# Multiply Multi-Digit by 1-Digit Number Contributed by: Learn how to multiply Multi-Digit Numbers with a one-digit number.
1. NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 10 4 3
Lesson 10
Objective: Multiply three- and four-digit numbers by one-digit numbers
applying the standard algorithm.
Suggested Lesson Structure
Fluency Practice (12 minutes)
Application Problem (5 minutes)
Concept Development (33 minutes)
Student Debrief (10 minutes)
Total Time (60 minutes)
Fluency Practice (12 minutes)
 Represent Expanded Form 2.NBT.3 (3 minutes)
 Multiply Mentally 4.NBT.4 (3 minutes)
 Multiply Using Partial Products 4.NBT.4 (6 minutes)
Represent Expanded Form (3 minutes)
NOTES ON
Materials: (S) Place value disks
MULTIPLE MEANS
Note: This activity incorporates expanded form fluency from OF ENGAGEMENT:
Lessons 8 and 9 while reviewing how to use place value disks. Extend Represent Expanded Form by
T: (Write 532.) Say the number in expanded form. to do one of the following:
S: 532 equals 500 plus 30 plus 2.  Use your disks to show
T: Say it in unit form. 1,000/100/10 less/more than
3,241.
S: 532 equals 5 hundreds 3 tens 2 ones.
 Use your disks to show another
T: Use your disks to show 5 hundreds 3 tens 2 ones. number that would be rounded to
the same ten/hundred as 2,053.
Repeat the process for the following possible sequence: 415,
204, 3,241, and 2,053.
Multiply Mentally (3 minutes)
Note: Reviewing these mental multiplication strategies provides a foundation for students to succeed during
the Concept Development.
Repeat the process from Lesson 7 for the following possible sequence: 342 × 2, 132 × 3, 221 × 4, and 213 × 4.
Lesson 10: Objective: Multiply three- and four-digit numbers by one-digit
numbers applying the standard algorithm. 143
2. NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 10 4 3
Multiply Using Partial Products (6 minutes)
Materials: (S) Personal white board
Note: This activity serves as a review of the Concept Development in Lessons 7 and 8.
T: (Write 322 × 7.) Say the multiplication expression.
S: 322 × 7.
T: Say it as a three-product addition expression in unit form.
S: (3 hundreds × 7) + (2 tens x 7) + (2 ones × 7).
T: Write 322 × 7 vertically, and solve using the partial product strategy.
Repeat the process for the following possible sequence: 7 thousands 1 hundred 3 tens 5 ones × 5 and
3 × 7,413.
Application Problem (5 minutes)
The principal wants to buy 8 pencils for every student at her school. If there are 859 students, how many
pencils does the principal need to buy?
Note: This problem is a review of Lesson 9. Students may solve using the algorithm or partial products. Both
are place value strategies.
Concept Development (33 minutes)
Materials: (S) Personal white board
Problem 1: Solve 5 × 2,374 using partial products, and then connect to the algorithm.
Display 5 × 2,374 vertically on the board.
T: With your partner, solve 5 × 2,374 using the partial products method.
Allow two minutes to solve.
T: Now, let’s solve using the algorithm. Say a multiplication sentence for the ones column.
Lesson 10: Objective: Multiply three- and four-digit numbers by one-digit
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3. NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 10 4 3
S: 4 ones times 5 is 20 ones or 2 tens.
T: Tell your partner how to record 20 ones or 2 tens.
S: I am going to record 2 tens on the line in the tens column and the 0 in the ones column.
T: Do you have 20 ones recorded in your answer from the partial products?
S: Yes!
T: What is multiplied in the tens column?
S: 7 tens times 5 is 35 tens.  I notice when I look back at the partial products, I also have 35 tens or
3 hundreds 5 tens.
T: Tell your partner what to do with 3 hundreds 5 tens
and the 2 tens we recorded on the line. NOTES ON
S: We have to add the 2 tens to get 37 tens or 3 hundreds MULTIPLE MEANS
7 tens.  Why do the partial products only show 350 OF REPRESENTATION:
though? Learners and mathematicians differ in
T: Discuss with your partner why the algorithm shows the strategies they use to solve a
MP.4 problem. Whether we use the
37 tens, but the partial product shows 35 tens.
standard algorithm or partial products
S: In the partial products method, we add the 2 tens to strategy, our product is the same.
35 tens later after multiplying each place value Cultivate a classroom culture of
separately. In the algorithm, you add as you go. acceptance of multiple methods to
T: Let’s record 3 hundreds 7 tens or 37 tens. Cross off the solve. Encourage students to share and
2 tens on the line because they’ve been added in. innovate efficient strategies for this
and other math topics.
T: What is our multiplication sentence for the hundreds
column?
S: 3 hundreds times 5 is 15 hundreds or 1 thousand 5 hundreds.  I noticed the 1,500 in the partial
products strategy came next. The algorithm is multiplying in the same order starting with the ones
column and moving left.  We add the 3 hundreds that were changed from tens. Now we have
18 hundreds. I cross out the 3 on the line because I’ve added it.
T: Right. Last, we have the thousands column.
S: 2 thousands times 5 plus 1 thousand is 11 thousands.
T: Notice that our answer is the same when we used the algorithm and the partial products strategy.
Repeat using 9 × 3,082.
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4. NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 10 4 3
Problem 2: Solve 6 × 3,817 using the algorithm.
Display 6 × 3,817 vertically on the board.
T: With your partner, solve 6 × 3,817 using the algorithm.
Allow students two minutes to solve. Listen for use of unit language to multiply,
such as 6 times 7 ones is 42 ones.
Repeat with 3 × 7,109.
Problem 3: Solve a word problem that requires four-digit by one-digit multiplication using the algorithm.
There are 5,280 feet in a mile. If Bryan ran 4 miles, how many feet did he run?
T: Discuss with your partner how you would solve this problem.
T: On your own, use the algorithm to solve for how many feet Bryan ran.
S: 5,280 × 4 is 21,120. Bryan ran 21,120 feet.
Problem Set (10 minutes)
Students should do their personal best to complete the Problem Set within the allotted 10 minutes. For some
classes, it may be appropriate to modify the assignment by specifying which problems they work on first.
Some problems do not specify a method for solving. Students should solve these problems using the RDW
approach used for Application Problems.
Student Debrief (10 minutes)
Lesson Objective: Multiply three- and four-digit numbers
by one-digit numbers applying the standard algorithm.
The Student Debrief is intended to invite reflection and
active processing of the total lesson experience.
Invite students to review their solutions for the Problem
Set. They should check work by comparing answers with a
partner before going over answers as a class. Look for
misconceptions or misunderstandings that can be
addressed in the Debrief. Guide students in a
conversation to debrief the Problem Set and process the
Any combination of the questions below may be used to
 What pattern did you notice while solving
Problems 1(a) and (b)?
 What happens to the product if one factor is
doubled? Halved?
 What other patterns did you notice while working on Problem 1?
Lesson 10: Objective: Multiply three- and four-digit numbers by one-digit
numbers applying the standard algorithm. 146
5. NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 10 4 3
 Problem 3 only gave one factor. How did you
find the other factor?
 If one of your classmates was absent for the past
week, how would you explain how you solved
Problem 4? Describe any visuals you could use to
lesson?
Exit Ticket (3 minutes)
After the Student Debrief, instruct students to complete
the Exit Ticket. A review of their work will help you assess
the students’ understanding of the concepts that were
presented in the lesson today and plan more effectively
for future lessons. The questions may be read aloud to the
Lesson 10: Objective: Multiply three- and four-digit numbers by one-digit
numbers applying the standard algorithm. 147
6. NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 10 Problem Set 4 3
Name Date
1. Solve using the standard algorithm.
a. 3 × 42 b. 6 × 42
c. 6 × 431 d. 3 × 431
e. 3 × 6,212 f. 3 × 3,106
g. 4 × 4,309 h. 4 × 8,618
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numbers applying the standard algorithm. 148
7. NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 10 Problem Set 4 3
2. There are 365 days in a common year. How many days are in 3 common years?
3. The length of one side of a square city block is 462 meters. What is the perimeter of the block?
4. Jake ran 2 miles. Jesse ran 4 times as far. There are 5,280 feet in a mile. How many feet did Jesse run?
Lesson 10: Objective: Multiply three- and four-digit numbers by one-digit
numbers applying the standard algorithm. 149
8. NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 10 Exit Ticket 4 3
Name Date
1. Solve using the standard algorithm.
a. 2,348 × 6 b. 1,679 × 7
2. A farmer planted 4 rows of sunflowers. There were 1,205 plants in each row. How many sunflowers did
he plant?
Lesson 10: Objective: Multiply three- and four-digit numbers by one-digit
numbers applying the standard algorithm. 150
9. NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 10 Homework 4 3
Name Date
1. Solve using the standard algorithm.
a. 3 × 41 b. 9 × 41
c. 7 × 143 d. 7 × 286
e. 4 × 2,048 f. 4 × 4,096
g. 8 × 4,096 h. 4 × 8,192
Lesson 10: Objective: Multiply three- and four-digit numbers by one-digit
numbers applying the standard algorithm. 151