value and mental math.
2. What method did Patty use to solve the problem?
Patty used place value and regrouping.
MATH
BOARD
© Houghton Mifflin Harcourt Publishing Company
Share
Share and
and Show
Sh
1. Look at the problem. Complete the sentences.
0 and _
27 to get 0.
Multiply _
27 to get 1,620.
60 and _
Multiply _
Add the partial products.
1,620
0 + 1,620 = __
4
27
×60
_
0
+1,620
__
1,620
172
Advanced Learners
Logical / Mathematical
Partners
• Have students choose 4 different digits from 1, 2, 3,
4, 5, 6, 7, 8, and 9, to make two 2-digit numbers, such
that their product is close to 1,500. Tell students the
goal is to get a product as close to 1,500 as possible,
without going over.
• Have students trade problems with a partner to find
the product.
• The student whose problem has a product closest to
1,500 without going over, wins.
35
× 42
_
27
× 54
_
ELL Strategy:
Rephrase
Review the definition of the Commutative
Property of Multiplication with the entire
class.
• Pair students with similar levels of language
proficiency. Have partners discuss and
develop a definition by rephrasing it in
their own words.
• Guide students to complete the task using
their language proficiency level:
Beginning: Draw and label an example.
Intermediate: Complete a sentence frame:
The Commutative Property of
Multiplication means that 15 × 6 =
___ × ___.
Advanced: Describe it step-by-step.
3 EXPLAIN
Share and Show
MATH
M
A
TH
ATH
TH
BOARD
B
Hands
On
The first problem connects to the learning
model.
Lesson 3.5
172
DO NOT EDIT--Changes must be made through "File info"
CorrectionKey=A
Name
Use the checked exercises for Quick Check.
Students should show their answers for the
Quick Check on the MathBoard.
Estimate. Then find the product. Possible estimates are given.
68
×
53
__
3,604
Math
Talk
Use Math Talk to focus on students’ understanding of multiplying by 0
and recording the results in partial products.
61
×
54
__
3,294
Estimate. Then find the product.
2
1
1,500
5. Estimate: __
4,800
6. Estimate: __
Rt I
Error Students may multiply by the
regrouped number instead of adding it in the regrouping method.
COMMON ERRORS
Example 4
​     
27 
​  
× 60
_
0 
​   
     
 
​
+
4,820
__
4,820
Springboard to Learning Discuss the idea
that the regrouped number is a placeholder
recording for the result when multiplying 60 × 7 ones. The regrouped number does
not need to be multiplied again, only added
to the result of multiplying by the tens.
173 Chapter 3
675
4,368
8. 34 × 65
2,100; 2,210
9. 42 × $13
$400; $546
10. 60 × 17
1,200; 1,020
11. 62 × 45
3,000; 2,790
12. 57 × $98
$6,000; $5,586
MATHEMATICAL
7 Look for a Pattern Algebra Write a rule for the pattern.
PRACTICE
Use your rule to find the unknown numbers. Possible rules are given.
© Houghton Mifflin Harcourt Publishing Company
13.
If students complete the checked exercises
correctly, they may continue with the
remaining exercises.
MP7 Look for and make use of structure. Exercise 13 requires students to use higher
order thinking skills as they find the unknown
numbers in the pattern. Encourage students to
use place value and basic multiplication facts
to determine a rule for the pattern.
COMMON ERRORS
× 25
__
Practice: Copy and Solve Estimate. Then find the product. Possible estimates are given.
© Houghton Mifflin Harcourt Publishing Company
On Your Own 900
7. Estimate: __
27
× 56
__
1,410
Differentiate Instruction with
• Reteach 3.5
• Personal Math Trainer 4.NBT.B.5
• RtI Tier 1 Activity (online)
Then
78
× 47
__
a student misses the checked
exercises
If
MATHEMATICAL PRACTICES 8
Generalize Why can you
omit zeros of the first
partial product when you
multiply 20 × 34?
Possible estimates are given.
30
Quick Check
Math
Talk
On
On Your
Your Own
Own
20 × 34
3
90
×
27
__
2,430
Possible explanation:
zero times any number is 0.
• What is the product of 0 times 34? 0
• If you add a partial product of 0 to the
partial product of 20 ∙ 34, what will the
sum of the partial products be? the product of
2,700
4. Estimate: __
3,000
3. Estimate: __
3,500
2. Estimate: __
14.
Hours
h
5
10
15
Minutes
m
300
600
900
20
1,200 1,500
DEEPER
Owners of a summer camp are
buying new cots for their cabins. There are
16 cabins. Each cabin needs 6 cots. Each cot
costs $92. How much will the new cots cost?
$8,832
25
15.
Multiply h by 60.
Rule: ____
DEEPER
A theater has 28 rows of 38 seats
downstairs and 14 rows of 26 seats upstairs.
How many seats does the theater have?
1,428 seats
Chapter 3 • Lesson 5 173
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3/20/14 1:54 AM
MATHEMATICAL PRACTICES
COMMUNICA5&t1&34E7&3&tCONSTRUCT ARGUMENTS
4 ELABORATE
Unlock
Unlock the
the Problem
Problem
16.
SMARTER
Machine A can label 11 bottles in 1 minute.
Machine B can label 12 bottles in 1 minute. How many bottles
can both machines label in 15 minutes?
a. What do you need to know?
Unlock the Problem
how many bottles both
MATHEMATICAL PRACTICES
machines can label in 15 minutes
b. What numbers will you use?
11, 12, and 15
SMARTER
c. Tell why you might use more than
one operation to solve the problem.
d. Solve the problem.
11
× 15
_
55
+ 110
_
165
Possible explanation: after I multiply, I
need to add to find the total number of
bottles labeled by both machines.
12
× 15
_
60
+ 120
_
180
Exercise 16 is a multistep problem in which
students need to multiply groups of two
2-digit numbers, and then add the products.
180
+
165
__
345
Math on the Spot
Video Tutor
345 bottles
So, both machines can label _
Use this video to help students model and
solve this type of Think Smarter problem.
15 minutes.
in _
MATHEMATICAL
PRACTICE
1
Make Sense of Problems
A toy company makes wooden blocks.
A carton holds 85 blocks. How many blocks
can 19 cartons hold?
18.
A company is packing cartons of
candles. Each carton can hold 75 candles.
So far, 50 cartons have been packed, but
only 30 cartons have been loaded on a truck.
How many more candles are left to load on
the truck?
1,615 blocks
1,500 candles
Personal Math Trainer
19.
Math on the Spot videos are in the Interactive
Student Edition and at www.thinkcentral.com.
DEEPER
SMARTER
Mr. Garcia’s class raised money for a field trip
to the zoo. There are 23 students in his class. The cost of the trip
will be $17 for each student. What is the cost for all the students?
Explain how you found your answer.
$391; possible explanation: I used the expression
(23 × 10) + (23 × 7) to find the cost. 230 + 161 = 391.
© Houghton Mifflin Harcourt Publishing Company • Image Credits: (t) Houghton Mifflin Harcourt
17.
174
DIFFERENTIATED INSTRUCTION
D
INDEPENDENT ACTIVITIES
MP1 Make sense of problems and
persevere in solving them. Discuss with
students what operation they can use to
solve this problem and why.
SMARTER
Personal Math Trainer
Be sure to assign Exercise 19 to students in
the Personal Math Trainer. It features a video
to help them model and answer the problem.
Students must complete a multiplication
problem with regrouping. Students who
answer 371 may have forgotten to regroup
21 ones as 2 tens and 1 one.
5 EVALUATE Formative
Assessment
Essential Question
Using the Language Objective
Differentiated Centers Kit
Activities
Product Power
Literature
Putting the
World on a Page
Games
Multiplication
Marathon
(BNFT
Students complete
purple Activity Card
5 by multiplying
multi-digit numbers
by single-digit
numbers.
Students read
about how Julia
uses multiplication
to decide how
to arrange the
stamps in a
collection.
Students take
turns using
number cards to
make and solve
2-digit by 1-digit
multiplication
problems.
Reflect Have students describe to a partner
to answer the Essential Question.
How can you use regrouping to multiply
2-digit numbers? Possible answer: I can multiply
the ones. Then I can rewrite the product as ones and
regrouped tens. Then I can multiply the tens and add the
regrouped tens to the product.
Math Journal
WRITE
Math
Write about which method you prefer
to use to multiply two 2-digit
numbers—regrouping, partial products, or
breaking apart a model. Explain why.
Lesson 3.5
174
Practice and Homework
Lesson 3.5
Name
Multiply with Regrouping
COMMON CORE STANDARD—4.NBT.B.5
Use place value understanding and properties
of operations to perform multi-digit arithmetic.
Possible estimates are given.
Practice and Homework
Estimate. Then find the product.
2,700
1. Estimate: __
2
1
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.
Think: 87 is close to 90 and 32 is close
to 30.
87
×
32
__
174
+
2,610
__
90 × 30 = 2,700
2,784
2,100
2. Estimate: __
2,000
3. Estimate: __
73
× 28
__
2,044
3,000
4. Estimate: __
48
× 38
__
1,824
59
× 52
__
3,068
Problem
Problem Solving
Solving
5. Baseballs come in cartons of 84 baseballs.
A team orders 18 cartons of baseballs. How
many baseballs does the team order?
6. There are 16 tables in the school lunch room.
Each table can seat 22 students. How many
students can be seated at lunch at one time?
© Houghton Mifflin Harcourt Publishing Company
1,512 baseballs
7.
352 students
Math Write about which method you prefer to use to
WRITE
multiply two 2-digit numbers—regrouping, partial products, or
breaking apart a model. Explain why.
Check students’ work.
Chapter 3
Cross-Curricular
SCIENCE
• Scientists can test water samples
to find if small living things,
called bacteria, are present. They
can place a water sample from a
lake, for example, onto a slide.
100 colonies per 1 ml
A material on the slide allows
bacteria to grow. After a certain
amount of time, the scientist can
look at the slide and count the
1,120 colonies per 1 ml
bacterial colonies.
• To estimate the number of bacterial colonies in two
1-milliliter samples of water, multiply the number of
bacterial colonies (a dot) by 20. Have students count
the bacterial colonies on each slide. Have them
multiply the number by 20 to find the number of
bacterial colonies in each 1-milliliter sample of water.
175 Chapter 3
175
SOCIAL STUDIES
Materials maps with scales shown, ruler
• Maps can help show the
distance between locations.
A scale on a map tells how
N
much one unit of length
represents on the map. For
example, 1 inch 5 20 miles.
1 inch = 20 miles
• Have students choose two
locations on a map and find
the actual distance between them. Discuss how
multiplication can be used to find the distance.
Check students’ work.
CorrectionKey=B
Lesson Check (4.NBT.B.5)
1. The art teacher has 48 boxes of crayons.
There are 64 crayons in each box. How
many crayons does the teacher have?
3,072 crayons
2. A basketball team scored an average of
52 points in each of 15 games. Based on
the average, how many points did the team
score 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.
780 points
Spiral Review (4.OA.A.1, 4.OA.A.2, 4.OA.A.3, 4.NBT.B.5)
apples. There are 27 apples in each bag.
How many apples were sold?
2,241 apples
5. Gabriella has 4 times as many erasers as
Leona. Leona has 8 erasers. How many
erasers does Gabriella have?
32 erasers
4. Hannah has a grid of squares that has
12 rows with 15 squares in each row. She
colors 5 rows of 8 squares in the middle
of the grid blue. She colors the rest of the
squares red. How many squares does
Hannah color red?
140 squares
6. Phil has 3 times as many rocks as Peter.
Together, they have 48 rocks. How many
more rocks does Phil have than Peter?
24 rocks
© Houghton Mifflin Harcourt Publishing Company
3. One Saturday, an orchard sold 83 bags of
FOR MORE PRACTICE
GO TO THE
176
4_MNLESE342200_C03P05.indd 176
Personal Math Trainer
07/10/14 7:58 PM
Lesson 3.5 176