Thank you for participating
in Teach It First!
This Teach It First Kit contains a Crosswalk Plus student lesson and teacher answer
key. Also included is a teacher mini-lesson and worksheet. The mini-lesson was
designed as an introduction to each chapter. Use the student lesson as your
instructional tool or begin with the mini lesson if you feel your students need a
refresher on the topic—you decide!
Are you transitioning to the Common Core State Standards? If you are getting
ready for change, or have already begun your shift to the new standards,
Crosswalk Coach PLUS for the Common Core State Standards has you covered!
This series is newly revised and better than ever—it now includes:
•Two Common Core Practice Tests
•Lots of additional practice
•New item types that reflect the rigor of the new CCSS assessments
Each lesson targets a single skill, promoting achievement through instruction
and practice, and allowing you to assess mastery of discrete skills. You’ll get
maximum flexibility in addressing areas of need. Plus, Coached Examples
throughout strengthen comprehension. Everything you need to transition to the
new standards is right here!
We are happy to provide you this complimentary sample and would love to know
what you think. Once you have read through this lesson, do what you do best—
present it to your students. Then, don’t forget to complete a quick survey by
going to www.triumphlearning.com/teach-it-first. By doing so, you will be
entered into our quarterly raffle for one of five American Express $100 gift cards.
Regards,
Triumph Learning
Join the conversation about Common Core today by visiting commoncore.com, the place
where teachers, parents, and experts come together to share best practices and practical
information for successfully implementing Common Core standards in the classroom.
Learn it Today, Use it tomorrow.
136 Madison Avenue • New York, NY 10016 • p: 212.652.0215 • f : 212.857.8499 • www.triumphlearning.com
Cr
os
s
wa
l
kPl
us
,
Ma
t
he
ma
t
i
c
s
,
T
e
a
c
he
rE
di
t
i
on,
Gr
a
de4
Mini-Lessons
Place Value
Teach
Practice/Apply
Explain how important it is to understand place value.
A digit’s value depends on its location in a number.
When we understand this idea, we can compare and
compute better.
Distribute Reproducible R1. Ask students to do
exercise 1. Then go over this exercise to make
sure everyone understands it.
Model
1. C. 900
Show students the numbers 325, 523, and 235. These
are different even though they all have the same digits:
2, 3, and 5.
Ask Students
Ask students to explain why the three numbers
are different. Make sure they understand that the
3 of 325 is 300, the 5 of 523 is 500, and the 2 of 235
is 200. Explain also the tens and ones places for all
three numbers.
Answers to Reproducible (R1)
2. 9,817 is greater than 8,917. The 9 in 9,817 stands
for 9,000, whereas the 8 in 8,917 stands for
8,000. So, 9,817 is greater than 9,000 whereas
8,917 is less than 9,000.
3. 965
4. C. 3 hundreds
5. B. 30
Estimation
Teach
Practice/Apply
Explain why rounding is an excellent tool for
estimation. Rounding to a number ending in 0
(10, 100, 1,000) allows for good estimates. It is easier
to work with numbers ending in 0.
Distribute Reproducible R2. Ask students to do
exercise 1. Then go over this exercise to make
sure everyone understands it.
Model
1. A. 20
Explain what it means to round numbers. Show how
to round the number 87 to the nearest 10. First, place
87 on a number line that goes from 80 to 90. Then,
show that 87 is closer to 90 than to 80. So, we say
that 87 rounded to the nearest 10 is 90.
80 81 82 83 84 85 86 87 88 89 90
Ask Students
Answers to Reproducible (R2)
2. 29 is closer to 30 than to 20, so 29 rounds to 30.
26 is also closer to 30 than to 20, so 26 rounds
to 30.
3. 40
4. 480
5. 400
6. If a number is halfway between two 100s (such as
700 and 800), round the number up to the greater
100. So, 750 rounded to the nearest 100 is 800.
Ask students to round 63 to the nearest 10.
Tell them to use a number line that goes from 60 to
70. Show that 63 is closer to 60 than 70, which means
that 63 rounded to the nearest 10 is 60.
14
T287NAG_Mth_G4_TG_PDF.indd 14
9/25/13 6:30 PM
Name:
Date:
Place Value
A number’s value depends on the place value of the digits.
63 is greater than 36 because of where the 3 and 6 are.
1. What is the value of the 9 in 8,917?
A. 9
B. 90
C. 900
2. Is 9,817 greater or less than 8,917? Explain.
3. Write the number that has 5 ones, 6 tens, and 9 hundreds.
4. How many hundreds more is 2,306 than 2,006?
A. 7 hundreds
B. 5 hundreds
C. 3 hundreds
5. What is the value of the 3 in 784,235?
A. 3
B. 30
© Triumph Learning, LLC
C. 300
R1
T287NAG_Mth_G4_TG_PDF.indd 17
9/25/13 6:30 PM
Answer Keys (continued)
B. 532 cherry pies; I multiplied 38 3 14. First
I multiplied 38 by 4 ones to get 152. Then I
multiplied 38 by 1 ten to get 380. Then I added
the partial products: 152 1 380 5 532.
10. A: True, B: False, C: True, D: False, E: True 11. A: area model 2, B: area model 3, C: area model 1,
D: area model 4.
12. 9
13. A: Yes, B: No, C: No, D: Yes
14. Correct Product: 15 3 52 5 780; 8 3 758 5
6,064; 4 3 1,654 5 6,616
Incorrect Product: 6 3 3,245 5 18,270;
74 3 16 5 1,164; 4 3 129 5 486
15. B, C, E
14. 11
15. A: Yes, B: Yes, C: No, D: Yes, E: No
16. B, C, E
Lesson 6
Coached Example
There are 32 classrooms.
There are 24 students in each class.
32 3 24 5 n
Express 24 in expanded form.
24 5 20 1 4
Rewrite the sentence with 24 in expanded form.
32 3 24 5 32 3 (20 1 4)
Distribute 32 to each addend.
Lesson 5
32 3 (20 1 4) 5 (32 3 20) 1 (32 3 4)
Coached Example
Use the commutative property of multiplication to
change the order of the factors.
Find each product.
5 3 2 3 14 5
Use the associative property of multiplication to group
the factors.
(32 3 20) 1 (32 3 4) 5 n
640 1 128 5 n
Add the products.
640 1 128 5 768
(5 3 2) 3 14 5
There are 768 students in all at the school.
Multiply inside the parentheses.
Lesson Practice
1. B
(10) 3 14 5
Multiply that factor and the other factor.
10 3 14 5 140
So, 5 3 14 3 2 5 140
2. B
3. A
4. D
5. C
Joey bought 140 jellybeans in all.
6. C
Lesson Practice
1. C
7. D
2. C
9. A. 32 3 64 5
3. B
4. B
5. A
6. C
7. D
8. D
9. A. Possible answer: 12 3 5 3 6 5
B. Possible answer: (12 3 5) 3 6 5
C.360 passengers
10. A, B, E
11. 32
12. A: True, B: True, C: False, D: False, E: True
13. A: 23, B: 13, C: 31, D: 1, E: 10
8. B
B. 2,048; Student work may vary. Possible work:
32 3 64 5 32 3 (60 1 4) 5 (32 3 60) 1
(32 3 4) 5 1,920 1 128 5 2,048
10. A: False, B: True, C: False, D: True, E: False
11. A: (5 3 10) 1 (5 3 5)
B: (15 3 20) 1 (15 3 5)
C: (12 3 10) 1 (12 3 6)
D: (6 3 10) 1 (6 3 2) 12. 60; 26
13. A: True, B: True, C: False, D: False, E: True,
F: False
14. 40; 10, 8; 43, 8
15. B, D, E
16. 1
24
T287NAG_Mth_G4_TG_PDF.indd 24
9/25/13 6:30 PM
Cr
os
s
wa
l
kPl
us
,
Ma
t
he
ma
t
i
c
s
,
S
t
ude
ntE
di
t
i
on,
Gr
a
de4
Domain 1 • Lesson 6
Common Core Standards:
4.OA.3, 4.NBT.5
Distributive Property of
Multiplication
Getting the Idea
The distributive property of multiplication can help you multiply numbers using
mental math. The property uses the expanded form of numbers.
Area models can help you understand the distributive property of multiplication.
Distributive Property of Multiplication
When you multiply a number by a sum, you can multiply the
number by each addend of the sum and then add the products.
5 3 14
5 3 (10 1 4)
(5 3 10) 1 (5 3 4)
50
1
20 5 70
5 14 70
5 10 50
5 4 20
Duplicating any part of this book is prohibited by law.
Example 1
Fred has 3 shelves of books. Each shelf has 18 books. How many books in all are
on the shelves?
Strategy
Step 1
Use the distributive property of multiplication and mental math.
Write the multiplication sentence for the problem.
There are 3 shelves. There are 18 books on each shelf.
There are x books in all.
3 3 18 5 x
T287NA_Mth_G4_SE_PDF.indd 57
57
9/25/13 7:16 PM
Step 2
Express 18 in expanded form.
18 5 10 1 8
Step 3
Rewrite the sentence with 18 in expanded form.
3 3 18 5 3 3 (10 1 8)
Step 4
Distribute the 3 to each addend.
3 3 (10 1 8) 5 (3 3 10) 1 (3 3 8)
3 18 3 (10 8)
3 10
Step 5
38
Find each product.
(3 3 10) 1 (3 3 8) 5 x
30
Step 6
1
24 5 x
Add the products.
30 1 24 5 54
Solution
There are 54 books in all on the shelves.
Example 2
Multiply.
12 3 34 5
Strategy
Step 1
Use the distributive property and mental math.
Express 34 in expanded form.
34 5 30 1 4
Step 2
Rewrite the sentence with 34 in expanded form.
12 3 34 5 12 3 (30 1 4)
Step 3
Distribute the 12 to each addend.
12 3 (30 1 4) 5 (12 3 30) 1 (12 3 4)
Duplicating any part of this book is prohibited by law.
58 • Domain 1: Number and Operations in Base Ten
T287NA_Mth_G4_SE_PDF.indd 58
9/25/13 7:16 PM
Lesson 6: Distributive Property of Multiplication
Step 4
Find each product.
(12 3 30) 1 (12 3 4) 5
360
Step 5
1
48
5
Add the products.
360 1 48 5 408
Solution
12 3 34 5 408
Example 3
A Blu-Ray DVD costs $25. Ms. Ely ordered 15 Blu-Ray DVDs. How much did
Ms. Ely spend in all on the DVDs?
Strategy
Step 1
Use the distributive property and mental math.
Write the multiplication sentence for the problem.
She bought 15 DVDs. Each DVD cost $25.
She spent n dollars in all.
15 3 $25 5 n
Step 2
Express 25 in expanded form.
25 5 20 1 5
Step 3
Rewrite the sentence with 25 in expanded form.
15 3 25 5 15 3 (20 1 5)
Step 4
Distribute the 15 to each addend.
15 3 (20 1 5) 5 (15 3 20) 1 (15 3 5)
Duplicating any part of this book is prohibited by law.
Step 5
Find each product.
(15 3 20) 1 (15 3 5) 5 n
300
Step 6
1
75 5 n
Add the products.
300 1 75 5 375
Solution
T287NA_Mth_G4_SE_PDF.indd 59
Ms. Ely spent $375 in all.
59
9/25/13 7:16 PM
Coached Example
Monroe Elementary School has 32 classrooms. Each classroom has
24 students. How many students in all are at the school?
Write the multiplication sentence for the problem.
There are _____________ classrooms.
There are _____________ students in each class.
There are n students in all.
_____________ 3 _____________ 5 _____________
Use the distributive property of multiplication.
Express 24 in expanded form.
24 5 ______________ 1 ______________
Rewrite the sentence with 24 in expanded form.
32 3 24 5 32 3 (________ 1 ________)
Distribute 32 to each addend.
32 3 (________ 1 ________) 5 (32 3 ________) 1 (32 3 ________)
Find each product.
(32 3 _______) 1 (32 3 ________) 5 n
_____________ 1 ______________ 5 n
_____________ 1 _____________ 5 _____________
There are _____________ students in all at the school.
Duplicating any part of this book is prohibited by law.
Add the products.
60 • Domain 1: Number and Operations in Base Ten
T287NA_Mth_G4_SE_PDF.indd 60
9/25/13 7:16 PM
Lesson 6: Distributive Property of Multiplication
Lesson Practice
Choose the correct answer.
1. Which is true?
A. 3 3 78 5 (3 3 70) 3 (3 3 8)
4. Multiply.
16 3 24 5
B. 3 3 78 5 (3 3 70) 1 (3 3 8)
A. 96
C. 3 3 78 5 (3 1 70) 3 (3 1 8)
B. 324
D. 3 3 78 5 (3 1 70) 1 (3 1 8)
C. 326
D. 384
2. Which is true?
A. 64 3 14 5 (64 3 10) 3 (64 3 4)
B. 64 3 14 5 (64 3 10) 1 (64 3 4)
5. Multiply.
23 3 23 5
C. 64 3 14 5 (64 1 10) 3 (64 1 4)
A. 115
D. 64 3 14 5 (64 1 10) 1 (64 1 4)
B. 246
3. Which is true?
C. 529
D. 1,024
A. 52 3 23 5 (52 3 20) 1 (52 3 3)
B. 52 3 23 5 (50 3 20) 1 (2 3 3)
C. 52 3 23 5 (52 3 20) 1 (2 3 3)
D. 52 3 23 5 (52 3 20) 3 (52 3 3)
Duplicating any part of this book is prohibited by law.
6. A club charges $26 for a
one-year membership. The club
has 62 members. How much does
the club collect in membership fees
each year?
A. $208
B. $1,560
C. $1,612
D. $2,408
T287NA_Mth_G4_SE_PDF.indd 61
61
9/25/13 7:16 PM
7. Rosa bought 15 cases of water for a
school fair. Each case has 24 bottles.
How many bottles of water did
Rosa buy?
8. A manatee’s heart normally beats
about 55 times a minute. How many
times does a manatee’s heart beat in
60 minutes?
A. 200
A. 33,000
B. 260
B. 3,300
C. 300
C. 3,000
D. 360
D. 330
9. The art teacher bought 32 boxes of crayons. Each box has 64 crayons.
A. Write a number sentence to find how many crayons the art teacher bought in all.
B. Use the distributive property of multiplication to find the total number
of crayons. Show your work.
A. 48 3 13 5 (48 3 10) 3 (48 3 3)
○ True ○ False
B. 48 3 13 5 (48 3 10) 1 (48 3 3)
○ True ○ False
C. 48 3 13 5 (48 1 10) 3 (48 1 3)
○ True ○ False
D. 13 3 48 5 (13 3 40) 1 (13 3 8)
○ True ○ False
E. 13 3 48 5 (13 3 40) 3 (13 3 8)
○ True ○ False
Duplicating any part of this book is prohibited by law.
10. Select True or False for each number sentence.
62 • Domain 1: Number and Operations in Base Ten
T287NA_Mth_G4_SE_PDF.indd 62
9/25/13 7:16 PM
Lesson 6: Distributive Property of Multiplication
11. Draw a line from each number sentence to the multiplication problem that can be
used to solve it.
A. 5 3 15 5
B. 15 3 25 5
C. 12 3 16 5
D. 6 3 12 5
•
•
•
•
• (12 3 10) 1 (12 3 6)
• (6 3 10) 1 (6 3 2)
• (15 3 20) 1 (15 3 5)
• (5 3 10) 1 (5 3 5)
12. Circle the numbers that make the sentence true.
26 3 62 5 (26 3
20
20
26
26
60
62
) 1 ( 60
3 2)
62
13. Select True or False for each number sentence.
Duplicating any part of this book is prohibited by law.
A. 3 3 45 5 (3 3 40) 1 (3 3 5)
○ True ○ False
B. 46 3 14 5 (46 3 10) 1 (46 3 4)
○ True ○ False
C. 5 3 67 5 (5 1 60) 1 (5 1 7)
○ True ○ False
D. 63 3 22 5 (63 3 20) 3 (63 3 2)
○ True ○ False
E. 33 3 33 5 (33 3 30) 1 (33 3 3)
○ True ○ False
F. 71 3 34 5 (71 3 30) 1 (3 3 4)
○ True ○ False
T287NA_Mth_G4_SE_PDF.indd 63
63
9/25/13 7:16 PM
14. Use numbers from the box to complete the sentences.
4
34 3 43 5 (34 3
) 1 (34 3 3)
18 3 18 5 (18 3
) 1 (18 3
43 3 18 5 ( 3 10) 1 (43 3
8
) 10
)
40
43
15. Which number sentence can be used to solve the problem? Circle all that apply.
Mina bought 24 packs of napkins for the school party. There were 35 napkins in
each pack. How many napkins did Mina buy?
A. (24 3 3) 1 (24 3 5) 5
B. 24 3 35 5
C. (24 3 30) 3 (24 3 5) 5
D. 24 3 (30 1 5) 5
E. (24 3 30) 1 (24 3 5) 5
16. Circle the operation sign that makes the sentence true.
11 3 88 5 (11 3 80)
(11 3 8)
Duplicating any part of this book is prohibited by law.
F. (24 1 30) 3 (24 1 5) 5
64 • Domain 1: Number and Operations in Base Ten
T287NA_Mth_G4_SE_PDF.indd 64
9/25/13 7:16 PM