Algebraic Expressions - Login your answers on page 440. Algebra Statement Algebraic Expression Some algebraic expressions: 2 - x m ∗ m C + 5 6 ∗ H (C + 5) (6 ∗ H) Other expressions

www.everydaymathonline.com

Lesson 10�3 797

Advance Preparation

Teacher’s Reference Manual, Grades 4–6 pp. 278–289

Key Concepts and Skills• Identify and use patterns in tables to

solve problems.

[Patterns, Functions, and Algebra Goal 1]

• Write algebraic expressions to model rules.


• Use variables to write number models

that describe situations.


Key ActivitiesStudents complete statements in which the

variable stands for an unknown quantity. They

state the rule for “What’s My Rule?” tables in

words and with an algebraic expression.

Ongoing Assessment: Recognizing Student Achievement Use journal page 341. [Patterns, Functions, and Algebra Goal 2]

Key Vocabularyalgebraic expression

MaterialsMath Journal 2, pp. 341–343

Student Reference Book, p. 218

Study Link 10�2

Class Data Pad � slate

Playing Name That NumberStudent Reference Book, p. 325

per partnership: 1 complete deck of

number cards (the Everything Math

Deck, if available)

Students apply number properties,

equivalent names, arithmetic

operations, and basic facts.

Math Boxes 10�3Math Journal 2, p. 344

compass � Geometry Template

or ruler

Students practice and maintain skills

through Math Box problems.

Study Link 10�3Math Masters, p. 299

Students practice and maintain skills

through Study Link activities.

READINESS

Exploring “What’s My Rule?” TablesMath Masters, p. 300

Students use patterns in tables to

solve problems.

EXTRA PRACTICE

Writing Algebraic ExpressionsStudent Reference Book, p. 218

Students choose variables to write

algebraic expressions.

ELL SUPPORT

Building a Math Word BankDifferentiation Handbook, p. 142

Students define and illustrate the term

algebraic expression.

ENRICHMENTAnalyzing Patterns and RelationshipsMath Masters, p. 300A

Students analyze patterns and relationships.

Teaching the Lesson Ongoing Learning & Practice

132

4

Differentiation Options

� Algebraic ExpressionsObjective To introduce the use of algebraic expressions to

represent situations and describe rules.

eToolkitePresentations Interactive Teacher’s

Lesson Guide

Algorithms Practice

EM FactsWorkshop Game™

AssessmentManagement

Family Letters

CurriculumFocal Points

Common Core State Standards

797_EMCS_T_TLG2_G5_U10_L03_576914.indd 797797_EMCS_T_TLG2_G5_U10_L03_576914.indd 797 2/21/11 9:45 AM2/21/11 9:45 AM

Check your answers on page 440.

Algebra

Statement Algebraic Expression

Some algebraic expressions:2 - xm ∗ mC + 56 ∗ H(C + 5) � (6 ∗ H)

Other expressions that are not algebraic: 7 + 5 6 ∗ 11(7 + 5) � (6 ∗ 11)

Algebraic Expressions

Variables can be used to express relationships between quantities.

H ∗ 6 is an example of an algebraic expression. An algebraic expression uses operation symbols (+, -, ∗, �, and so on) to combine variables and numbers.

Evaluating Expressions

To evaluate something is to find out what it is worth. To evaluate an algebraic expression, first replace each variable with its value.

Evaluate each algebraic expression.

6 ∗ H x ∗ x ∗ x

If H = 3, then 6 ∗ H is 6 ∗ 3, or 18. If x = 3, then x ∗ x ∗ x is 3 ∗ 3 ∗ 3, or 27.

1. Alan is A inches tall. If Barbara is 3 inches shorter than Alan, what is Barbara’s height in inches?

2. Toni runs 2 miles every day. How many miles will she run in D days?

What is the value of each expression when k = 4?

3. k + 2 4. k ∗ k 5. k � 2 6. k2 + k - 2

Claude earns $6 an hour. Use a variable to express the relationship between Claude’s earnings and the amount of time worked.

If you use the variable H to stand for the number of hours Claude worked, you can write his pay as H ∗ 6.

Write the statement as an algebraic expression.

Write an algebraic expression for each situation using the suggested variable.

Marshall is 5 years older than Carol.

If Carol is C years old, then Marshall’s age in years is C + 5.

215_234_EMCS_S_SRB_G5_ALG_576515.indd 218 3/8/11 5:09 PM

Student Reference Book, p. 218

Student Page

798 Unit 10 Using Data; Algebra Concepts and Skills

Getting Started

1 Teaching the Lesson

▶ Math Message Follow-Up WHOLE-CLASSDISCUSSION

Algebraic Thinking On the Class Data Pad, draw and label the table for the Math Message. Ask students to share heights listed in their tables. Record them on the Class Data Pad table.

Ask: How tall is Ava? Expect that students will respond with one of the heights from the table. Ask them to explain their reasoning. Sample answer: Ava’s height is 1 centimeter more than Joe’s. How did you determine Joe’s height? Sample answer: Joe is 2 cm taller than Maria. How tall is Maria? Sample answer: Maria’s height isn’t given, so I picked a likely height for a fifth grader.

Emphasize that Ava’s height depends on Joe’s height, and Joe’s depends on Maria’s. We only know that Ava is 1 cm taller than Joe, and that Joe is 2 cm taller than Maria. If Maria could be any height, then there would be an infinite number of possibilities for Joe’s and Ava’s heights. If Maria is 147.5 cm tall, then Joe’s height is 149.5 cm, and Ava’s height is 150.5 cm. If Maria is 1.48 m tall, then Joe is 1.50 m tall, and Ava is 1.51 m tall.

Ask: How does Ava’s height compare with Maria’s height? Ava is 3 cm taller than Maria. If Maria is 151.5 cm tall, how tall is Ava? 154.5 cm If Ava is 150.2 cm tall, how tall is Maria? 147.2 cm

▶ Introducing Algebraic WHOLE-CLASSDISCUSSION

Expressions(Student Reference Book, p. 218)

Algebraic Thinking On the board or Class Data Pad, make a table of just Maria’s and Joe’s heights. Point out that it is similar to a “What’s My Rule?” table. Label Maria’s Height in and Joe’s Height out. Ask: What is the rule for this table? out = in + 2

ELL

Mental Math and Reflexes Students solve extended multiplication and division facts problems involving powers of 10. Write the problems on the board or Class Data Pad.

Math MessageAva, Joe, and Maria are 5th graders. Ava is 1 centimeter taller than Joe, and Joe is 2 centimeters taller than Maria. Make a table of 4 possible heights for Ava, Joe, and Maria.

Study Link 10�2 Follow-UpHave partners compare answers and resolve differences.

6 ∗ 102 = 600

0.254 ∗ 103 = 254

7.538 ∗ 102 = 753.8

4.3 ∗ 103 = 4,300

7.6 ÷ 10 = 0.76

24 ∗ 107 = 240,000,000

0.56 ÷ 102 = 0.0056

36.5 ÷ 103 = 0.0365

8 ÷ 102 = 0.08

Heights

Ava Joe Maria

798-802_EMCS_T_TLG2_G5_U10_L03_576914.indd 798798-802_EMCS_T_TLG2_G5_U10_L03_576914.indd 798 3/22/11 3:16 PM3/22/11 3:16 PM

Lesson 10�3 799

Ask volunteers to represent Joe’s height using an algebraic expression. Let M represent Maria’s height in inches. Then M + 2 represents Joe’s height in inches. Add M and M + 2 to the column headings in the table on the Class Data Pad.

Review and discuss Student Reference Book, page 218. Have students study the examples of expressions that are algebraic and those that are not algebraic. Ask students to explain how the examples are similar and how they are different. Expressions use operation symbols (+, -, ∗, ÷) to combine numbers, but algebraic expressions combine variables and numbers.

Tell students that it is important to remember the following points. To support English language learners, write the statements on the board:

� A situation can often be represented in several ways: in words, in a table, or in symbols.

� Algebraic expressions use variables and other symbols to represent situations.

� To evaluate an algebraic expression means to substitute values for the variable(s) and calculate the result.

Ask students to propose algebraic expressions to fit simple situations. To support English language learners, write the situations and respective expressions on the board. For example:

� Sue weighs 10 pounds less than Jamal. If J = Jamal’s weight, then J - 10 represents Sue’s weight.

� Isaac collected twice as many cans as Alex. If A = the number of cans Alex collected, then 2 ∗ A, or 2A, represents the number of cans Isaac collected.

� There are half as many problems in today’s assignment as there were in yesterday’s. If y = the number of problems in yesterday’s assignment, then there are 1 _ 2 y, 1 _ 2 ∗ y, or y _ 2 problems in today’s assignment.

Pose the following problems. Ask students to write an algebraic expression for each problem on their slates.

● Six times the sum of 9 and some number 6 (9 + n)

● 10 times the product of a number and 6 10 (n ∗ 6)

● Triple the sum of a number and 20 3 (n + 20)

● 10 less than a number n - 10

● 7 less than the product of a number and 6 n ∗ 6 - 7

Algebraic expressions can be combined with relation symbols (=, <, >, and so on) to make number sentences. For example, x + 2 = 15, or 3y + 7 < 100. Ask volunteers for the name of number sentences that contain algebraic expressions. Algebraic equations

Links to the FuturePictures, diagrams, and graphs are important

ways to represent situations, and they are

discussed throughout Everyday Mathematics.

Graphs in an algebra context are discussed

in Lesson 10-4.


Complete each statement below with an algebraic expression, using the suggested

variable. The first problem has been done for you.

1. If Beth’s allowance is $2.50 more

than Kesia’s, then Beth’s allowance is

.

2. If Leon gets a raise of $5 per week,

then his salary is

.

3. If Ali’s grandfather is 50 years

older than Ali, then Ali is

years old.

4. Seven baskets of potatoes weigh

pounds.7 � P, or 7P

G � 50

S � $5

Algebraic ExpressionsLESSON

10 �3

Date Time

Kesia’s allowance

is D dollars.

Beth

Pay to the order of: Leon

First Hometown Bank

Amount: S dollarsThe Boss

141

Leon’s salary is S dollars per week.

Ali’s grandfather

is G years old.

Ali

A basket of potatoes

weighs P pounds.

�

D�$2.50

Math Journal 2, p. 341

Student Page

Algebraic Expressions continuedLESSON

10 �3

Date Time

5. If a submarine dives 150 feet,

then it will be traveling at a depth of

feet.

6. The floor is divided into 5 equal-size

areas for gym classes. Each class

has a playing area of

ft2.

7. The charge for a book that is

D days overdue is

cents.

8. If Kevin spends 2 _ 3 of his allowance on

a book, then he has

dollars left.

X ft

A submarine is traveling

at a depth of X feet.

The gym floor has anarea of A square feet.

A library charges 10 cents for each

overdue book. It adds an additionalcharge of 5 cents per day for each

overdue book.

Sports Heroes

Kevin’s allowance

is X dollars.

X + 150

1 _ 5 * A, 1

_ 5 A, or A _ 5

10 + (5 * D), 5D + 10,

or 10 + 5D

1 _ 3 * X, 1

_ 3 X, or X _ 3

EM3MJ2_G5_U10_333-368.indd 342 4/1/10 1:04 PM


Student Page


▶ Writing Algebraic Expressions PARTNER ACTIVITY

(Math Journal 2, pp. 341 and 342)

Algebraic Thinking Go over Problem 1 on journal page 341. Partners then complete the statements on journal pages 341 and 342.

When most students have finished, discuss students’ answers, and point out that there are often several ways to write an algebraic expression. The answer to Problem 7 can be written 10 + (5 ∗ D), 5D + 10, or 10 + 5D. The answer to Problem 8 can be written 1 _ 3 ∗ X, 1 _ 3 X, or X _ 3 .

Ask students for the algebraic equation they would write to represent Problem 1. B = D + $2.50 Have students choose and write the algebraic equation for two problems. They should write their equations in the space beneath the problem answer line.

Ongoing Assessment: Journal

Page 341 �Recognizing Student Achievement

Use journal page 341 to assess students’ ability to write algebraic expressions

that model situations. Students are making adequate progress if they correctly

identify and write the expressions for Problems 3 and 4. Some students will

correctly write the algebraic equations for the two problems of their choice.


▶ Expressing a Rule as an PARTNER ACTIVITY

Algebraic Expression(Math Journal 2, p. 343)

Algebraic Thinking Have students complete journal page 343. Everyday Mathematics students are very familiar with “What’s My Rule?” tables because of their experiences with them starting in first grade. Use the Readiness activity in Part 3 with students who do not understand “What’s My Rule?” tables.

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 Number. Encourage students to find number sentences that use all 5 numbers and to use numbers as exponents or to form fractions.

PROBLEMBBBBBBBBBBBOOOOOOOOOOOBBBBBBBBBBBBBBBBBBBBBBBBBB MMMMMEEEEMMMMLELELBLEBLELLLBLEBLEBLEBLEBLEBLEBLEEEEMMMMMMMMMMMMMOOOOOOOOOOOOBBBBBBBLBLBBLBLBLBLLLLPROPROPROPROPROPROPROPROPROPROPROPPRPROPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPROROROROROOROOPPPPPPP MMMMMMMMMMMMMMMMMMMEEEEEEEEEEEELLELEEEEEEEEEELLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRRRRRRPROBLEMSOLVING

BBBBBBBBBBBBBBBBBBBBB ELEELEEMMMMMMMMMOOOOOOOOOBBBLBLBBLBLBBBLOOORORORORORORORORORORORO LELELLEEEEEELEMMMMMMMMMMMLEMLLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRGGGGGLLLLLLLLLLLLLVVINVINVINVINNNNVINVINVINNVINVINVINVINV GGGGGGGGGGGOLOOOLOOLOLOLOO VVINVINVLLLLLLLLLVINVINVINVINNVINVINVINVINVINVINVINVINNGGGGGGGGGGOOOLOLOLOLOLLOOO VVVLLLLLLLLLLVVVVVVVVVOOSOSOSOOSOSOSOSOSOSOOSOSOSOSOOOOSOOSOSOSOSOSOSOSOOSOSOSOSOSOSOSOSOSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS VVVVVVVVVVVVVVVVVVVVVLLLLLLLVVVVVVVVVLLLVVVVVVVVLLLLLLLLVVVVVLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLSSSSSSSSSSSSSSSSSSSSOOOOOOOOOOOOOOOOOO GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGNNNNNNNNNNNNNNNNNNNNNNNNNNIIIIIIIIIIIIIIIIIIIIISOLVING

798-802_EMCS_T_TLG2_G5_U10_L03_576914.indd 800798-802_EMCS_T_TLG2_G5_U10_L03_576914.indd 800 2/21/11 9:45 AM2/21/11 9:45 AM

“What’s My Rule?”LESSON

10 �3

Date Time

1. a. State in words the rule for the “What’s My Rule?”

table at the right.

b. Circle the number sentence that describes the rule.

Y = X / 5 Y = X - 4 Y = 4 - X


table at the right.


Z = Q + 2 Z = 2 ∗ Q Z = 1

_ 2 Q ∗ 1


table at the right.


g = 2 ∗ t t = 2 ∗ g t = 4 ∗ g

Subtract 4 from X.

Add 2 to Q.

Multiply g by 4.

X Y

5 1

4 0

- 1 - 5

1 - 3

2 - 2

g t

1

_ 2 2

0 0

2.5 10

1 _ 4 1

5 20

Q Z

1 3

3 5

-4 -2

-3 -1

-2.5 -0.5

333-368_EMCS_S_G5_MJ2_U10_576434.indd 343 2/22/11 5:21 PM


Student Page

Math Boxes LESSON

10 �3

Date Time

1. Identify the point named by each ordered number pair.

a. (0,4) B

b. (3,3) A

c. (5,4) D

d. (4,0) C 10 2 3 4 5

1

0

2

4

3

5

y

x

A

B

C

D

208

3. Multiply. Use the algorithm of your choice.

Show your work.

a. b. c.

2. Add or subtract.

a. 20 + (-10) = 10

b. -8 + (-17) =

c. -12 – (-12) = 0

d. -45 + 45 = 0

e. -31 - 14 =

5. The rectangular prism below has a volume

of .

Write a number model for the formula.

4. a. Draw a circle that has a

diameter of 4 centimeters.

b. The radius of the circle is 2 cm .

-25

-45

43

* 78

3,354

19

* 86

1,634

79

* 42

3,318

Area of base 42 cm

3 cm

2

92

153 164

19

197

42 ∗ 3 = 126 cm3

(unit)

126 cm3

333-368_EMCS_S_MJ2_G5_U10_576434.indd 344 3/22/11 12:43 PM


Student Page

Lesson 10�3 801

▶ Math Boxes 10�3

INDEPENDENT ACTIVITY

(Math Journal 2, p. 344)

Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 10-1. The skill in Problem 4 previews Unit 11 content.

Writing/Reasoning Have students write a response to the following: Explain the strategy and reasoning you would use to solve Problem 3b with the standard multiplication algorithm. Answers vary.

Writing/Reasoning Have students write a response to the following: Explain how you found the volume for Problem 5. I knew the base (B) of the prism was 42 cm2

and the height (h) of the prism was 3 cm. I used the formula B ∗ h to calculate the volume (V ): 42 ∗ 3 = 126 cm3.

▶ Study Link 10�3 INDEPENDENT

ACTIVITY (Math Masters, p. 299)

Home Connection Students complete statements with algebraic expressions. They write the rule and identify the related number sentence for “What’s My Rule?” tables.

3 Differentiation Options

READINESS PARTNER ACTIVITY

▶ Exploring “What’s My Rule?” 5–15 Min

Tables(Math Masters, p. 300)

Algebraic Thinking To provide experience with using patterns in tables to solve problems, have students make rules and then complete the related table. Partners work together to complete each of their Math Masters pages.

When students have finished, discuss the rules and tables they made. Ask partners to share what they think is important to remember when solving “What’s My Rule?” tables. Sample answers: If you know the in value, follow the rule to find the out value. If you know the out value, do the opposite of the rule to find the in value.

798-802_EMCS_T_TLG2_G5_U10_L03_576914.indd 801798-802_EMCS_T_TLG2_G5_U10_L03_576914.indd 801 4/7/11 9:33 AM4/7/11 9:33 AM

STUDY LINK

10�3 Writing Algebraic Expressions

Complete each statement below with an algebraic expression, using the

suggested variable.

1. Lamont, Augusto, and Mario grow carrots in three

garden plots. Augusto harvests two times as many

carrots as the total number of carrots that Lamont and

Mario harvest. So Augusto harvests

carrots.

2. Rhasheema and Alexis have a lemonade stand at their school fair. They

promise to donate one-fourth of the remaining money (m) after they repay the

school for lemons (l ) and sugar (s). So the girls donate

dollars.

3. a. State in words the rule for the “What’s My Rule?” table at the right.


Q = (3 + N) ∗ 5 Q = 3 ∗ (N + 5) Q = 3N + 5

4. a. State in words the rule for the “What’s My Rule?” table at the right.


R = E ∗ 6 ∗ 15 R = (E ∗ 6) + 15 R = E ∗ 15 + 6

Augusto Lamont and Marioharvested

L + M carrots.

N Q

2 11

4 17

6 23

8 29

10 35

E R

7 57

10 75

31 201

3 33

108 663

Practice

5. 384 ∗ 1.5 = 6. 50.3 ∗ 89 =

7. 843

_ 7 = 8. 70.4 / 8 =

218 231232

Name Date Time

Multiply N by 3 and add 5.

1

_ 4 ∗ (m - (l + s)), or 1

_ 4 (m - (l + s))

2 ∗ (L + M ), or 2(L + M )

Multiply E by 6 and add 15.

4,476.7

8.8

576

120 3 _ 7

294-322_439_EMCS_B_MM_G5_U10_576973.indd 299 2/23/11 4:21 PM

Math Masters, p. 299

Study Link Master

Name Date Time

Patterns and RelationshipsLESSON

10� 3

A car is traveling at a given speed over a stretch of highway. You can find the distance

the car travels by multiplying its speed by the amount of time it travels.

1. Car A travels at a speed of 30 miles per hour (mph). Car B travels at 60 miles per hour.

Complete the tables to find the distance each car travels for the given times.

2. For each car, write the rule that is used to find the distance.

Car A: Car B:

Multiply each hour by 30. Multiply each hour by 60.

3. Use the tables to write a set of ordered pairs in the form

(Time, Distance) for each car. Then graph the data and

connect the points for each car. Label each graph.

4. As the amount of time increases, explain how the distance

Car B travels compares with the distance Car A travels?

Sample answer: For each hour, Car B travels twice as far

as Car A. This is because Car B is traveling twice as fast.

Car A

Speed: 30 mph Time (hr) Distance (mi)

0 0

1 30

2 60 3 90 4 120

Car B


0 0 1 60 2 120 3 180 4 240

0

30

60

90

120

150

180

210

240

270

0 1 2 3 4

Dis

tan

ce

(m

iles)

Time (hours)

Car B

Car

A

Car A Car B

(0,0) (0,0)

(1,30) (1,60)

(2,60) (2,120)

(3,90) (3,180)

(4,120) (4, 240)

300A-300B_EMCS_B_MM_G5_U10_576973.indd 300A 3/22/11 9:37 AM

Math Masters, p. 300A

Teaching Master


EXTRA PRACTICE


▶ Writing Algebraic Expressions 5–15 Min

(Student Reference Book, p. 218)

Algebraic Thinking Students complete the Check Your Understanding problems on Student Reference Book, page 218. Ask students to write algebraic expressions for the first two problems and to describe how they chose the variables to use.

ELL SUPPORT

SMALL-GROUP ACTIVITY

▶ Building a Math Word Bank 5–15 Min

(Differentiation Handbook, p. 142)

To provide language support for algebra concepts, have students use the Word Bank Template found on Differentiation Handbook, page 142. Ask students to write the term algebraic expression, draw pictures relating to the term, and write other related words. See the Differentiation Handbook for more information.

ENRICHMENT


▶ Analyzing Patterns and 5–15 Min

Relationships(Math Masters, p. 300A)

To extend students’ understanding of rules and patterns, students use two sets of rules to generate two tables of values. They form ordered pairs consisting of corresponding terms from two patterns, and graph the ordered pairs on a coordinate plane. Students then use the tables of values, rules, ordered pairs, or graphs to identify a relationship between corresponding terms from each pattern.


Copyright

© W

right

Gro

up/M

cG

raw

-Hill

Name Date Time

300A

Patterns and RelationshipsLESSON

10� 3

A car is traveling at a given speed over a stretch of highway. You can find the distance

the car travels by multiplying its speed by the amount of time it travels.

1. Car A travels at a speed of 30 miles per hour (mph). Car B travels at 60 miles per hour.

Complete the tables to find the distance each car travels for the given times.

2. For each car, write the rule that is used to find the distance.

Car A: Car B:

3. Use the tables to write a set of ordered pairs in the form

(Time, Distance) for each car. Then graph the data and

connect the points for each car. Label each graph.

4. As the amount of time increases, explain how the distance

Car B travels compares with the distance Car A travels?

Car A


0 0

1 30

2

3

4

Car B


0

1

2

3

4

0

30

60

90

120

150

180

210

240

270

0 1 2 3 4

Dis

tance (

mile

s)

Time (hours)

Car A Car B

(0,0)

(1,30)

300A-300B_EMCS_B_MM_G5_U10_576973.indd 300A300A-300B_EMCS_B_MM_G5_U10_576973.indd 300A 3/22/11 9:21 AM3/22/11 9:21 AM

Documents

Algebraic Expressions - Login your answers on page 440. Algebra Statement Algebraic Expression Some algebraic expressions: 2 - x m ∗ m C + 5 6 ∗ H (C + 5) (6 ∗ H) Other expressions