2.1
Multiply by 1-Digit Numbers
?
Essential Question How do you multiply by 1-digit numbers?
Texas Essential
Knowledge and Skills
Number and Operations—5.3.B
Multiply with fluency a three-digit number by a two-digit
number using the standard algorithm Also 5.3.A
MATHEMATICAL PROCESSES
5.1.B Use a problem-solving model
How do you multiply by
1-digit numbers?
Are You Ready?
Access Prior Knowledge
Use the Are You Ready? 2.1 in the
Assessment Guide to assess students’
understanding of the prerequisite skills
for this lesson.
Vocabulary
Go to Multimedia eGlossary at
thinkcentral.com
Lesson Opener
Making Connections
Invite students to tell you what they know about fishing.
Why do you think people fish? (Answers will vary.) Have you ever fished? Where? Did
you catch a fish? (Answers will vary.) What other equipment besides a fishing rod do
you need to fish? (hooks, line, nets, reels, etc.) What do people attach to the ends of a
fishing pole to attract fish? (bait)
Using the Digital Lesson
Review the concept of regrouping from one place to another, starting from the ones
place. Remind students that the digit in the ones place in the product of 5 times any
whole number will be either 0 or 5.
Learning Task
Resources
What is the problem the students are trying to solve? Connect the story to the problem.
• What information is given in the problem? (The price of the fishing pole is $385.)
• How would you use a place-value chart to write the digits in the price of the fishing
rod? (Possible answer: I would write the digit 3 in the hundreds place, the digit 8 in
the tens place, and the digit 5 in the ones place.)
• What is one way you could you check the product of 385 and 5? (Possible answer:
I could find the sum of 385 + 385 + 385 + 385 + 385.)
• What information are you being asked to find? (The total cost of 5 fishing poles.)
Literacy and Mathematics
• Have each student create a word problem that involves multiplication. Ask students
to share their problems and solutions.
For the student
For the teacher
Interactive
Student Edition
provides students
with an interactive learning
environment!
Digital Management
Center organizes program
resources by TEKS!
eTeacher
Edition
Math on the Spot
Video Tutor
Online Assessment
System
iTools Virtual
Manipulatives
Soar to Success Math
Online Intervention
Lesson 2.1
55A
Name
2.1
?
Unlock the Problem
Read through the problem with students and explain
how to find a good estimate for a multiplication
problem.
Number and
Operations—5.3.B
Also 5.3.A
MATHEMATICAL PROCESSES
5.1.B
Multiply by 1-Digit Numbers
Essential Question
How do you multiply by 1-digit numbers?
Unlock
Unlock the
the Problem
Problem
Each day an airline flies 9 commercial jets from New York to London,
England. Each plane holds 293 passengers. If every seat is taken on all flights,
how many people fly on this airline from New York to London in 1 day?
• In Step 2, describe what the blue digit 2 means.
Possible answer: Multiplying the ones gives 27, which is
2 tens 7 ones. The blue digit 2 represents the 2 tens,
which are regrouped.
Math Talk
Use place value and regrouping.
Mathematical Processes
Explain how you multiply any
number by a 1-digit number.
STEP 1 Estimate: 293 × 9
2,700
Think: 300 × 9 = ___
• How do the regrouped tens affect the results of
Step 3? Possible answer: The 2 regrouped tens are added
to the 81 tens that are found by multiplying 9 × 9 tens.
STEP 2 Multiply the ones.
2
2 93
× 9
__
7
• When you multiply a multi-digit number by a
1-digit number, why do you begin by multiplying
the ones digits? Possible answer: Starting with the least
9 × 3 ones =
Possible explanation: To
multiply a number by a 1-digit
number, repeat the process
of multiplying and regrouping
until every place value is
multiplied.
27 ones
_
Write the ones and the
regrouped tens.
STEP 3 Multiply the tens.
place value will help me determine if regrouped numbers
need to be added to the products in greater place values.
I can add the regrouped tens or hundreds as I record the
products of those place values.
82
2 93
×
9
__
37
9 × 9 tens =
81
_
tens
Add the regrouped tens.
81 tens + 2 tens = _
83 tens
_
Write the tens and the regrouped hundreds.
Math Talk
STEP 4 Multiply the hundreds.
Mathematical Processes
82
2 93
× 9
__
2,637
Use Math Talk to focus on students’ understanding
of multiplying any number by a 1-digit number.
9 × 2 hundreds =
18 hundreds
_
Add the regrouped hundreds.
26 hundreds
18 hundreds + 8 hundreds = _
_
© Houghton Mifflin Harcourt Publishing Company
Write the hundreds.
English Language Learners
Leveled Activities
ELPS
Beginning: Activity 50
1.B.1, 2.E.3, 4.F.5
Intermediate: Activity 3
2.D.2, 2.E.3, 3.F.2
Advanced: Activity 46
1.F, 2.I.4, 4.G.2
Advanced High: Activity 18
4.C.4, 4.E, 4.F.7,
Go to thinkcentral.com for the ELL Activity
Guide containing these leveled activities.
2,637
So, in 1 day, ___
passengers fly from New York to London.
I can compare my answer to my estimate.
• How can you tell if your answer is reasonable? ________
Since 2,637 is close to the estimate, 2,700, the answer is reasonable.
ELL Language Support
Module 2 55
Visual / Linguistic
Small Group
ELPS 4.F.7, 4.F.8, 4.G.3
Strategy: Creative Grouping
• English learners may benefit from working with fluent speakers as they
solve word problems.
• Have English learners point to unfamiliar terms or phrases. Guide
fluent speakers as they explain or illustrate unfamiliar terms to group
members.
• Once English learners understand
"We can regroup the tens in
the problem, ask them to describe
this problem."
or model the solution or one of
the steps to solve the problem.
"The tens can be regrouped in
this problem."
55
Module 2
Share
Share and
and Show
Show
Complete to find the product.
Share and Show
3,000
18,000
Estimate: 6 × ___
= ___
1. 6 × 2,796
Multiply the ones
and regroup.
3
53
4 53
2, 7 96
×
6
__
76
2,7 96
×
6
__
6
4 53
2, 7 9 6
×
6
__
776
Estimate. Then find the product.
Possible estimates are given.
4,800
2. Estimate: ___
2,400
3. Estimate: ___
The first problem connects to the learning model.
Have students use the MathBoard to explain their
thinking.
Multiply the
thousands and
add the regrouped
thousands.
Multiply the
hundreds and add
the regrouped
hundreds. Regroup.
Multiply the
tens and add the
regrouped tens.
Regroup.
Use the checked exercises for Quick Check. Students
should show their answers for the Quick Check on the
MathBoard.
2, 7 9 6
×
6
__
16,776
14,000
4. Estimate: ___
3
2
608
× 8
__
4,864
556
× 4
__
2,224
1,925
× 7
__
13,475
Quick Check
1
a student misses the checked exercises
IF
Problem
Problem Solving
Solving
THEN
Differentiate Instruction with
RtI Tier 1 Lesson 10
Algebra Solve for the unknown number.
5.
396
× 6
__
2,376
6.
5,127
×
8
__
41,016
7.
8,576
×
7
__
60,032
Problem Solving
Problem
Problem 6 requires students to work backward from
the tens place to determine whether the unknown
ones digit is 2 or 7.
Practice: Copy and Solve Estimate. Then find the product. Possible estimates are given.
300; 348
12. 5 × 1,012
5,000; 5,060
9. 338 × 4
1,200; 1,352
13. 2,921 × 3
9,000; 8,763
10. 6 × 219
1,200; 1,314
14. 8,813 × 4
36,000; 35,252
11. 7 × 456
3,500; 3,192
15. 9 × 3,033
27,000; 27,297
16. Multi-Step A commercial airline makes a flight each day from New
York to Paris, France. The aircraft seats 524 passengers and serves
2 meals to each passenger per flight. How many meals are served in
one week?
7,336
56
© Houghton Mifflin Harcourt Publishing Company
8. 116 × 3
COMMON ERRORS
C
E
Error
Students may add regrouped digits before
multiplying the next place value.
Example
22
237
× 4
__
1,608
Springboard to Learning Remind students that the
regrouped digit is added to the product of the next
place and not to the factor in the next place. Point
out that the regrouped digit is already part of a
product.
Enrich
Visual
Individual
• Have students solve the problem below.
• The product of 9 and a 4-digit number is about 31,000. The product of
9 and a different 4-digit number is about 51,000. Both 4-digit numbers
have consecutive digits, starting in the thousands place. What are the
two 4-digit numbers, and what are the exact products?
3,456 × 9 = 31,104; 5,678 × 9 = 51,102
• If there is time, suggest that students look at the products 2,345 × 9
and 4,567 × 9 to see how they are similar. 2,345 × 9 = 21,105 and
4,567 × 9 = 41,103; both products have a 0 in the tens place and 1s in the
thousands and hundreds places.
Go to Go to thinkcentral.com for additional enrichment
activities in the Enrich Activity Guide.
Lesson 2.1
56
Name
Problem
Problem Solving
Solving
Problems
What’s the Error?
Problems 17–20 require students to use higher order
thinking skills as they analyze Brian’s and Jermaine’s
mistakes using skills learned in the lesson.
17. The Plattsville Glee Club is sending 8 of its members to a singing
contest in Cincinnati, Ohio. The cost will be $588 per person. How
much will it cost for the entire group of 8 students to attend?
Both Brian and Jermaine solve the problem. Brian says the answer is
$40,074. Jermaine’s answer is $4,604.
$4,800 . Accept all reasonable estimates.
Estimate the cost. A reasonable estimate is _
M
Math
on the Spot
Video Tutor
V
Although Jermaine’s answer seems reasonable, neither Brian nor Jermaine
solved the problem correctly. Find the errors in Brian’s and Jermaine’s work.
Then, solve the problem correctly.
Jermaine
Brian
Through the Math on the Spot Video Tutor,
students will be guided through an interactive
solving of this type of H.O.T. problem. Use this
video to also help students solve the H.O.T.
problem in the Interactive Student Edition. With
these videos and H.O.T. problems, students will
build skills needed in the TEXAS assessment.
6
6
$ 5 8 8
x
8
$ 4 0, 7 0 4
Math on the Spot videos are in the
Interactive Student Edition and at
thinkcentral.com.
Correct Answer
6
7
$ 5 8 8
x
8
$ 4, 6 0 4
6
$ 5 8 8
x
8
$ 4, 7 0 4
Possible explanation: When Brian multiplied the tens, he
18. What error did Brian make? Explain. __________
wrote the total number of tens in the product instead of regrouping, so the place values
of his product are incorrect.
Possible explanation: Jermaine regrouped the wrong
19. What error did Jermaine make? Explain. _________
amount of hundreds. He regrouped the tens as 6 hundreds instead of 7 hundreds.
20. Multi-Step How could you predict that Jermaine’s answer might be
© Houghton Mifflin Harcourt Publishing Company
incorrect using your estimate?
Possible answer: I used 600 × 8 to estimate the product; 588 is 12 less than 600. Since
12 × 8 = 96, and 4,604 is almost 200 less than the estimate of 4,800, the answer is
probably too low.
Module 2 • Lesson 1 57
3
RtI Tier 1 Lesson 10
2
1
Enrich 9
Name
Name
LESSON
10
Enrich 9
1
Multiply by 1-Digit Numbers
5.3.B
OBJECTIVE Multiply by 1-digit numbers.
Multiplication Number Puzzle
Use the clues to complete the puzzle.
You can use place value to help you multiply by 1-digit numbers.
1
Estimate. Then find the product. 378 × 6
Estimate: 400 × 6 = 2,400
7
7
0
1 1 4
9
1 1 9 3 4
2
2
7
9
2
6
6
2
6 3 2
6
0
6 8
Step 1 Multiply
the ones.
Step 2 Multiply
the tens. Add the
regrouped tens
Step 3 Multiply
the hundreds. Add
the regrouped
hundreds.
7
8
4
×
4
6
7
×
© Houghton Mifflin Harcourt Publishing Company
8
Tens
Ones
Thousands
Hundreds
4
7
×
8
6
2,
Complete to find the product.
1. 7 × 472
Estimate: 7 ×
Multiply the ones.
472
× 7
__
4
Number and Operations
500
=
2
6
8
3,500
Multiply the tens.
Add the regrouped tens.
51
472
× 7
__
04
12
13
4
So, 378 × 6 = 2,268. Since 2,268 is close to the estimate of 2,400,
the answer is reasonable.
1
Module 2
6
11
3
8
6
8
57
Tens
4
3
8
Ones
Hundreds
Thousands
Tens
7
Ones
Hundreds
Thousands
10
3
2
3
5
Multiply the hundreds.
Add the regrouped
hundreds.
51
6
5
0
4
8
2
1 7 2 2
6
8
8 8
Across
7,704
1. 856 3 9
5,082
2. 847 3 6
15,246
3. 5,082 3 3
42,168
4. 7,028 3 6
193,296
5. 24,162 3 8
12,762
8. 2,127 3 6
16,445
9. 3,289 3 5
3,606
12. 601 3 6
114,858
1,722
11,934
7. 1,326 3 9
16,108
9. 4,027 3 4
24,162
10. 4,027 3 6
63,252
11. 7,028 3 9
6,888
13. 1,722 3 4
× 7
__
5.
12,762 3 9
6.
287 3 6
Stretch Your Thinking Write a different clue that has the same
product as 1,326 3 9.
Possible answer: 1,989 3 6
3,304
19
4
Down
14.
472
9
1
8 5 8
2
4
1 6 1 0
6
4 1 6 2
4
5 2
Enrich
© Houghton Mifflin Harcourt Publishing Company
E9
Mathematical Processes
Model ¥ Reason ¥ Communicate
Daily
Daily Assessment
Assessment Task
Task
3
Fill in the bubble completely to show your answer.
Daily Assessment Task
21. A minivan weighs 4,275 pounds. You would need 6 minivans to balance
2 elephants on a balance scale. Which could be the combined weight of
the 2 elephants?
A
25,650 pounds
B
12,825 pounds
C
24,650 pounds
D
25,620 pounds
2
1
Can students multiply by a 1-digit number?
THEN
IF
NO
•
Soar to Success Math
Warm-Up 12.55, 12.59
22. A small sports arena can hold 274 people in each section. The arena has
YES
7 sections. Estimate how many people the arena can hold, and then give
the exact total.
A
estimate: 1,400; exact: 1,818
B
estimate: 1,400; exact: 1,918
C
estimate: 2,100; exact: 1,898
D
estimate: 2,100; exact: 1,918
Enrich 9
• Homework and Practice
•
Lesson 2.1
TEXAS Test Prep Coach
23. Multi-Step The 133 students in the fifth grade each made 6 bookmarks
In the Test Prep exercise, if students selected:
for the school library. The 128 students in the fourth grade each made
7 bookmarks for the school library. Which class made more bookmarks
and how many more did they make?
A They did not add the regrouped tens.
A
fourth grade, 108
C
fifth grade, 108
B They did not add the regrouped hundreds.
B
fourth grade, 98
D
fifth grade, 98
D They did not add the regrouped thousands.
?
TEXAS Test Prep
24. The Memorial School has 1,362 students enrolled for the current school
A
6,800
C
6,810
B
6,510
D
5,810
58
© Houghton Mifflin Harcourt Publishing Company
year. The school is purchasing 5 notebooks for each student. How many
notebooks does the school need to purchase for the students?
Essential Question
Write
Math
How do you multiply by 1-digit numbers? Possible
answer: I can use place value and regrouping. I start by
multiplying the ones, then the tens, and so on, regrouping
as necessary.
Differentiated Centers Kit
Activities
Amazing Areas
Students complete
blue Activity
Card 11 by
measuring and
calculating the
area of rectangles.
Literature
A Drive Through History
Students read about how
the Alvarez family uses
multiplication and division
to plan their vacation.
Activities
Multiplication
Relay
Students complete
purple Activity
Card 11 by working
in teams to solve
multiplication
problems.
Lesson 2.1
58
5
Number and Operations—5.3.B
Also, 5.3.A
MATHEMATICAL PROCESSES 5.1.B
2.1
Name
Fill in the bubble completely to show your answer.
15. A baker sold 1,246 cakes in November. He sold
Multiply by 1-Digit Numbers
4.
2.
574
× 4
_
2,296
5.
7,593
×
2
__
15 ,186
3,852
×
7
__
26,9 64
3,729
A
$9,670.00
B
3,738
B
$9,640.00
× 5
__
6,865
C
3,728
C
$9,840.00
D
3,628
D
$9,870.00
835
×
4
__
3, 34 0
17. A commercial airline makes several flights
Estimate. Then find the product. Possible estimates are given.
7. 4 × 923
8. 227 × 3
3,600; 3,692
9. 4 × 1,238
600; 681
10. 384 × 2
4,800; 4,952
11. 2,831 × 3
9,000; 8,493
800; 768
6 months. How much had Wendy earned at
the end of 6 months?
A
6.
1 79
×
3
__
537
12. 4 × 2,899
12,000; 11,596
a goal to save 8 jars full of pennies. Estimate
how many pennies Leo will have if he saves
8 jars of pennies and then give the exact total.
A
13,796
A
estimate: 2,400; exact 2,448
B
13,346
B
estimate: 2,400; exact 3,048
C
13,846
C
estimate: 3,200; exact 3,088
D
1,985
D
estimate: 3,200; exact 3,048
contest during the month of April. The
168 fifth grade students each ran a total of
3 miles during the contest. The 154 fourth
grade students each ran a total of 2 miles
during the contest. What is the total number
of miles run by all students in the contest?
Problem
Problem Solving
Solving
© Houghton Mifflin Harcourt Publishing Company
Each tire costs $129.00. What is the total cost
of four tires? Estimate. Then solve.
14. The drama club sold 386 tickets to the
school play. Each ticket costs $7. How much
money did the club raise for the school?
Estimate. Then solve.
$400.00, $516.00
$2,800, $2,702
Module 2 • Lesson 1
Homework and Practice
Use the Homework and Practice pages to provide
students with more practice on the concepts and
skills of this lesson.
59-60
Module 2
59
60
18. Leo’s penny jar holds 386 pennies. Leo has set
each week from New York to Paris, France.
If the airline serves 1,978 meals each day, how
many meals are served the entire week?
19. Multi-Step Jefferson School held a fitness
13. Mrs. Sampson is buying new tires for her car.
16. Wendy earned $1,645.00 each month for
three times as many cakes in December. How
many cakes did he sell in December?
3. 1, 3 73
Solve for the unknown number.
1.
TEXAS Test Prep
Lesson
Lesson Check
Check
A
802 miles
B
792 miles
C
812 miles
D
712 miles
20. Multi-Step Mr. Benson is buying supplies for
his office. He bought 8 boxes of large rubber
bands, which come 195 to a box. He bought
6 boxes of small rubber bands, which come
256 to a box. What is the total number of
rubber bands that Mr. Benson bought?
A
3,096
B
4,576
C
3,066
D
3,520
© Houghton Mifflin Harcourt Publishing Company
Ho mewo rk
and Practice