Name
Lesson 4.4
Mental Math: Use the Properties
Use properties and mental math to find the value.
1. 12 ⫹ 18 ⫹ 39
2. 53 ⫹ 64 ⫹ 37
3. 6 ⫻ 103
4. (20 ⫻ 4) ⫻ 3
5. 41 ⫹ 29 ⫹ 46
6. 26 ⫹ 43 ⫹ 34
7. 6 ⫻ 15 ⫻ 2
8. 4 ⫻ 180
9. 72 ⫹ 18 ⫹ 32
10. 7 ⫻ 4 ⫻ 15
11. 34 ⫻ 6
12. 33 ⫹ (37 ⫹ 32)
13. 42 ⫻ 7
14. 29 ⫹ 46 ⫹ 51
15. 5 ⫻ 6 ⫻ 12
16. 62 ⫻ 4
17. 36 ⫹ 18 ⫹ 24
18. 12 ⫻ 6 ⫻ 4
Problem Solving and Test Prep
19. FAST FACT A group of sea lions
20. Tell which property you would use to
mentally find the value of 5 ⫻ 4 ⫻ 45.
Then find the value.
together in the water are called a raft. In
a raft, sea lions can safely rest together.
During one afternoon, a research team
saw 4 rafts of sea lions. Each raft had 16
sea lions in it. How many sea lions did
the research team see?
21. There are 6 shelving units containing
22. Tickets for the movies cost $13 each.
5 shelves each. Each shelf holds
35 DVDs. Find the total number of
DVDs on the shelving unit.
James’ family buys 6 tickets. Explain
how to use mental math to find the total
cost of the movie tickets.
A 210
B
450
C
950
D 1,050
PW27
Practice
© Harcourt • Grade 5
Name
Lesson 4.4
Name
Lesson 4.5
Mental Math: Use the Properties
Write Equations
Use properties and mental math to find the value.
Write an equation for each. Tell what the variable represents.
1. 12 ⫹ 18 ⫹ 39
2. 53 ⫹ 64 ⫹ 37
69
4. (20 ⫻ 4) ⫻ 3
103
8. 4 ⫻ 180
9. 72 ⫹ 18 ⫹ 32
204
294
16. 62 ⫻ 4
Let p number of album
pages; p 5 60
Let t minutes practice
with trumpet; 45 t 15
3. 7t ⫽ 63
102
4. 6 ⫹ b ⫽ 11
Check students’ answers.
Check students’ answers.
15. 5 ⫻ 6 ⫻ 12
360
126
17. 36 ⫹ 18 ⫹ 24
248
for 45 minutes. He practiced piano for
15 minutes. How long did he practice
the trumpet?
Write a problem for each equation. Tell what the variable represents.
12. 33 ⫹ (37 ⫹ 32)
14. 29 ⫹ 46 ⫹ 51
2. Jarrod practiced the trumpet and piano
60 photos. Each page contains
5 photos. How many pages does
the album have?
122
720
11. 34 ⫻ 6
420
13. 42 ⫻ 7
6. 26 ⫹ 43 ⫹ 34
116
180
10. 7 ⫻ 4 ⫻ 15
1. Paulina has a photo album with
618
5. 41 ⫹ 29 ⫹ 46
240
7. 6 ⫻ 15 ⫻ 2
3. 6 ⫻ 103
154
Possible answers given.
18. 12 ⫻ 6 ⫻ 4
78
288
Problem Solving and Test Prep
Problem Solving and Test Prep
5. Jaime has $130 in her savings account.
19. FAST FACT A group of sea lions
20. Tell which property you would use to
mentally find the value of 5 ⫻ 4 ⫻ 45.
Then find the value.
together in the water are called a raft. In
a raft, sea lions can safely rest together.
During one afternoon, a research team
saw 4 rafts of sea lions. Each raft had 16
sea lions in it. How many sea lions did
the research team see?
Associative Property
of Multiplication; 900
64 sea lions
21. There are 6 shelving units containing
22. Tickets for the movies cost $13 each.
5 shelves each. Each shelf holds
35 DVDs. Find the total number of
DVDs on the shelving unit.
D
James’ family buys 6 tickets. Explain
how to use mental math to find the total
cost of the movie tickets.
A 210
Break apart $13 to $10 and
$3 and then multiply each part
C 950
by 6. Then add the products to
D 1,050
find the total cost; $78
Circled problems are suggested homework problems.
B
450
PW27
6. What if Jamie already bought the bike
She wants to buy a bike for $225. How
much more money does Jaime need to
buy the bike? Write an equation with a
variable to represent the problem.
and has $29 left in her account. How
much money did she have before
buying the bike? Write an equation with
a variable to represent the problem.
Possible answer:
$130 m $225
Possible answer:
m $29 $225
7. The Amsco building is 135 feet tall.
8. Tam had downloaded 25 songs for her
The Tyler building is 30 feet shorter than
the Amsco building. What is the Tyler
building’s height? Write an equation to
represent this problem.
B
MP3 player. She then downloaded some
more songs. She now has 31 songs for
her MP3 player. How many songs did
Tam download? Write an equation to
A
represent this problem.
A 135 ⫽ h ⫹ 30
A 25 ⫹ s ⫽ 31
B
h ⫽ 135 ⫺ 30
B
s ⫺ 31 ⫽ 25
C
135 ⫽ 30 ⫺ h
C
s ⫺ 25 ⫽ 31
D 56 ⫺ s ⫽ 31
D h ⫽ 135 ⫹ 30
Circled problems are suggested homework problems.
Practice
PW28
© Harcourt • Grade 5
Lesson 4.4
Item
Practice
© Harcourt • Grade 5
Lesson 4.5
Suggested rationale
Item
Suggested rationale
1
use properties to solve
1
write an equation
3
use properties to solve
2
write an equation
4
use properties to solve
4
write a problem
6
use properties to solve
5
problem solving
7
use properties to solve
6
test prep: multiple choice
17
problem solving
7
test prep: multiple choice
18
test prep: multiple choice
20
problem solving
PW27-PW28
Practice
© Harcourt • Grade 5
MXENL08AWK5X_PHTE_RatA.indd PW28
7/2/07 3:00:45 PM