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Lesson Guide

AssessmentManagement

Common Core State Standards

Lesson 7�4 557

Advance Preparation

Teacher’s Reference Manual, Grades 4–6 pp. 98, 99, 102, 103, 288, 289

Key Concepts and Skills• Identify and write sentences that model

number stories.

[Patterns, Functions, and Algebra Goal 2]

• Solve problems involving parentheses and

nested parentheses.


• Insert parentheses in order to make true

number sentences.


Key ActivitiesStudents 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.

Ongoing Assessment: Recognizing Student Achievement Use an Exit Slip (Math Masters, page 414). [Patterns, Functions, and Algebra Goal 3]

Key Vocabularyexpression � ambiguous � nested

parentheses

MaterialsMath Journal 2, pp. 219 and 220

Study Link 7�3

Math Masters, p. 414

slate

Playing Name That NumberStudent Reference Book, p. 325

per partnership: 1 complete deck of

number cards (from the Everything

Math Deck, if available)

Students apply number properties,

equivalent names, arithmetic

operations, and basic facts.

Math Boxes 7� 4Math Journal 2, p. 221

Students practice and maintain skills

through Math Box problems.

Study Link 7� 4Math Masters, p. 197

Students practice and maintain skills

through Study Link activities.

READINESS

Reviewing Parentheses in Number SentencesMath Masters, p. 198

Students insert parentheses to make

number sentences true.

ENRICHMENTDescribing Dot Patternswith Number ModelsMath Masters, p. 199

Students partition dot grids and use the

patterns to write number models.

EXTRA PRACTICE

5-Minute Math5-Minute Math™, pp. 77 and 78

Students practice using grouping symbols.

Teaching the Lesson Ongoing Learning & Practice

132

4

Differentiation Options

Parentheses inNumber Sentences

Objective To review the use of parentheses.

��

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Date Time

Math Message

1. Write each statement as an expression.

a. Add 8 and 3, and then multiply by 5. (8 + 3) ∗ 5

b. Add 8 to the product of 3 and 5. 8 + (3 ∗ 5)

c. 10 times the difference of 7 subtracted from 8. 10 ∗ (8 - 7)

d. The product of 10 and 8, minus 7. (10 ∗ 8) - 7

2. Insert parentheses to rewrite the following problem to make four different

true sentences.

6 ∗ 4 – 2 / 2 = ?

((6 ∗ 4)) – 2) / 2 = 116 ∗ (4 – 2) / 2 = 6

(6 ∗ 4) – (2 / 2) = 236 ∗ (4 – (2 / 2)) = 18

Draw a line to match each number story with the expression that fits it.

3. Story 1 Tom’s Total Number of Bottles of Juice

Tom had 4 bottles of juice. (4 + 3) ∗ 6

He went shopping and bought

3 six-packs of bottles of juice.

Story 2

Tom had 4 six-packs of bottles of juice. 4 + (3 ∗ 6)

He went shopping and bought 3 more

six-packs of bottles of juice.

Parentheses and Number StoriesLESSON

7�4

Sample answers:

209-247_EMCS_S_MJ2_G5_U07_576434.indd 219 3/18/11 5:26 PM

Math Journal 2, p. 219

Student Page

558 Unit 7 Exponents and Negative Numbers

Getting Started

1 Teaching the Lesson

▶ Math Message Follow-Up

WHOLE-CLASS ACTIVITY

(Math Journal 2, p. 219)

Algebraic Thinking Discuss students’ answers. Ask: What do parentheses mean in number sentences? Operations inside parentheses are done first.

Write the statements from Problem 1 on the board with their correct expressions, 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.

NOTE An expression is a group of mathematical symbols (numbers, operation

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 <.

Example: The number sentence 6 ∗ 4 - 2 / 2 = n includes the expression

6 ∗ 4 - 2 / 2, the variable n, and the equal symbol =.

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:

Steps Numerical Expression

Multiply 6 times 4. 6 ∗ 4

Subtract 2 from the result. (6 ∗ 4) - 2

Divide that result by 2. ((6 ∗ 4) - 2) / 2

Math MessageComplete Problems 1 and 2 at the top of journal page 219.

Study Link 7�3 Follow-UpHave partners compare answers and resolve differences.

Mental Math and Reflexes Use your slate procedures for problems such as the following:

47 ∗ 104 = 470,000

4.7 ∗ 103 = 4,700

0.47 ∗ 102 = 47

0.047 ∗ 10 = 0.47

356 ∗ 103 = 356,000

42.6 ∗ 102 = 4,260

0.862 ∗ 102 = 86.2

0.009 ∗ 103 = 9

0.109 ∗ 103 = 109

7.08 ∗ 104 = 70,800

0.084 ∗ 102 = 8.4

79.04 ∗ 103 = 79,040

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Parentheses and Number Stories continuedLESSON

7� 4

Date Time

4. Story 1 Number of Cookies Alice Ate

Alice ate 3 cookies before going to a 3 � (45 / 5)

party. At the party, Alice and 4 friends

ate equal shares of 45 cookies.

Story 2

There was a full bag with 45 cookies (45 � 3) / 5

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

Mr. Chung baked 5 batches of cookies. 15 � (4 � 5)

Each of the first 4 batches contained

15 cookies. The final batch contained

only 5 cookies.

Story 2

In the morning, Mr. Chung baked (4 � 15) � 5

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.

Sample answer: (120 � (4 � 6)) � 9

�


Student Page

Name That Number

Materials � 1 complete deck of number cardsPlayers 2 or 3Skill 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 theremaining cards number-side down on the table between theplayers. 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 manyof their cards as possible. A card may only be used once.

3. Players write their solutions on a sheet of paper. Whenplayers 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.♦ The old target number is placed on the bottom of the deck.♦ A new target number is turned over, and another round

is played.

4. Play continues until there are not enough cards left toreplace all of the players’ cards. The player who has setaside the most cards wins the game.

Games

Target number: 16

Player 1’s cards:

Some possible solutions:

10 � 8 � 2 � 16 (3 cards used)

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 drawsthe same number of cards from the top of the deck.

7

7

5

5

8

8

2

2

10

10

Student Reference Book, p. 325

Student Page

Links to the Future

Lesson 7�4 559

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.

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.

▶ Matching Number Stories 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.

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: Exit Slip �

Recognizing Student Achievement

Use an Exit Slip (Math Masters, page 414) to assess students’ facility with

writing expressions containing parentheses to represent a number story. Have

students explain how they 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.


2 Ongoing Learning & Practice

▶ Playing Name That Number PARTNER ACTIVITY

(Student Reference Book, p. 325)

Students practice applying number properties, equivalent names, arithmetic operations, and basic facts by playing Name That

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Math Boxes LESSON

7� 4

Date Time

3. Measure �M to the nearest degree.

�M measures about �

. 167

M

4. Calculate the sale price.

1. Measure the length and width of each of the following

objects to the nearest half inch.

a. journal cover b. desktop

length in. width in. length in. width in.

c. index card d. (your choice)

length in. width in. length in. width in.

2. a. Make a stem-and-leaf plot of the

hand-span measures in Ms. Grip’s

fifth-grade class.

163, 179, 170, 165, 182, 157,

154, 165, 170, 175, 162, 185,

158, 170, 165, 154

b. Find the following landmarks for the data.

Median:

Minimum:

Range:

Mode(s): 165,170

31

154

165

15 4 4 7 8

16 2 3 5 5 5

17 0 0 0 5 9

18 2 5

(1s)(100s and 10s)

LeavesStems

10�78

� 8�12

�

Answers vary for b–d. 183

117–119

204

RegularDiscount

SalePrice Price

$8.99 20%

$11.99 25%

$89.00 20%

$9.99 20%

$7.19

$8.99

$71.20

$7.99 51


Student Page

Make each sentence true by inserting parentheses.

1. 2 = 3 � 2 � 4 / 1 2. 3 = 4 � 3 � 1 / 2 3. 4 � 3 � 1 � 4 / 2

4. 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.

STUDY LINK

7�4 Using Parentheses

Name Date Time

Reminder: When you have a pair of parentheses

inside another pair, the parentheses are called

nested parentheses.

Example: 8 � ((5 � 6) � 2) / 4

Make each sentence true by inserting parentheses.

5. 1 � 4 � 1 � 3 / 2 6. 7 � 4 � 3 / 2 � 1

7. Add two names to your name-collection box in Problem 4.

Use nested parentheses.

Find the number that each variable represents.

8. 2�1

5

2� � (1�

1

1

2� � a) 9. (1�

1

2� � p) � 22 � 12

10. 6�5

8� � d � 7�

1

8

5� 11. 6.4 � y � 6�

2

5� y � 0d � 2�

28

�, or 2�14

�

p � 1�12

�a � 1�142�, or 1�

13

�

Sample answers forProblems 1–6:

Practice

8

(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)

(�12

� � 8) � (9 � 5)

(72 � 9) � 5

(42 � (3 � 3)) � 1

((2 � 1)4 � 9) � 1

222 223

( ) ( )

(( ) (( ) ))

( ) ( ) ( )


Study Link Master

560 Unit 7 Exponents and Negative Numbers

Number. Encourage students to extend the game by using the cards in their hands to form exponents and/or fractions.

▶ Math Boxes 7�4

INDEPENDENT ACTIVITY

(Math Journal 2, p. 221)

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.

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.

▶ Study Link 7�4


(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 PARTNER ACTIVITY

▶ Reviewing Parentheses in 15–30 Min

Number Sentences(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.


LESSON

7�4

Name Date Time

Reviewing Parentheses

1. Read the following sentence. Mary Grace the lizard ate three crickets.

This sentence could have multiple meanings.

1. The speaker is telling someone named Mary Grace

that the lizard ate three crickets.

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.

Without commas, it’s hard to tell which meaning was intended. Write the

number of the meaning next to each sentence below.

a. Mary Grace, the lizard, ate three crickets.

b. Mary Grace, the lizard ate three crickets.

c. 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. Insert parentheses in each sentence to make the sentence true.

a. 3 � 4 � 7 � 33

b. 6 � 9 � 5 � 51

c. 27 / 4 � 5 � 6 � 9

3. Insert parentheses in the expressions below, and find their solutions.

a. 7 � 5 � 4 �

b. 6 � 9 � 3 �

27 / (4 � 5) � 6 � 96 � (9 � 5) � 51

3 � (4 � 7) � 33

3

1

2

(7 � 5) � 4 � 31; 7 � (5 � 4) � 7(6 � 9) � 3 � 5; 6 � (9 � 3) � 9


Teaching Master

LESSON

7�4

Name 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:

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:

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?

(11 � 11) � (4 � (5 � 4)) � (12 � 4) � (4 � 4) � 265

((3 � 3) � (4 � 3) � 4)


Teaching Master

Lesson 7�4 561

ENRICHMENT


▶ Describing Dot Patterns 15–30 Min

with Number Models(Math Masters, p. 199)

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.

EXTRA PRACTICE

SMALL-GROUP ACTIVITY

▶ 5-Minute Math 5–15 Min

To offer students more experience with grouping symbols, see 5-Minute Math, pages 77 and 78.

Planning Ahead

In Lesson 7-6, you will need newspapers and magazines that contain line graphs.


parentheses in number sentences - everyday math · pdf fileparentheses in number sentences ......

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