ALGEBRA
Name
Lesson 1.10
Numerical Expressions
Essential Question How can you use a numerical expression
to describe a situation?
Operations and Algebraic
Thinking—5.OA.A.1, 5.OA.A.2
MATHEMATICAL PRACTICES
MP3, MP4, MP6
Unlock
Unlock the
the Problem
Problem
A numerical expression is a mathematical phrase that has numbers
and operation signs but does not have an equal sign.
Tyler caught 15 small bass, and his dad caught 12 small bass in the
Memorial Bass Tourney in Tidioute, PA. Write a numerical expression
to represent how many fish they caught in all.
Choose which operation to use.
You need to join groups of different sizes, so use addition.
15 small bass
plus
12 small bass
↓
↓
↓
15
+
12
So, 15 + 12 represents how many fish they caught in all.
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Example 1 Write an expression to match the words.
A Addition
B Subtraction
Emma has 11 fish in her
aquarium. She buys 4 more fish.
Lucia has 128 stamps. She uses
38 stamps on party invitations.
fish
plus
more fish
stamps
↓
↓
↓
↓
minus
↓
stamps used
↓
11
+
4
128
−
_
C Multiplication
D Division
Karla buys 5 books.
Each book costs $3.
Four players share 52 cards
equally.
books
multiplied
by
cost per
book
cards
divided
by
players
↓
↓
↓
↓
↓
↓
_
×
_
_
÷
_
Math
Talk
MATHEMATICAL PRACTICES 4
What does the expression
model in each example?
Chapter 1
61
Expressions with Parentheses The meaning of the words in a
problem will tell you where to place the parentheses in an expression.
Example 2 Which expression matches
• Underline the events for each day.
• Circle the number of days these
the meaning of the words?
Doug went fishing for 3 days. Each day he put $15 in his pocket.
At the end of each day, he had $5 left. How much money did
Doug spend by the end of the trip?
events happened.
Think: Each day he took $15 and had $5 left. He did this for 3 days.
($15 − $5)
← Think: What expression can you
write to show how much money
Doug spends in one day?
← Think: What expression can you
3 × ($15 − $5)
Math
Talk
write to show how much money
Doug spends in three days?
MATHEMATICAL PRACTICES 3
Explain how the expression of what
Doug spent in three days compares
to the expression of what he spent
in one day?
Example 3 Which problem matches
the expression $20 − ($12 + $3)?
Kim has $20 to spend for her fishing trip. She
spends $12 on a fishing pole. Then she finds $3.
How much money does Kim have now?
Kim has $20 to spend for her fishing trip. She
spends $12 on a fishing pole and $3 on bait.
How much money does Kim have now?
List the events in order.
List the events in order.
First: Kim has $20.
First: Kim has $20.
Next:
_____.
Next:
_____.
Then:
_____.
Then:
_____.
__
Share
hhow
Share and
and Show
Sh
Do these words
match the expression?
__
MATH
M
BOARD
B
Circle the expression that matches the words.
1. Teri had 18 worms. She gave 4 worms to
Susie and 3 worms to Jamie.
(18 – 4) + 3
62
18 − (4 + 3)
2. Rick had $8. He then worked 4 hours for
$5 each hour.
$8 + (4 × $5)
($8 + 4) × $5
© Houghton Mifflin Harcourt Publishing Company
Do these words
match the expression?
Name
Write an expression to match the words.
3. Greg drives 26 miles on Monday and
90 miles on Tuesday.
4. Lynda has 27 fewer fish than Jack.
Jack has 80 fish.
Write words to match the expression.
5. 34 − 17
6. 6 × (12 − 4)
Math
Talk
MATHEMATICAL PRACTICES 6
Is 4 × 8 = 32 an expression?
Explain why or why not.
On
On Your
Your Own
Own
Write an expression to match the words.
7. José shared 12 party favors equally among
6 friends.
9. Isabelle bought 12 bottles of water
at $2 each.
8. Braden has 14 baseball cards. He finds
5 more baseball cards.
10. Monique had $20. She spent $5 on lunch and
$10 at the bookstore.
Write words to match the expression.
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11. 36 ÷ 9
12. 35 − (16 + 11)
Draw a line to match the expression with the words.
13. Fred catches 25 fish. Then he releases •
10 fish and catches 8 more.
Nick has 25 pens. He gives 10 pens to •
one friend and 8 pens to another friend.
Jan catches 15 fish and lets 6 fish go.
•
Libby catches 15 fish and lets 6 fish go •
for three days in a row.
• 3 × (15 − 6)
• 15 − 6
• 25 − (10 + 8)
• (25 − 10) + 8
Chapter 1 • Lesson 10 63
MATHEMATICAL PRACTICES .0%&-t3&"40/tM",&4&/4&
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Use the rule and the table for 14–15.
15.
MATHEMATICAL
PRACTICE
4
Write an Expression
to represent the total number of lemon
tetras that could be in a 20-gallon aquarium.
SMARTER
There are tiger
barbs in a 15-gallon aquarium
and giant danios in a 30-gallon
aquarium. Write a numerical
expression to represent the
greatest total number of fish
that could be in both aquariums.
Type of Fish
Length
(in inches)
Lemon Tetra
2
Strawberry Tetra
3
Giant Danio
5
Tiger Barb
3
Swordtail
5
▲ The rule for the number of fish in
an aquarium is to allow 1 gallon
of water for each inch of length.
WRITE
16.
17.
64
Math t Show Your Work
DEEPER
Write a word problem for an
expression that is three times as great as
(15 + 7). Then write the expression.
SMARTER
Daniel bought 30 tokens when
he arrived at the festival. He won 8 more
tokens for getting the highest score at the
basketball contest, but lost 6 tokens at the ring
toss game. Write an expression to find the
number of tokens Daniel has left.
© Houghton Mifflin Harcourt Publishing Company • Image Credits: (tr) ©Juniors Bildarchiv/Alamy
14.
Aquarium Fish
Practice and Homework
Name
Lesson 1.10
Numerical Expressions
COMMON CORE STANDARD—5.OA.A.1,
5.OA.A.2 Write and interpret numerical
expressions.
Write an expression to match the words.
1. Ethan collected 16 seashells. He lost 4 of them
while walking home.
2. Yasmine bought 4 bracelets. Each
bracelet cost $3.
16 − 4
3. Amani did 10 jumping jacks. Then she did
7 more.
4. Darryl has a board that is 8 feet long. He
cuts it into pieces that are each 2 feet long.
Write words to match the expression.
5. 3 + (4 × 12)
6. 36 ÷ 4
7. 24 − (6 + 3)
Problem
Problem Solving
Solving
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8. Kylie has 14 polished stones. Her friend
gives her 6 more stones. Write an
expression to match the words.
_______
10.
WRITE
9. Rashad had 25 stamps. He shared them equally
among himself and 4 friends. Then Rashad found
2 more stamps in his pocket. Write an expression
to match the words.
_______
Math Write a numerical expression. Then write words to
match the expression.
Chapter 1
65
Lesson Check (5.OA.A.1)
1. Jenna bought 3 packs of bottled water,
with 8 bottles in each pack. Then she
gave 6 bottles away. Write an expression
to match the words.
2. Stephen had 24 miniature cars. He gave
4 cars to his brother. Then he passed the
rest of the cars out equally among 4 of
his friends. Which operation would you use
to represent the first part of this situation?
3. To find 36 + 29 + 14, Joshua rewrote the
expression as 36 + 14 + 29. What property did
Joshua use to rewrite the expression?
4. There are 6 baskets on the table. Each
basket has 144 crayons in it. How many
crayons are there?
5. Mr. Anderson wrote (7 × 9) × 103 on the board.
What is the value of that expression?
6. Barbara mixes 54 ounces of granola and
36 ounces of raisins. She divides the mixture
into 6-ounce servings. How many servings does
she make?
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Spiral Review (5.NBT.A.2, 5.NBT.B.5, 5.NBT.B.6)