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Objective
1
To review the use of parentheses.
materials
Teaching the Lesson
Key Activities
Students use parentheses in number sentences involving more than one operation. They
translate number stories into number sentences, inserting parentheses in the proper places,
and determine whether number sentences containing parentheses are true or false.
Key Concepts and Skills
Math Journal 2, pp. 219 and 220
Study Link 7 3
Teaching Aid Master
(Math Masters, p. 414; optional)
slates
• Identify and write sentences that model number stories.
[Patterns, Functions, and Algebra Goal 2]
• Solve problems involving parentheses and nested parentheses.
[Patterns, Functions, and Algebra Goal 2]
• Insert parentheses in order to make true number sentences.
[Patterns, Functions, and Algebra Goal 2]
Key Vocabulary
expression • ambiguous • nested parentheses
Ongoing Assessment: Recognizing Student Achievement Use journal page 220.
[Patterns, Functions, and Algebra Goal 3]
2
materials
Ongoing Learning & Practice
Students play Name That Number.
Students practice and maintain skills through Math Boxes and Study Link activities.
3
materials
Differentiation Options
READINESS
Students insert parentheses
to make number sentences
true.
ENRICHMENT
Students partition dot grids
and use the patterns to write
number models.
Math Journal 2, p. 221
Student Reference Book, p. 325
Study Link Master
(Math Masters, p. 197)
Per partnership: 1 complete deck
of number cards, (from the
Everything Math Deck, if available)
EXTRA PRACTICE
Students practice using
grouping symbols.
Teaching Masters (Math Masters,
pp. 198 and 199)
5-Minute Math, pp. 77, 78
Technology
Assessment Management System
Journal page 220
See the iTLG.
Lesson 7 4
557
Getting Started
Mental Math and Reflexes
Math
Message
Have students supply the missing decimal for dictated phrases. Suggestions:
11 tens equal
1.1 hundreds
26 hundreds equal
2.6 thousands
142 hundreds equal
14.2 thousands
3 million 5 hundred-thousands equal
3.5 millions
45 tens equal
4.5 hundreds
13 hundreds equal
1.3 thousands
6 hundreds equal
0.6 thousands
100 thousands equal
0.1 million
155 hundreds equal
15.5 thousands
Complete Problems 1 and 2 at the
top of journal page 219.
Study Link 7 3
Follow-Up
Have partners compare answers
and resolve differences.
1 Teaching the Lesson
Math Message Follow-Up
WHOLE-CLASS
ACTIVITY
(Math Journal 2, p. 219)
Discuss students’ answers. Ask: What do parentheses mean in
number sentences? Operations inside parentheses are done first.
Write the number sentences from Problem 1 on the board, with
their answers, but without parentheses. Guide students to see
that without the mathematical punctuation of parentheses,
number expressions can take on different values depending on the
order in which the operations are performed. Without parentheses,
the expression is said to be ambiguous because it has more
than one possible meaning.
Student Page
Date
LESSON
74
NOTE An expression is a group of mathematical symbols (numbers, operation
Time
signs, variables, grouping symbols) that represents a number—or can represent
a number if values are assigned to any variables it contains. A number sentence
is made up of at least two numbers or expressions separated by a relation
symbol such as , , or .
Parentheses and Number Stories
Math Message
1. Make a true sentence by filling in the missing number.
a. 7 (2 1) b. (7 2) 1 4
6
c. 2.0 (7.5 1.5) d. (2.0 7.5) 1.5 Example: The number sentence 6 4 2 / 2 n includes the expression
6 4 2 / 2, the variable n, and the equal symbol .
18
16.5
2. Insert parentheses to rewrite the following problem in as many different true
Ask volunteers to share their answers to Problem 2 and explain
the steps they used to solve the problem. As the students explain
the steps, list them on the board. For example:
sentences as possible.
642/2?
((6 4)) 2) / 2 11
6 (4 2) / 2 6
(6 4) (2 / 2) 23
6 (4 (2 / 2)) 18
Steps
Draw a line to match each number story with the expression that fits it.
3. Story 1
Tom had 4 cans of soda.
He went shopping and bought
3 six-packs of soda cans.
(4 3) 6
Story 2
Tom had 4 six-packs of soda cans.
He went shopping and bought 3 more
six-packs of soda cans.
4 (3 6)
219
Math Journal 2, p. 219
558
Numerical Expression
Tom’s Total Number of Soda Cans
Unit 7 Exponents and Negative Numbers
4
Multiply 6 times 4.
6
Subtract 2 from the result.
(6
Divide that result by 2.
((6
4) 2
4) 2) / 2
Student Page
Point out that when two or more sets of parentheses are used in
the same expression, the operation inside the inner parentheses is
done first. In ((6 4) 2) / 2, 6 times 4 is the operation in the
inner parentheses. The operation in the outer parentheses is done
next, followed by all the remaining operations. Parentheses inside
parentheses are referred to as nested parentheses.
Date
Time
LESSON
Parentheses and Number Stories
74
4. Story 1
3 (45 / 5)
Alice ate 3 cookies before going to a
party. At the party, Alice and 4 friends
ate equal shares of 45 cookies.
Story 2
(45 3) / 5
There was a full bag with 45 cookies
and an opened bag with 3 cookies.
Alice and 4 friends ate equal shares
of all these cookies.
5. Story 1
Number of Cookies Baked
15 (4 5)
Mr. Chung baked 5 batches of cookies.
Each of the first 4 batches contained
15 cookies. The final batch contained
only 5 cookies.
Links to the Future
This lesson stresses the use of parentheses to create unambiguous expressions.
Lesson 7-5 will introduce the conventional order of operations, which often
reduces or eliminates the need for grouping symbols in many number sentences.
continued
Number of Cookies Alice Ate
Story 2
(4 15) 5
In the morning, Mr. Chung baked
4 batches of 15 cookies each. In the
afternoon, he baked 5 more batches
of 15 cookies each.
6. A grocery store received a shipment of 120 cases of apple juice. Each
case contained 4 six-packs of cans. After inspection, the store found that
9 cans were damaged.
Write an expression that represents the number of undamaged cans.
Matching Number Stories
Sample answer: (120 (4 6)) 9
PARTNER
ACTIVITY
to Appropriate Expressions
(Math Journal 2, pp. 219 and 220)
Ask students to read the two number stories in Problem 3 on
journal page 219 and match each story with an expression. Ask
volunteers to explain their choices. Story 1 goes with the second
expression since 3 must be multiplied by 6 to find the total
number of cans in 3 six-packs. Story 2 goes with the first
expression since 4 3 stands for the total number of six-packs.
Math Journal 2, p. 220
Assign journal page 220. When most students are done, bring the
class together and go over the answers. Have students explain
their reasons for matching a given number story with a
particular expression.
Ongoing Assessment:
Recognizing Student Achievement
Journal
Page 220
Problem 6
Use journal page 220, Problem 6 to assess students’ facility with writing
expressions containing parentheses to represent a number story. Have
students complete an Exit Slip (Math Masters, page 414) for the following:
Explain how you used parentheses in Problem 6 on journal page 220 to
write the expression for the total number of undamaged cans. Students
are making adequate progress if they refer to the use of nested parentheses
to identify the total number of undamaged cans.
[Patterns, Functions, and Algebra Goal 3]
Student Page
Games
Name That Number
Materials 1 complete deck of number cards
Players
2 or 3
Skill
Naming numbers with expressions
Object of the game To collect the most cards.
Directions
1. Shuffle the deck and deal 5 cards to each player. Place the
remaining cards number-side down on the table between the
players. Turn over the top card and place it beside the deck.
This is the target number for the round.
2. Players try to match the target number by adding,
subtracting, multiplying, or dividing the numbers on as many
of their cards as possible. A card may only be used once.
3. Players write their solutions on a sheet of paper. When
players have written their best solutions:
♦ Each player sets aside the cards they used to match the
target number.
♦ Each player replaces the cards they set aside by
drawing new cards from the top of the deck.
Target number: 16
Player 1’s cards:
7
5
8
5
7
(Student Reference Book, p. 325)
Example
2
8
PARTNER
ACTIVITY
10
2
Playing Name That Number
is played.
4. Play continues until there are not enough cards left to
replace all of the players’ cards. The player who has set
aside the most cards wins the game.
10
2 Ongoing Learning & Practice
♦ The old target number is placed on the bottom of the deck.
♦ A new target number is turned over, and another round
Some possible solutions:
10 8 2 16 (3 cards used)
Students practice applying number properties, equivalent names,
arithmetic operations, and basic facts by playing Name That
7 * 2 10 8 16 (4 cards used)
8 / 2 10 7 5 16 (all 5 cards used)
The player sets aside the cards used to make a solution and draws
the same number of cards from the top of the deck.
Student Reference Book, p. 325
Lesson 7 4
559
Student Page
Date
Time
LESSON
Number. Encourage students to extend the game by using the
cards in their hands to form exponents and/or fractions.
Math Boxes
74
1. Measure the length and width of each of the following
objects to the nearest half inch.
a. journal cover
length
10 78 in.
width
Answers vary for b–d.
812
in.
length
c. index card
length
in.
width
width
in.
length
2. a. Make a stem-and-leaf plot of the
INDEPENDENT
ACTIVITY
(Math Journal 2, p. 221)
in.
165
154
Range: 31
Mode(s): 165,170
Mixed Practice Math Boxes in this lesson are paired
with Math Boxes in Lessons 7-2 and 7-6. The skill in
Problem 4 previews Unit 8 content.
478
3555
0059
5
117–119
3. Measure M to the nearest degree.
4. Calculate the sale price.
M
M measures about
width
Minimum:
Leaves
(1s)
4
2
0
2
in.
Median:
163, 179, 170, 165, 182, 157,
154, 165, 170, 175, 162, 185,
158, 170, 165, 154
15
16
17
18
b. Find the following landmarks for the data.
hand-span measures in Ms. Grip’s
fifth-grade class.
Stems
(100s and 10s)
Math Boxes 7 4
in.
(your choice)
d.
in.
183
b. desktop
167 .
204
Regular
Price
Discount
$8.99
20%
$11.99
25%
$89.00
20%
$9.99
20%
Sale
Price
$7.19
$8.99
$71.20
$7.99
Writing/Reasoning Have students write a response to the
following: Use your solution for Problem 2 to explain how
to read a stem-and-leaf plot. Sample answer: In this
problem, the stems are the hundreds and tens digits for each
number, and the leaves are the ones digits. The first number on
this stem-and-leaf plot has 1 in the hundreds place, 5 in the tens
place, and 4 in the ones place. It is read one hundred fifty-four.
51
221
Math Journal 2, p. 221
Study Link 7 4
INDEPENDENT
ACTIVITY
(Math Masters, p. 197)
Home Connection Students insert parentheses to make
number sentences true. In several cases, students will
need to insert nested parentheses.
3 Differentiation Options
READINESS
Study Link Master
Name
Date
STUDY LINK
74
4.
2 =(3 2)(4 / 1)
2.
3 =(4 3 1) / 2
Write seven names for 8. Use only numbers
less than 10, and use at least three different
operations in each name. Use parentheses.
Follow the directions in Problem 7 to fill in
the last two rows.
Reminder: When you have a pair of parentheses
inside another pair, the parentheses are called
nested parentheses.
Example: 8 ((5 6) 2) / 4
5.
7.
1 ((4 1) 3) / 2
6.
Sample answers for
Problems 1–6:
3. 4 (3 1) (4 / 2)
8
Make each sentence true by inserting parentheses.
(9 1) (1 / 1)
(9 5) (2 2)
(0.5 / 1) (2.5 3)
(6.3 9.7) / (6 4)
(6.2 / 2) (7 2.1)
1
(2 8) (9 5)
(72 9) 5
(42 (3 3)) 1
((2 1)4 9) 1
7 ((4 3) / 2) 1
Add two names to your name-collection box in Problem 4.
Use nested parentheses.
Practice
Find the number that each variable represents.
4
1
112 , or 13 9. (11 p) 22 12
5
1
8. 2 (1 a) a 2
12
12
2
1
28, or 24
5
15
2
10. 6 d 7 d 11. 6.4 y 6 8
8
5
1
p 12
y0
Math Masters, p. 197
560
15–30 Min
Number Sentences
222 223
Make each sentence true by inserting parentheses.
1.
Reviewing Parentheses in
Time
Using Parentheses
PARTNER
ACTIVITY
Unit 7 Exponents and Negative Numbers
(Math Masters, p. 198)
To explore the use of parentheses in number sentences, have
students insert parentheses to make true sentences. Students
compare the use of commas in text sentences to the use of
parentheses in number sentences. When students have finished
the page, have them share why they think parentheses are
important.
Teaching Master
ENRICHMENT
Describing Dot Patterns
INDEPENDENT
ACTIVITY
Name
with Number Models
Time
Reviewing Parentheses
74
Read the following sentence. Mary Grace the lizard ate three crickets.
1.
15–30 Min
Date
LESSON
This sentence could have multiple meanings.
1. The speaker is telling someone named Mary Grace
that the lizard ate three crickets.
(Math Masters, p. 199)
2. The lizard, named Mary Grace, ate three crickets.
3. The speaker is telling someone named Mary that the
lizard, named Grace, ate three crickets.
To apply students’ understanding of parentheses, have
them write number sentences to describe dot patterns.
Students partition a dot grid and write number sentences
to model the indicated number patterns.
Without commas, it’s hard to tell which meaning was intended. Write the
number of the meaning next to each sentence below.
a.
b.
c.
5-Minute Math
Mary Grace, the lizard ate three crickets.
Mary, Grace the lizard, ate three crickets.
Insert parentheses in each sentence to make the sentence true.
SMALL-GROUP
ACTIVITY
3 (4 7) 33
6 (9 5) 51
27 / 4 5 6 9 27 / (4 5) 6 9
a.
3 4 7 33
b.
6 9 5 51
c.
5–15 Min
Insert parentheses in the expressions below, and find their solutions.
3.
To offer students more experience with grouping symbols, see
5-Minute Math, pages 77 and 78.
Planning Ahead
Mary Grace, the lizard, ate three crickets.
By adding commas, the meaning of a sentence becomes clear. In number
sentences, parentheses are used to indicate what to calculate first.
2.
EXTRA PRACTICE
2
1
3
a.
754
b.
693
(7 5) 4 31; 7 (5 4) 7
(6 9) 3 5; 6 (9 3) 9
Math Masters, p. 198
In Lesson 7-6, you will need newspapers and magazines that
contain line graphs.
Teaching Master
Name
LESSON
74
Date
Time
Describing Dot Patterns
The total dots in this dot array can be found by using patterns.
Here is one way to find the total:
((3 3) (4 3) 4)
Use shape outlines or colors to identify a pattern
on this dot array. Write a number model for your
pattern. Then write a number story that
matches your number model.
Sample answers:
Number model:
(11 11) (4 (5 4)) (12 4) (4 4) 265
Number story:
Sample answer: In a large city school, the fifth graders fill
the auditorium in colorful choir robes. Students wearing purple
robes stand in 11 rows of 11 students each. Four groups in
gold robes stand in 4 rows of 5 students each. There are 4
groups of 12 students in black robes and 4 groups of 4 students
in green robes. How many students are in the auditorium?
Math Masters, p. 199
Lesson 7 4
561