Develop Skills and Strategies
Lesson 11
Part 1: Introduction
CCSS
4.NBT.B.5
Multiply Whole Numbers
You have learned how to multiply one-digit numbers by multiples of 10. Take a
look at this problem.
There are 100 stickers on each roll, and a box of stickers has 3 rolls.
How many stickers are there in 4 boxes?
Explore It
Use the math you already know to solve the problem.
How many boxes are there? How many rolls of stickers are in each box? What multiplication expression shows how many rolls of stickers there are in all
the boxes? How many stickers are on each roll? What multiplication expression shows how many stickers there are in all?
How can you show 100 using tens as factors? Write an expression that is equal to
the one above using tens as factors. Explain how to use what you know about multiplying by 10 to solve the problem.
96
L11: Multiply Whole Numbers
©Curriculum Associates, LLC Copying is not permitted.
Part 1: Introduction
Lesson 11
Find Out More
To multiply with 3-digit and 4-digit numbers, you need to understand how to
multiply by multiples of 10, 100, and 1,000. Take a look at the chart below.
Expression
433
4 3 30
4 3 300
4 3 3,000
Think of it as...
4 3 3 ones
4 3 3 tens
4 3 3 hundreds
4 3 3 thousands
Think of it as...
12 ones
12 tens
12 hundreds
12 thousands
Product
12
120
1,200
12,000
In each expression, the factor 4 is the same. The other factor increases by one place
value each time.
Look at the products. The digits 1 and 2 from the basic fact 4 3 3 5 12 appear in each
product. In the second expression, 4 is multiplied by 30, which is the same as 3 tens.
That’s 4 times 3 tens which is 12 tens or 120. The factor 30 is 10 times as great as 3 and
the product 120 is 10 times as great as 12.
Reflect
1 Choose a basic multiplication fact that you know. Show how to multiply the
product of the fact by 10, 100, and 1,000. Explain how you know your answer is
correct.
L11: Multiply Whole Numbers
©Curriculum Associates, LLC Copying is not permitted.
97
Part 2: Modeled Instruction
Lesson 11
Read the problem below. Then explore different ways to multiply a 4-digit number
by a 1-digit number.
Ezekiel has 3 building sets. Each set includes 1,125 pieces. How many pieces
are in all 3 sets?
Picture It
You can use an area model to help understand the problem.
1,000
3 3 1,000
3
1
100
3 3 100
1
20
1 5
3 3 20 3 3 5
3 3 1,125 5 (3 3 1,000) 1 (3 3 100) 1 (3 3 20) 1 (3 3 5)
5 3,000 1 300 1 60 1 15
5 3,375
Model It
You can also use partial products to multiply the numbers.
1,125
3    3
98
15
60
300
1 3,000
3,375
3 3 5 ones
3 3 2 tens
3 3 1 hundred
3 3 1 thousand
L11: Multiply Whole Numbers
©Curriculum Associates, LLC Copying is not permitted.
Part 2: Guided Instruction
Lesson 11
Connect It
Now you will explore the problem from the previous page further.
2 What is the expanded form of 1,125? 1 1 1 3 Where do you see the expanded form in the area model?
4 How is the expanded form used in the partial products equation?
5 The partial products equation shows the 3 being multiplied by the ones column
first. Would the product change if you multiplied the 3 by the thousands column
first, followed by the hundreds, tens, and ones? Explain. 6 Describe how the factor 3 is used with the factor 1,125 to find the product.
7 Explain how you multiply a 4-digit number by a 1-digit number. Try It
Use what you just learned to solve these problems. Show your work on a
separate sheet of paper.
8 2,041 3 6 5 9 5,342 3 4 5 L11: Multiply Whole Numbers
©Curriculum Associates, LLC Copying is not permitted.
99
Part 3: Modeled Instruction
Lesson 11
Read the problem below. Then explore different ways to multiply a 2-digit
number by a 2-digit number.
Folding chairs are set up in a school auditorium for a play. There are 16 rows of
chairs, each with 28 chairs. How many folding chairs are there?
Picture It
You can use an area model to multiply 2-digit numbers.
To solve this problem, multiply 16 3 28.
10
20
6
1
20 3 10
2 tens 3 1 ten 5 2 hundreds
200
20 3 6
2 tens 3 6 5 12 tens
120
8 3 10
8 3 1 ten 5 8 tens
80
8 3 6 5 48
1
8
200 1 80 1 120 1 48 5 448
Model It
You can also use partial products to multiply 2-digit numbers.
16
3 28
100
48
80
120
1 200
448
8 ones 3 6 ones
8 ones 3 1 ten
2 tens 3 6 ones
2 tens 3 1 ten
L11: Multiply Whole Numbers
©Curriculum Associates, LLC Copying is not permitted.
Part 3: Guided Instruction
Lesson 11
Connect It
Now you will explore the problem from the previous page further.
10 Why is the area model divided into four sections? 11 How do the four steps in the partial products equation relate to the four sections
in the area model? 12 Would the product change if 20 1 8 on the left side of the area model were
changed to 10 1 10 1 8? Explain. 13 List two different ways that you could break up the numbers in 34 3 12 to find the
product. Explain why both ways would have the same product.
Try It
Use what you just learned to solve these problems. Show your work on a
separate sheet of paper.
14 27 3 21 5 15 37 3 23 5 L11: Multiply Whole Numbers
©Curriculum Associates, LLC Copying is not permitted.
101
Part 4: Guided Practice
Lesson 11
Study the model below. Then solve problems 16–18.
Student Model
The student multiplied
6 by the value of the digit
in each place in 1,785.
An aquarium has 6 female sea turtles. Each turtle lays up to
1,785 eggs a year. If each turtle lays 1,785 eggs this year, how
many eggs will there be in all?
Look at how you could show your work using an area model.
1,000
6
Pair/Share
How else could you
solve this problem?
Should you multiply
15 3 24 or 24 3 15?
6 3 1,000
1
700
6 3 700
1
80
1
6 3 80
5
635
6 3 1,785 5 (6 3 1,000) 1 (6 3 700) 1 (6 3 80) 1 (6 3 5)
5 6,000 1 4,200 1 480 1 30
5 10,710
Solution: 10,710 eggs
16 A deli is preparing trays of sandwiches. There are 15 trays, each
with 24 sandwiches. How many sandwiches are there?
Show your work.
Pair/Share
How did you decide
which model to use to
help you solve the
problem?
102
Solution: L11: Multiply Whole Numbers
©Curriculum Associates, LLC Copying is not permitted.
Part 4: Guided Practice
17 The owner of 12 bookstores is buying 32 copies of a new book for
each of the stores. How many books is the owner buying in all?
Show your work.
Lesson 11
Could you use an area
model to help solve the
problem?
Pair/Share
Solution: 18 A hardware store has 147 containers of paint. If each container
holds 5 gallons of paint, how many gallons of paint are at the
store? Circle the letter of the correct answer.
How is this problem
different than the one
modeled on page 102?
Multiply 5 by the value
of the digit in each place
in 147.
A235
B505
C735
D905
Dale chose A as the correct answer. How did he get that answer?
L11: Multiply Whole Numbers
©Curriculum Associates, LLC Copying is not permitted.
Pair/Share
Does Dale’s answer
make sense?
103
Part 5: Common Core Practice
Lesson 11
Solve the problems.
1 A person blinks about 16 times per minute. About how many times does a person
blink in 3 hours? [Hint: 1 hour 5 60 minutes]
A48
B96
C960
D2,880
2 Mr. Larson is planning a pizza party for 273 people. He plans on 3 slices of pizza for
each person. How many slices of pizza is this in all?
A276
B546
C619
D819
3 Tell whether each expression can be used to solve 29 3 14.
104
a.(9 3 4) 1 (20 3 4) 1 (9 3 1) 1 (20 3 1)
Yes
No
b.(14 3 9) 1 (14 3 20)
Yes
No
c.(9 3 4) 1 (20 3 4) 1 (9 3 10) 1 (20 3 10)
Yes
No
d.(29 3 4) 1 (29 3 10)
Yes
No
L11: Multiply Whole Numbers
©Curriculum Associates, LLC Copying is not permitted.
Part 5: Common Core Practice
Lesson 11
4 Which model(s) below could represent the solution to the problem 45 3 15? Circle the
letter for all that apply.
40
A
5
10
5
B
0 15 30 45
C(4 3 1) 1 (4 3 5) 1 (5 3 1) 1 (5 3 5)
D(4 3 1) 1 (5 3 5)
E
0
45
90
135 180 225 270 315 360 405 450 495 540 585 630 675
5 Mo attended 14 tutoring sessions. Each session was 45 minutes long.
How many minutes long were all 14 sessions?
Show your work.
Answer Mo was tutored for minutes.
6 Fourth grade students held a recycling drive. During one week they collected an
average of 1,238 water bottles each day. How many water bottles did the fourth
graders collect? [Hint: There are 7 days in one week.]
Show your work.
Answer The fourth grade students collected water bottles.
Self Check Go back and see what you can check off on the Self Check on page 95.
L11: Multiply Whole Numbers
©Curriculum Associates, LLC Copying is not permitted.
105
Develop Skills and Strategies
Lesson 11
(Student Book pages 96–105)
Multiply Whole Numbers
Lesson Objectives
The Learning Progression
•Multiply whole numbers of up to four digits by
one-digit whole numbers.
In Grade 3, students used equations, rectangular
arrays, and the properties of operations to develop an
understanding of multiplication. They multiplied
one-digit whole numbers by multiples of 10, within
100. In Grade 4, students should continue to utilize
equations, rectangular arrays, and the properties of
operations as they multiply a whole number up to four
digits by a one-digit number, and as they multiply
two-digit numbers. This foundation will prepare them
for Grade 5, when they become fluent with the
standard multiplication algorithm with multi-digit
whole numbers.
•Multiply a two-digit number by a two-digit number.
•Use equations, rectangular arrays, and area models
to illustrate and explain calculations.
Prerequisite SkilLs
In order to be proficient with the concepts/skills in this
lesson, students should:
•Recall basic multiplication facts.
•Know properties of operations.
Teacher Toolbox
•Understand place value.
•Understand and use rectangular arrays and
area models.
Teacher-Toolbox.com
Prerequisite
Skills
Ready Lessons
Vocabulary
Tools for Instruction
There is no new vocabulary. Review the following
key terms.
Interactive Tutorials
✓✓
✓
4.NBT.B.5
✓
✓✓
✓
multiplication: an operation used to find the total
number of items in equal-sized groups
product: the answer to a multiplication problem
factor: numbers that are multiplied together to get
a product
multiple: the product of the number and any other
whole number (0, 4, 8, 12, etc. are multiples of 4)
CCSS Focus
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.
ADDITIONAL STANDARDS: 4.OA.A.2, 4.OA.A.3, 4.NBT.A.1 (See page A42 for full text.)
STANDARDS FOR MATHEMATICAL PRACTICE: SMP 1, 2, 3, 4, 5, 7 (See page A9 for full text.)
L11: Multiply Whole Numbers
©Curriculum Associates, LLC Copying is not permitted.
105
Part 1: Introduction
Lesson 11
At a Glance
Students read a word problem and answer a series of
questions designed to explore a method for multiplying
a 3-digit number by a 1-digit number.
Develop skills and strategies
Lesson 11
Part 1: introduction
ccss
4.nbt.b.5
Multiply Whole numbers
you have learned how to multiply one-digit numbers by multiples of 10. take a
look at this problem.
Step By Step
There are 100 stickers on each roll, and a box of stickers has 3 rolls.
•Tell students that this page models how to multiply
two numbers by a factor of 10.
How many stickers are there in 4 boxes?
•Have students read the problem at the top of the page.
explore it
•Work through Explore It as a class.
use the math you already know to solve the problem.
How many boxes are there?
•Ask students to explain how they found the total
number of rolls of stickers in all of the boxes. Point
out that they may find it helpful to write “100” under
each roll of stickers.
4
How many rolls of stickers are in each box?
3
What multiplication expression shows how many rolls of stickers there are in all
the boxes? 4 3 3
How many stickers are on each roll?
100
What multiplication expression shows how many stickers there are in all?
•Explain to students that putting a zero at the end of a
number is a shortcut for multiplying by 10. Make
sure they understand what is happening to the value
of the number when it is multiplied by a factor of 10.
4 3 3 3 100
How can you show 100 using tens as factors? Write an expression that is equal to
the one above using tens as factors. 4 3 3 3 10 3 10
Explain how to use what you know about multiplying by 10 to solve the problem.
Possible explanation: When you multiply by 10, the digits in the other
factor move one place to the left and a 0 goes in the ones place.
SMP Tip: Point out to students that when
multiplying by multiples of 10, there is a pattern
of putting zeros at the end of the number you are
multiplying. In other words, when multiplying
by 10, add 1 place value or 1 zero; when multiplying
by 100, add 2 places or 2 zeros; when multiplying
by 1,000, add 3 place values, or 3 zeros, and so on.
(SMP 1)
106
96
L11: Multiply Whole Numbers
©Curriculum Associates, LLC
Copying is not permitted.
Mathematical Discourse
•If you have a multiplication problem such as
100 3 12, will it change your answer if you write it
as 12 3 100?
Students’ responses should be that both
problems have the same answer. This is an
example of the Commutative Property of
Multiplication, of which students understand
the concept, but may not necessarily know the
name. It states that regardless of the order in
which you multiply two numbers, the product
is the same.
L11: Multiply Whole Numbers
©Curriculum Associates, LLC Copying is not permitted.
Part 1: Introduction
Lesson 11
At a Glance
Students find a pattern for multiplying by multiples of
10, such as 10, 100, and 1,000. They learn that when
multiplying basic facts by a multiple of 10, the product
increases by the same place value as the multiple of 10.
Part 1: introduction
Find out More
To multiply with 3-digit and 4-digit numbers, you need to understand how to
multiply by multiples of 10, 100, and 1,000. Take a look at the chart below.
expression
433
4 3 30
4 3 300
4 3 3,000
Step By Step
•Read Find Out More as a class.
•Using base-ten blocks, emphasize to students that
120 is 10 times greater than 12.
•Use the chart to show how the product increases by
one place-value position as the multiple of 10
increases.
•Make sure students know how many zeros are
associated with each place value name.
[ones 5 no zeros, tens 5 1 zero, hundreds 5 2 zeros,
thousands 5 3 zeros]
Lesson 11
think of it as...
4 3 3 ones
4 3 3 tens
4 3 3 hundreds
4 3 3 thousands
think of it as...
12 ones
12 tens
12 hundreds
12 thousands
Product
12
120
1,200
12,000
In each expression, the factor 4 is the same. The other factor increases by one place
value each time.
Look at the products. The digits 1 and 2 from the basic fact 4 3 3 5 12 appear in each
product. In the second expression, 4 is multiplied by 30, which is the same as 3 tens.
That’s 4 times 3 tens which is 12 tens or 120. The factor 30 is 10 times as great as 3 and
the product 120 is 10 times as great as 12.
reflect
1 Choose a basic multiplication fact that you know. Show how to multiply the
product of the fact by 10, 100, and 1,000. Explain how you know your answer is
correct.
answers may vary. Look for explanations that include following a pattern
of shifting the product one place to the left or adding a place value to each
product.
97
L11: Multiply Whole Numbers
©Curriculum Associates, LLC
Hands-On Activity
Use a Bingo game to understand multiplying
numbers (multiples of ten).
Materials: Bingo game cards that have squares filled
with various types of answers to multiplication
problems involving multiples of ten.
•Distribute a bingo card and some markers to each
student or pair of students.
Copying is not permitted.
Real-World Connection
Encourage students to think of any everyday
situation where they may encounter the need to
multiply.
Examples: calculating the number of minutes in a
given number of hours, calculating the number of
pennies, nickels, or dimes in a given number of
dollars, calculating the number of rows of items
•Choose a multiplication problem (from a set you
have) and read it aloud (e.g., 5 times 60).
•Students will then look for any way that this
problem may be represented on their bingo card.
•Repeat the steps of reading problems and covering
spaces until a student has covered all the spaces
in a column or in a row on his or her card.
L11: Multiply Whole Numbers
©Curriculum Associates, LLC Copying is not permitted.
107
Part 2: Modeled Instruction
Lesson 11
At a Glance
Part 2: Modeled instruction
Students use partial products and an area model to find
the product of a 4-digit number and a 1-digit number.
Lesson 11
read the problem below. then explore different ways to multiply a 4-digit number
by a 1-digit number.
Step By Step
Ezekiel has 3 building sets. Each set includes 1,125 pieces. How many pieces
are in all 3 sets?
•Read the problem at the top of the page as a class.
Picture it
•Read Picture It. Have a volunteer explain how the
number is written in the area model and why it is
written this way. [The number 1,125 is written in
expanded form to multiply 3 by a multiple of 10 and
make calculations easier.]
you can use an area model to help understand the problem.
1,000
3 3 1,000
3
1
100
1
3 3 100
20 1 5
3 3 20 3 3 5
3 3 1,125 5 (3 3 1,000) 1 (3 3 100) 1 (3 3 20) 1 (3 3 5)
5 3,000 1 300 1 60 1 15
5 3,375
Model it
•Ask students how they could use addition to check
the answer. [1,125 1 1,125 1 1,125 5 3,375]
you can also use partial products to multiply the numbers.
3
1,125
3
15
60
300
1 3,000
3,375
•Read Model It.
•Make sure students understand that the digits in the
tens, hundreds, and thousands places represent 20,
100, and 1,000.
3 3 5 ones
3 3 2 tens
3 3 1 hundred
3 3 1 thousand
SMP Tip: Discuss with students the benefits of
using an area model. An area model is a tool they
can use to help visualize the multiplication
problem, which can sometimes seem abstract.
Models also break down the problem into smaller,
simpler pieces that can be easier to multiply.
(SMP 5)
ELL Support
To help students understand the concept of
multiplication, let them know that multiplication is
the same as repeated addition. Show a few simple
examples, such as:
3 3 7 5 3 1 3 1 3 1 3 1 3 1 3 1 3
108
98
L11: Multiply Whole Numbers
©Curriculum Associates, LLC
Copying is not permitted.
Mathematical Discourse
•How can you determine if your answer to the
problem is reasonable?
Students should explain that 1,125 is close to
1,000. Replacing 1,125 with 1,000 in the
problem, you get an estimate of 3,000. The
actual product should be close to 3,000.
L11: Multiply Whole Numbers
©Curriculum Associates, LLC Copying is not permitted.
Part 2: Guided Instruction
Lesson 11
At a Glance
Students revisit the problem on page 98.
Step By Step
•Read Connect It as a class. Be sure to point out that
the questions refer to the problem on page 98.
•Make sure that students see the connection between
the expanded form and base-ten blocks: 5 is 5 ones
blocks, 20 is 2 tens rods, 100 is 1 hundreds flat,
1,000 is 1 thousands cube.
•Have students explain their answer to problem 4.
Have them use colored pencils to connect the partial
products in the Model It to the area model in the
Picture It.
•Have students explain their answer to problem 5.
Make sure they understand that multiplication can
be performed in any order and the product remains
the same.
Part 2: guided instruction
Lesson 11
connect it
now you will explore the problem from the previous page further.
2 What is the expanded form of 1,125?
1,000 1
100
1
20
1
5
3 Where do you see the expanded form in the area model?
one side of the area model is separated into the expanded form.
4 How is the expanded form used in the partial products equation?
each number in the expanded form is multiplied by the other factor, 3.
5 The partial products equation shows the 3 being multiplied by the ones column
first. Would the product change if you multiplied the 3 by the thousands column
first, followed by the hundreds, tens, and ones? Explain. no, the product
would be the same. you would add the partial sums in a different order,
but the sum doesn’t change when you add in a different order.
6 Describe how the factor 3 is used with the factor 1,125 to find the product.
the 3 is multiplied by the number in each place-value position in 1,125.
then all the partial products are added.
7 Explain how you multiply a 4-digit number by a 1-digit number. Multiply the
numbers in each place-value position of the 4-digit number by the 1-digit
number. Find the partial products and then add to find the final product.
try it
use what you just learned to solve these problems. show your work on a
separate sheet of paper.
8 2,041 3 6 5
12,246
9 5,342 3 4 5
21,368
L11: Multiply Whole Numbers
©Curriculum Associates, LLC
Copying is not permitted.
99
Try It Solutions
Concept Extension
Relate the partial products method to the
Distributive Property.
The partial products method is an example of the
Distributive Property.
The Distributive Property states that you can
multiply a number and a sum by multiplying the
number by each part of the sum and then adding
these products.
•Explain that when breaking down the numbers
into expanded form, you get 1,000 1 100 1
20 1 5.
8Solution: 12,246; Multiply 6 by each digit in 2,041:
(2,000 3 6) 1 (0 3 6) 1 (40 3 6) 1 (1 3 6).
Find the partial products: 12,000 1 240 1 6.
Add to find the product: 12,246
ERROR ALERT: Students who wrote 1,446
multiplied 6 by 241 instead of 2,041. Those students
added partial products of 1,200, 240, and 6.
9Solution: 21,368; Multiply 4 by each digit in 5,342:
(5,000 3 4) 1 (300 3 4) 1 (40 3 4) 1 (2 3 4).
Find the partial products:
20,000 1 1,200 1 160 1 8.
Add to find the product: 21,368.
•You can write the problem like this:
3 3 1,125 5 3(1,000 1 100 1 20 1 5)
•Using the Distributive Property, this simplifies to
3,000 1 300 1 60 1 15, which matches the
partial products shown.
L11: Multiply Whole Numbers
©Curriculum Associates, LLC Copying is not permitted.
109
Part 3: Modeled Instruction
Lesson 11
At a Glance
Part 3: Modeled instruction
Students use an area model and partial products to
multiply a 2-digit number by a 2-digit number.
Lesson 11
read the problem below. then explore different ways to multiply a 2-digit
number by a 2-digit number.
Step By Step
Folding chairs are set up in a school auditorium for a play. There are 16 rows of
chairs, each with 28 chairs. How many folding chairs are there?
•Read the problem at the top of the page as a class.
Picture it
•Read Picture It.
you can use an area model to multiply 2-digit numbers.
To solve this problem, multiply 16 3 28.
•Relate one side of the area model to the number of
rows and one side of the area model to the number of
chairs in each row.
10
20
6
1
20 3 10
2 tens 3 1 ten 5 2 hundreds
200
20 3 6
2 tens 3 6 5 12 tens
120
8 3 10
8 3 1 ten 5 8 tens
80
8 3 6 5 48
1
•Have students identify the multiplication expression
for each section of the area model.
[10 3 20, 10 3 8, 6 3 20, 6 3 8]
8
200 1 80 1 120 1 48 5 448
Model it
•Encourage students to circle the partial products
within each section to help them distinguish the
addends for the final step.
you can also use partial products to multiply 2-digit numbers.
16
3 28
48
80
120
1 200
448
•Read Model It.
•Be sure students use placeholder zeros as they
multiply by the multiples of ten.
100
8 ones 3 6 ones
8 ones 3 1 ten
2 tens 3 6 ones
2 tens 3 1 ten
L11: Multiply Whole Numbers
©Curriculum Associates, LLC
Copying is not permitted.
Visual Model
Present the lattice multiplication method for multiplying two 2-digit numbers. The following is an example of
how to use this method to find 53 3 41.
5
1Draw a 2-by-2 table. Draw diagonal lines through
all four squares. Write the digits in 53 above the
columns and the digits in 41 next to the rows.
2Multiply 3 times 4, and record the product, 12, in
the corresponding box (keeping the digit in the
tens place above the diagonal and the digit in the
ones place below the diagonal).
3Repeat Step 2 for the other numbers.
3
2
2
1
2
0
0
0
5
1
7
3
4
1
3
4Add the numbers you recorded in the diagonals,
writing their sums outside the lattice boxes.
(In the sample shown, the answers are underlined.)
5Read the answer from top left to bottom right,
so the final product is 2,173.
110
L11: Multiply Whole Numbers
©Curriculum Associates, LLC Copying is not permitted.
Part 3: Guided Instruction
Lesson 11
At a Glance
Students revisit the problem on page 100.
Step By Step
•Read Connect It as a class. Be sure to point out that
the questions refer to the problem on page 100.
•Have students explain their answer to problem 10.
Ask, When you multiply the ones in 28 and the tens in
16, why is the product 80 and not 8? [There are
8 groups of 10, which is 80.]
Part 3: guided instruction
Lesson 11
connect it
now you will explore the problem from the previous page further.
10 Why is the area model divided into four sections? each number in the
expanded form of one factor is multiplied by each number in the
expanded form of the other factor. each section shows a product.
11 How do the four steps in the partial products equation relate to the four sections
in the area model? each step shows the product in one section of the
area model.
12 Would the product change if 20 1 8 on the left side of the area model were
changed to 10 1 10 1 8? Explain. no, the product would be the same.
instead of a partial product of 200, you would have two partial products of
100. instead of a partial product of 120, you would have two partial
SMP Tip: Discuss the importance of being able to
use mathematical language accurately. Review the
meanings of the terms digit, factor, and product,
showing examples of each. Encourage students to
practice using these terms in the right context at
the appropriate time. (SMP 1)
products of 60. the total of all the partial products would still be the same.
13 List two different ways that you could break up the numbers in 34 3 12 to find the
product. Explain why both ways would have the same product.
Possible answer: 30 1 4 and 10 1 2 or 20 1 10 1 4 and 5 1 5 1 2. as long
as the sum of the numbers equals the factor, the partial products will add
up to the same product.
try it
use what you just learned to solve these problems. show your work on a
separate sheet of paper.
•Have students explain their answer to problem 11.
Students should understand how the partial products
and the area model are related. [The partial products
are the same numbers as the areas in each section of
the area model.]
Concept Extension
Use base-ten blocks to multiply a 2-digit
number by a 2-digit number.
Materials: base-ten blocks
•Group students in pairs. Distribute base-ten
blocks to each pair. Use the steps below to model
43 3 14 (similar to using an area model).
•Model 43 on a flat surface by displaying 4 tens
rods and 3 unit cubes in a single row.
14 27 3 21 5
567
15 37 3 23 5
851
L11: Multiply Whole Numbers
©Curriculum Associates, LLC
Copying is not permitted.
101
Try It Solutions
14 Solution: 567; Students can use any method shown
to find the product. The partial products are
(20 3 20) 1 (20 3 7) 1 (1 3 20) 1 (1 3 7) 5
400 1 140 1 20 1 7.
15 Solution: 851; Students can use any method shown
to find the product. The partial products are
(20 3 30) 1 (20 3 7) 1 (3 3 30) 1 (3 3 7) 5
600 1 140 1 90 1 21.
•Model 14 by displaying 1 tens rod and 4 unit
cubes in a single column to the left and below the
row showing 43.
•Fill the inside with the largest blocks that match
the area of each row and column. For this
example, use 4 flats, 19 rods, and 12 unit cubes.
•The product is the value of the inside blocks.
[400 1 190 1 12 5 602]
•Model other products as time allows.
L11: Multiply Whole Numbers
©Curriculum Associates, LLC Copying is not permitted.
111
Part 4: Guided Practice
Lesson 11
Part 4: guided Practice
Lesson 11
study the model below. then solve problems 16–18.
An aquarium has 6 female sea turtles. Each turtle lays up to
each of the stores. How many books is the owner buying in all?
Show your work.
10
1,785 eggs a year. If each turtle lays 1,785 eggs this year, how
many eggs will there be in all?
30
Look at how you could show your work using an area model.
1,000
6
Pair/share
How else could you
solve this problem?
Should you multiply
15 3 24 or 24 3 15?
1
6 3 1,000
700
6 3 700
1
80
1
6 3 80
102
2
635
6 3 1,785 5 (6 3 1,000) 1 (6 3 700) 1 (6 3 80) 1 (6 3 5)
5 6,000 1 4,200 1 480 1 30
5 10,710
1
Could you use an area
model to help solve the
problem?
2
30 3 10
3 tens 3 1 ten 5 3 hundreds
300
30 3 2
3 tens 3 2 5 6 tens
60
2 3 10
2 3 1 ten 5 2 tens
20
23254
Solution: 384 books
Pair/share
How is this problem
different than the one
modeled on page 102?
Solution: 10,710 eggs
18 A hardware store has 147 containers of paint. If each container
16 A deli is preparing trays of sandwiches. There are 15 trays, each
with 24 sandwiches. How many sandwiches are there?
15
3 24
How did you decide
which model to use to
help you solve the
problem?
1
5
Show your work.
Pair/share
Lesson 11
17 The owner of 12 bookstores is buying 32 copies of a new book for
Student Model
The student multiplied
6 by the value of the digit
in each place in 1,785.
Part 4: guided Practice
20
40
100
1 200
360
4 ones 3 5 ones
4 ones 3 1 ten
2 tens 3 5 ones
2 tens 3 1 ten
holds 5 gallons of paint, how many gallons of paint are at the
store? Circle the letter of the correct answer.
Multiply 5 by the value
of the digit in each place
in 147.
a 235
b
505
c
735
D 905
Dale chose a as the correct answer. How did he get that answer?
Dale multiplied 5 by the tens and 5 by the ones. he did not
multiply 5 by the hundreds.
Pair/share
Does Dale’s answer
make sense?
Solution: 360 sandwiches
L11: Multiply Whole Numbers
L11: Multiply Whole Numbers
©Curriculum Associates, LLC
Copying is not permitted.
©Curriculum Associates, LLC
Copying is not permitted.
103
At a Glance
Solutions
Students solve problems involving multiplication of a
whole number of up to 4 digits by a 1-digit number and
a 2-digit number by a 2-digit number.
Ex Multiplying using partial products in an area model
is shown as one way to solve the problem. Students
need to multiply 6 by each digit in 1,785. Then add
the partial products.
Step By Step
•Ask students to solve the problems individually and
label units in their calculations.
•When students have completed each problem, have
them Pair/Share to discuss their solutions with a
partner or in a group.
16 Solution: 360 sandwiches; Multiply 10 by each digit
in 24, and multiply 5 by each digit in 24 to find the
partial products: 200 1 40 1 100 1 20. Then add.
(DOK 1)
17 Solution: 384 books; Multiply 10 by each digit in 32
and multiply 2 by each digit in 32 to find the partial
products: 300 1 20 1 60 1 4. Then add. (DOK 1)
18 Solution: C; Multiply 5 by each digit in 147, and
then add the partial products.
Explain to students why the other two answer
choices are not correct:
B is not correct because 5 3 100 5 500 and
47 3 5 is more than 5.
D is not correct because 5 should be multiplied by
(100 1 40 1 7), not (1 1 40 1 700) (DOK 3)
112
L11: Multiply Whole Numbers
©Curriculum Associates, LLC Copying is not permitted.
Part 5: Common Core Practice
Part 5: common core Practice
Lesson 11
Solve the problems.
1
2
Lesson 11
Part 5: common core Practice
4
Lesson 11
Which model(s) below could represent the solution to the problem 45 3 15? Circle the
letter for all that apply.
40
A person blinks about 16 times per minute. About how many times does a person
blink in 3 hours? [Hint: 1 hour 5 60 minutes]
A
48
B
96
C
960
D
2,880
A
5
10
5
B
0 15 30 45
C
(4 3 1) 1 (4 3 5) 1 (5 3 1) 1 (5 3 5)
Mr. Larson is planning a pizza party for 273 people. He plans on 3 slices of pizza for
each person. How many slices of pizza is this in all?
D
(4 3 1) 1 (5 3 5)
A
276
E
B
546
C
619
D
819
5
0
45
90
135 180 225 270 315 360 405 450 495 540 585 630 675
Mo attended 14 tutoring sessions. Each session was 45 minutes long.
How many minutes long were all 14 sessions?
Show your work.
3
Tell whether each expression can be used to solve 29 3 14.
a.
(9 3 4) 1 (20 3 4) 1 (9 3 1) 1 (20 3 1)
b.
(14 3 9) 1 (14 3 20)
c.
(9 3 4) 1 (20 3 4) 1 (9 3 10) 1 (20 3 10)
d.
(29 3 4) 1 (29 3 10)
Yes
3 No
3 Yes
3 Yes
3 Yes
Answer Mo was tutored for
No
630
minutes.
No
No
6
Fourth grade students held a recycling drive. During one week they collected an
average of 1,238 water bottles each day. How many water bottles did the fourth
graders collect? [Hint: There are 7 days in one week.]
Show your work.
Answer The fourth grade students collected
8,666
water bottles.
self check Go back and see what you can check off on the Self Check on page 95.
104
L11: Multiply Whole Numbers
L11: Multiply Whole Numbers
©Curriculum Associates, LLC
Copying is not permitted.
At a Glance
Students solve multiplication problems that might
appear on a mathematics test.
Solutions
1Solution: D; Multiply 3 by each digit in 16:
(10 3 3) 1 (6 3 3). Add the partial products:
30 1 18 5 48. Multiply 60 by each digit in 48:
(60 3 40) 1 (60 3 8). Add the partial products:
2,400 1 480 5 2,880. (DOK 1)
2Solution: D; Multiply 3 by each digit in 273. Find
the partial products. Add to find the product.
(DOK 1)
©Curriculum Associates, LLC
Copying is not permitted.
105
4Solution: A; The area model can be split into four
sections: 40 3 10, 40 3 5, 5 3 10, and 5 3 5. Those
partial products can be added together to equal the
product of 45 3 15.
E; The number line shows 45 added 15 times, which
is the same as multiplying 45 3 15. (DOK 2)
5630; Multiply 10 by each digit in 45 and multiply
4 by each digit in 45. Add the partial products:
400 1 50 1 160 1 20 5 630 (DOK 1)
68,666; Multiply 7 by each digit in 1,238.
Add the partial products:
7,000 1 1,400 1 210 1 56 5 8,666 (DOK 1)
3Solution: a. No; b. Yes; c. Yes; d. Yes (DOK 2)
L11: Multiply Whole Numbers
©Curriculum Associates, LLC Copying is not permitted.
113
Differentiated Instruction
Lesson 11
Assessment and Remediation
•Ask students to find the product of 36 and 15. [540]
•For students who are still struggling, use the chart below to guide remediation.
•After providing remediation, check students’ understanding. Ask students to explain their thinking while
finding the product of 18 and 27. [486]
•If a student is still having difficulty, use Ready Instruction, Level 3, Lesson 2.
If the error is . . .
Students may . . .
To remediate . . .
51
have added.
Remind students that “product” means multiplication.
54
have found all partial
products as ones times
ones.
Demonstrate using base-ten blocks that 36 is 30 1 6 and 15 is
10 1 5. Draw an area model to show students each partial
product.
270
have incorrectly found
the tens by tens partial
product as 3 3 10.
Remind students that when multiplying tens by tens, the result is
30 3 10 5 300, not 3 3 10 5 30.
440
have incorrectly added
partial products.
Remind students that they must regroup 14 tens as 1 hundred
and 4 tens when adding partial products.
Hands-On Activity
Challenge Activity
Use play money to understand multiplying
numbers.
Present the students with the following
problems.
Materials: play money: one-dollar bills (for
hundreds); dimes (for tens); pennies (for ones)
(You can also use hundred-dollar bills for hundreds,
ten-dollar bills for tens, and one-dollar bills
for ones.)
Each problem will require two steps to solve,
multiplication being one of the steps involved.
•Have students work in pairs.
•Present a multiplication problem to students.
•Have students model the problem with the play
money. For example: 154 3 3 would be modeled
with 3 sets of 1 one-dollar bill, 5 dimes, and
4 pennies.
•Have students exchange 10 of the pennies for
1 dime and 10 of the dimes for a one-dollar bill.
•The final result would be: 4 one dollar bills,
6 dimes, and 2 pennies, which is 462.
114
•Brandon had 48 collectible cards. He gave 3 cards
to each of his 10 friends. How many cards does
Brandon have left? [18 cards]
•Amelia earns $12 an hour babysitting. She babysat
for 16 hours. She also earned $25 for watering her
neighbor’s tomato garden. How much has Amelia
earned altogether? [$217]
•Mr. Rutledge is taking inventory of the items
on the shelves of his store. He has 9 unopened
boxes of soap and 16 bars of soap on the shelf.
Each unopened box of soap has 312 bars in it.
How many total bars of soap does Mr. Rutledge
have? [2,824 bars]
L11: Multiply Whole Numbers
©Curriculum Associates, LLC Copying is not permitted.