summerboost playbook for future 6th through 8th graders!

SummerboostI D E A P U B L I C S C H O O L S

Playbookfuture 6th - 8th Graders

SUMMER2015

NAME: ___________________________________ SCHOOL: ______________________________


Conceptualized and Produced by 2015 IDEA Public Schools ALP Team: Vanessa Barry, Cecilia Gallagher, Renee Livesay, Alisa Ozuna and Emily Tucker. Advised by IDEA Public Schools Vice President, Elizabet Garza.

Dear College Prep Parent,

Summer is a great time for your child to practice what s/he has learned throughout the school year. There is no better activity for your child than to engage in reading, writing, and math for the summer months of June and July. Not only will your child discover the joy of being lost in a book, but s/he will practice the many skills and strategies s/he has learned all year.

Teachers and other educators identify summer learning loss as a major challenge when starting off the new school year. However, students who read over the summer return to school ready to continue learning with little or no learning loss. On average, students regress (backslide) one full grade level in reading if they don’t read over the summer. Imagine all of that hard work and dedication lost.

The great news is that IDEA Public Schools has established SummerBoost to combat this with the support of an at-home summer education guide -- this playbook!

Your child was sent home with this playbook with engaging, fun activities that help prevent the summer learning loss referenced above. One of the key elements for this home component is completing the Power Hour at home with the playbook. The Power Hour is simple, your child simply engages in a minimum of 20 minutes of Reading, 20 minutes of Writing, and 20 minutes of Math every day over the summer from June 1 through August 9, the eve of the first day of school.

Summer learning is meant to be enjoyable and we do not want students to have to struggle. We want reading, writing, and math to be fun and exciting.

The enclosed playbook includes: required reading lists, open response journals, math activities and more.

Sincerely,

Summer BOOST T eam

SummerBOOST

Estimado padre de College Prep,

Es una buena idea utilizar parte del verano para que su hijo/a practique lo aprendido a través del año escolar. No hay mejor actividad para su hijo/a que leer en el verano. Su hijo/a no sólo descubrirá el gozo de perderse en un libro, sino que también practicará las muchas destrezas y estrategias que ha aprendido durante todo el año.

Los maestros y otros educadores saben que la pérdida del aprendizaje durante el verano es uno de los mayores desafíos que enfrentan al empezar el nuevo año escolar. Sin embargo, los alumnos que leen durante el verano vuelven a la escuela listos para seguir su aprendizaje con poca o ninguna pérdida del aprendizaje.

La buena noticia es que IDEA Public Schools ha establecido SummerBoost para combatir esto con el apoyo de una guía de la educación en el hogar de verano - Este libro de jugadas!

Su hijo fue enviado a casa con este libro de jugadas con actividades divertidas, atractivas que ayudan a prevenir la pérdida de aprendizaje durante el verano. Uno de los elementos clave de este medioambiente casero es sumergir a su hijo/a en la Power Hour en casa con el libro de jugadas. El Power Hour es simple, su hijo simplemente tiene que dedicar un mínimo de 20 minutos de lectura, a 20 minutos de la escritura, y 20 minutos de matemáticas todos los días durante el verano del 1 de junio al 9 de agosto, la víspera del primer día de clases.

El aprendizaje de verano está destinado a ser agradable y no queremos que los estudiantes tengan que luchar. Queremos que la lectura, escritura y matemáticas sea divertido y emocionante.

El libro de jugadas incluye: listas de lecturas requeridas para el ano entrante, diarios de respuestas abiertas, actividades de matemáticas y más.

Atentamente,

Summer BOOST T eam

SummerBOOST

Table of ContentsREADING AND WRITING

Reading Summer Goal Sheet 1

Online Software (URL) 2

Local Library Information 4

College Prep Required English / Language Arts Summer Reading 8

College Prep Required Humanities Summer Reading 9

Power Hour 10

Reader Response Journals 12

MATH

Math Fun Pages 41

Summer boost Goal sheet

1

Number of words read: __________

Number of AR points to earn

(if internet access is available) _____ points

Number of books read(if access to the internet is limited) _____ books

Completed Writing Response Journals _____ journals

2

OnlineSoftware

Name of software

Grade Levels description URL log-in

Tumblebooks K - 6

Online collection of animated, talking pictue

books and chapter books

www.tumblebooks.com

Username:ideaps

Password:reads

AR (Accelerated

Reader)1 - 7

Once students complete a book, they log into this software to take a com-prehension quiz over the

book.

https://hosted274.renlearn.com/2406896

Username: School ID #

Password:ABC123

Reasoning Mind

2 - 5 (6th at IDEA

Carver)

Students should work through guided study or

wall of mastery. www.rmcity.org

Username: School ID #

Password:School Password

Think Through Math

6 - 7

An adaptive online learning program that deepens

students’ understanding of critical math concepts and

problem-solving skills

http://lms.thinkthroughmath.com/

users/sign_in

Username:School ID #


Spacial Temporal Math

from Mind Research Institute

6

Game-based instructional software designed to boost math comprehension and proficiency through visual

learning

http://web.stmath.com/entrance/

Username:School ID #


FolletShelf 1 - 8 Online eBooks

https://ips.follettdestiny.com

(1. select your school, 2. enter username and

password, 3. select “FollettShelf” at top of

the screen)

Username:School ID#

Password:abc123

3

public libraries

PUBLIC LIBRARIESR I O G R A N D E VA L L E Y

Alamo Public Library416 N. Tower RoadAlamo, TX 78516(956) 787-6160

Harlingen Public Library410 76th Drive

Harlingen, TX 78550(956) 216-5800

Mercedes Memorial Library434 South Ohio Street

Mercedes, TX 78570-3196(956) 565-2371

Brownsville Public Library (Main Branch)

2600 Central Blvd.Brownsville, TX 78520

(956) 548-1055 ext. 2115

Hidalgo Public Library710 E Texano Dr

Hidalgo, TX 78557(956) 843-2093

Mission Public Library801 E. 12th St.

Mission, TX 78572(956) 580-8750

Brownsville Public Library (Southmost Branch)

4320 Southmost Blvd.Brownsville, TX 78521

(956) 548-1055 ext. 2201

La Joya Public Library201 Palm Shores Blvd.

La Joya, TX 78560(956) 581-4533

Pharr Public Library121 E Cherokee Ave.

Pharr, TX 78577(956) 787-3966

Donna Public Library301 N. Main St.

Donna, TX 78537(956) 464-2221

McAllen Public Library (Main Library)

4001 N. 23rd St.McAllen, TX 78504

(956) 681-3000

San Benito Public Library101 W. Rose

San Benito, TX 78586(956) 361-3860

Edinburg Public Library401 E Cano St.

Edinburg, TX 78539(956) 383-6246

McAllen Public Library (Lark Branch)

2601 Lark Ave.McAllen, TX 78504

(956) 681-3100

San Juan Public Library1010 S Standard Ave. San Juan, TX 78589

(956) 702-0926

Elsa Public Library711 N. HidalgoElsa, TX 78543(956) 262-3061

McAllen Public Library (Palm View Branch)

3401 Jordan Ave.McAllen, TX 78503

(956) 681-3110

Weslaco Public Library525 S. Kansas Ave.

Weslaco, TX 78596(956) 968-4533

4

PUBLIC LIBRARIES

Faulk Central Library800 Guadalupe St.Austin, TX 78701(512) 974-7400

Howson Branch2500 Exposition Blvd.

Austin, TX 78703(512) 974-8800

Old Quarry Branch7051 Village Center Dr.

Austin, TX 78731(512) 974-8860

Carver Branch1161 Angelina St. Austin, TX 78702(512) 974-1010

Little Walnut Creek Branch835 W. Rundberg Ln.

Austin, TX 78758(512) 974-9860

Pleasant Hill Branch211 E. William Cannon Dr.

Austin, TX 78745(512) 974-3940

Cepeda Branch651 N. Pleasant Valley Rd.

Austin, TX 78702(512) 974-7372

Manchaca Road Branch5500 Manchaca Rd.

Austin, TX 78745(512) 974-8700

Hampton Branch At Oak Hill5125 Convict Hill Rd.

Austin, TX 78749(512) 974-99006

North Village Branch2505 Steck Ave. Austin, TX 78757(512) 974-9960

A U S T I N

5

PUBLIC LIBRARIES

Bazan Branch Library2200 W. Commerce

San Antonio, TX 78207Phone: (210) 207-9160

Guerra Branch Library7978 Military Drive WestSan Antonio, TX 78227Phone: (210) 207-9070

Mission Branch Library3134 Roosevelt Ave.


Brook Hollow Branch Library530 Heimer


Igo Branch Library13330 Kyle Seale PkwySan Antonio, TX 78249Phone: (210) 207-9080

Pan American Branch Library1122 W. Pyron Ave.


Carver Branch Library3350 E. Commerce


Johnston Branch Library6307 Sun Valley


Parman Branch Library at Stone Oak20735 Wilderness OakSan Antonio, TX 78258Phone: (210) 207-2703

Cody Branch Library11441 Vance Jackson


Landa Branch Library233 Bushnell


San Pedro Branch Library1315 San Pedro Ave.


Collins Garden Branch Library200 N. Park


Las Palmas Branch Library515 Castroville Rd.


Semmes Branch Library15060 Judson Rd.


Cortez Branch Library2803 Hunter Blvd.


Maverick Branch Library8700 Mystic Park


Thousand Oaks Branch Library4618 Thousand Oaks


Forest Hills Branch Library5245 Ingram Rd.


McCreless Branch Library1023 Ada St.


Tobin Branch Library at Oakwell4134 Harry WurzbachSan Antonio, TX 78209Phone: (210) 207-9040

Great Northwest Branch Library9050 Wellwood


Memorial Branch Library3222 Culebra


Westfall Branch Library6111 Rosedale Ct.


S A N A N T O N I O

6

summer reading texts

8

english/language arts

These classic and modern texts are riveting, emotionally charged, and unforgettable. The summer months will never be the same again!

Every student should:

• Read the text(s) listed for their upcoming grade level

• Complete the summer reading assignment for the text (provided by the teacher)

• Begin school prepared to discuss the text (the first assessment is over the summer reading)

• Contact your campus’ English teacher if there are any questions

9th GradeThe Lord of

the Fliesby William Golding

12th

The Things They Carried

by Tim O’brien

10th GradeThe Kite Runner

by Khaled Hosseini

11th GradeThe Great Gatsby

by F. Scott Firzgerald&

The Autobiography of Malcom X: As Told

BY Alex Haley

6th GradeThe Watsons Go to

Birminghamby Christopher Paul Curtis

7th GradeThe Outsiders

by S.E. Hinton

8th GradeEnder’s Gameby Orson Scott Card

The Alchemist by Paulo Coelho

Bless Me, Ultima by Rodolfo Anaya

Flowers for Algernon by Daniel Keyes

The Adventures of Huckleberry Finn by Mark Twain

The Catcher in the Rye by J.D. Salinger

Also, 12th grade students must choose one of these additional texts:

9

Humanities Summer reading in Humanities creates a common culture and shared experience among students and gives them a framework for upcoming course content.

Every student should:

• Teachers will assign students to read at least one of the text(s) listed for their upcoming course.

• Complete the summer reading assignment for the text (provided by the teacher).

• Begin school prepared to discuss the text (the first assessment is over the summer reading).

• Contact your campus’ English teacher if there are any questions.

6th GradeA Long Walk to Water

by Linda Sue Park

Three Wishes: Palestinian and Israeli Children

Speak by Deborah Ellis

Journey to Jo ‘Burg-A South African Story

by Beverly Naidoo

One Day in the Tropical Rainforest

by Jean Craighead

ap human geography

Kiss the Dust by Elizabeth Laird

How Soccer Explains the World

by Franklin Foer

Fast Food Nation: The Dark Side of the All-

American Meal by Eric Schlosser

Nickel and Dimed: On Not Getting by in

America by Barbara Ehrenreich

From Columbus to ConAgra by Alessandro

Bonanno

ap World history

A History of the World in 6 Glasses

by Tom Standage

Guns, Germs and Steelby Jared Diamond

Year of the Hyenas: A Novel of Murder in

Ancient Egyptby Brad Geagley

The Creation of Patriarchy

by Gerda Lerner

Mexico: From the Olmecs to the Aztecs

by M. Coe & R. Koontz

ap US history

The Tragedy of American Diplomacy

by William Appleman Williams

A People’s History of the United Statesby Howard Zinn

Bury My Heart at Wounded Knee

by Dee Brown

The Cold Warby John Gaddis

Unbrokenby Lauren Hillenbrand

ap Government & economics

The Libery Amendments: Restoring the American

Repulicby Mark Levin

The Orange Book: Reclaiming Liberalism

Basic Economics 5th Ed: A Common Sense Guide to

the Economyby Thomas Sowell

Freakonomics: A Rogue Economist Explores the

Hidden Side of Everythingby S. Dubner and S. Levitt

1984by George Orwell

7th GradeThe Bugles are Silent

by John Knaggs

Lone Star: A history of Texas and the Texans

by T.R. Fehrenbach

Story of Texas by Edward Weems

The Circuit by Francisco Jimenez

8th GradeChains by Laurie Halse

and Forge by Laurie Halse

Blood on the River: Jamestown, 1607

by Elisa Carbone

The Fifth of March: A Story of the Boston

Massacre by Ann Rinaldi

The Slave Dancer by Paula Fox

10

Humanities power houruse it or lose it

20 Minutes of reading, AR testing, computer-based software

1. Achieve 3000

2. Accelerated Reader

3. Imagine Learning

4. Newsela.com

5. Folletshelf

20 minutes of Math Worksheet or Computer based software

1. Think through Math

2. Khan Academy

20 minutes of Journal Writing

1. Text Connections

2. Text to Text

3. Text to Self

4. Text to World

5. Reading Log Journals

11

reADER RESPONSE JOURNAL ENTRIES

INSTRUCTIONS:

1. On the days listed on this sheet, we recommend you read 30 minutes per day.

2. Answer the question listed in the box for the day. Each night’s answer must be at least 5 sentences.

3. After completing your reading and writing, your parent/guardian must sign your reading log.

4. Reading Logs must be completed from Monday through Friday. Saturday and Sunday give you extra points (cha-ching)! You will turn in your log when you return from summer to cash in for prizes!

12

Reader RESPONSEJOURNAL ENTRIES

In 5 sentences, write about how you can connect your life to what you read today.

In 5 sentences, describe the setting of the text you are reading.

MONDAY:

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Copy a quote from your book/text that has meaning for you, then explain the meaning and why you chose it in 5 sentences.

Create a 5 sentence paragraph using 4 words you had difficulty understanding or have learned from your reading. (Don’t be afraid to use dictionary.com to look up words!)

WEDNESDAY:

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READER responseJournal Entries

In 5 sentences, explain what you like about this book so far.

In 5 sentences, explain what you dislike about this book so far.

What events in the story reminded you of another story you’ve read?

Take a picture of what you’re

reading, share it on social

media,

and tag #IDEASummerBoost for

the chance to win a gift ca

rd to

Main Event!

FRIDAY:

SATURDAY:

SUNDAY:

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MONDAY:

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WEDNESDAY:

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17







media,



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Cinemark!

FRIDAY:

SATURDAY:

SUNDAY:

DA

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MONDAY:

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WEDNESDAY:

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FRIDAY:

SATURDAY:

SUNDAY:

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MONDAY:

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WEDNESDAY:

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FRIDAY:

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maTHFUN

PAGES

multiplying & Dividing decimalsMULTIPLYING WHOLE NUMBERS

BY DECIMALSDIVIDING DECIMALS BY

WHOLE NUMBERS

MULTIPLYING WHOLE NUMBERS BY DECIMALS

USING GRIDS TO MULTIPLY DIVIDING A DECIMAL BY A DECIMAL

• Add the number of decimal places in each factor. • Place the decimal point in the product

There are ______ sets of ______ tenths.

• Multiply as you would with whole numbers. • Add the number of decimal places in each factor.• Place the decimal point in the product.

• The overlapping squares that are shaded twice show the product of 0.6 x 0.3.

• Multiply as you would with whole numbers. How many 2 tenths are there in 3 wholes?

Multiply: 6 x 5.37 = m Divide: 3 ÷ 0.2 = p

Divide: 5.4 ÷ 0.8 = n

3 ÷ 0.2 = ____

Multiply: 6 x 5.37 = n

0.8 5.4 8. 54.

m=____

n=6.75

=

0.59 x 4.8=____

5.37x 6

___ decimal places

move decimal ___ places

___ decimal places+

0.59x4 .8

___ decimal places

move decimal ___ places

___ decimal places+

• Shade 0.6 of the grid

• Shade 0.3 of the grid with a different color or pattern in the other direction.

0.6 x 0.3 =___ or

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

VOCABULARY TERMS decimal multiply

decimal place power of 10

decimal point product

divide quotient

dividend tenth

divisor whole number

• Change the divisor and the divident to a whole number by multiplying each by the same power of 10.

• Divide as you would divide whole numbers. Add zeros as needed.

• Place the decimal point in the quotient directly above the decimal point in the dividend.

5.40.8

08. 54.00

42

multiplying & Dividing decimalsNAME:_____________________ DATE :______________ CLASS:______________

MULTIPLY:

MULTIPLY:

DIVIDE:

DIVIDE:

DIVIDE: MULTIPLY:

78.9x 14.0

$1.25x 23

80.1 ÷ 9 =

806.4 ÷ 0.6 =

13.86 ÷ 3.3 = 13.5 ÷ .35 =

A. 2,102.54B. 21.0254C. 210.254D. 2.10254

A. 1,104.6B. 11.4405C. 11,046D. 1.1046

A. 910B. 5460C. 105D. 312

A. $28.75B. $29.50C. $2,875D. $8.75

A. 89B. 0.89C. 8.9D. 9.1

A. 134.4B. 1,344C. 13.44D. 1.344

A. 42.0B. .42C. 4.2D. 40.2

A. 1,225B. .1225C. 1.225D. 12.25

Jenny works 17.5 hours a week at the library. How many hours does Jenny work in 52 weeks?

Ms. Jackson, a third grade teacher, wants to giver her students pencils. She has 23 students in her class. If each pencil is $1.25, how much money will Ms. Jackson need?

17.5x 52

1.006x2.090

MULTIPLYING FRACTIONS

multiplying & dividing fractions

MODEL MULTIPLICATION

MODELING DIVISION DIVIDING FRACTIONS

VOCABULARY

denominator multiplydivide numeratordivisor productfraction reciprocalgreatest common factor (GCF) whole number

Multiply 3/4 x 2/3

Divide 9/16 ÷ 3/16 Divide 6 ÷ 2/3

Multiply 3/4 x 2/3

3/4 x 2/3 =

Therefore, 3/4 x 2/3 = _or _ The answer of 1/2 is

the simplest form.

Shade 3/4 of the rectangle.

Step 1: Multiply the numerators.Step 2: Multiply the denominators.

Step 1: Write the whole number as a fraction.

Step 2: Flip the divisor (2/3) upside down to find the reciprocal.

The reciprocal of 2/3 is

Step 3: Rewrite as multiplication using the reciprocal.

Step 4: Simplify before multiplying.

Step 3: Use the greatest common factor (GCF) to simplify the product, if necessary. The GCF of 6 & 12 is 6.

How many sets of 3/16 are there in 9/16?

There are ___ groups of 3/16 in 9/16?

Therefore 9/16 ÷ 3/16 =

Divide rectangle into thirds.

Shade 2/3 of the rectangle with a different color or pattern in the other direction. The overlapping sections

(green) that are shaded twice show the product of 3/4 x 2/3.

xx

=

=6/12

9/166 ÷ 2/3 = ÷

dividend divisor

x

x = =

44

multiplying & dividing fractionsNAME:_____________________ DATE :______________ CLASS:______________

What is the product of 4/7 x 1/9?

12 ÷ 4

20 ÷ 4

5/10 ÷ 4/6 =

You can reduce 12/20 to ___.

Divide the following fractions and reduce the quotient to its lowest terms.

A. 5/16B. 4/9C. 4/63D. 4/56

A. 4/17 B. 4/10C. 3.10

D. 3/70

A. correctB. incorrect

1/9

1/10

4/7

3/7

3/7 x 1/10 =

A. 12/17B. 32/56C. 32/56D. 35/63

A. 3/5B. 2/3C. 4/5D. 3/4

A. 1/3B. 20/30C. 30/40D. 3/4

A. correctB. incorrect

7/9

1/10

4/10

5/85/8 x 7/9 =

1/10 x 4/10 = 4/10

1/2 ÷ 4/5 = 1/2 x 5/4 =

3/10 ÷ 3/5 = 9/50

÷

÷

A. 4/10B. 8/5C. 2/5D. 5/8

Equal ratios: 4/1 = =

Ratio, proportion & Percents

RATIO

PROPORTION

PERCENT

Lemonade Making Directions

What percent of this grid is shaded.

A ratio is a comparison of two numbers. These numbers are called the terms of radio.

A _____________ is an equation showing that two ratios are equal. Ratios that are equal to each other are called ___________ ____________.

Percents show up everywhere in our daily live - sales tax on purchases, tips at restaurants, discounts at stores, among others. Percent means “per hundreds”. It is a ratio that compares a number to 100. For sample, 36 percent is a 36 to 100 or 36 out of 100.

Mix 4 parts water with 1 part lemon juice.

Change 4/5 to an equivalent fraction with a denominator of 100.

= water = lemon juice

Step 1: Count the number of green marbles: ___Count the number of blue marbles: ___

Step 2: Write a ratio to compare. Ratios can be written in three different ways.

Write a ratio to compare the number of green and blue marbles. RATIO FRACTION

FORMWORD FORM

USING A COLON

green to blue

blue to the total number of marbles

green to the total number of marbles

4/5 x = = %

1/10 x = % 1/4 x = % 1/2 x = %

to :

:

:

to

to

= = =÷ ÷ ÷= = =

VOCABULARYdenominatorequal ratioequivalent fractionfractionpercentproportionratio

1/51/51/51/5

3/4 x = % 10/10 x100/100= %

46

Ratio, proportion & percentsNAME:_____________________ DATE :______________ CLASS:______________

A. 6/20B. 20/6C. 20.6

D. 1/6

A. 10:5

B. 10 to 5

C. 5/10D. 1/5

A. 7:19

B. 7:28

C. 19:7

D. 19:24

A. 4:4

B. 1:4

C. 4:12

D. 1:12

A. 1/100B. 11/1000C. 11/100D. 11/10

A. 5/10B. 5/100C. 50/100D. 5/1

A. 30%

B. 3%

C. 300%

D. 0.3%

A. 10:7

B. 10 to 7

C. 7:10

D. 1/10

Another way to write 20 to 6 is ______. Write the percent as a fraction.

Write the percent as a fraction.

Write the fraction as a percent.

Another way to write the ratio 7/10 is

Another way to write 5:10 is ______.

While cleaning his room, Max found the following marbles: 7 black, 19 red, and 2 violet. What is the ratio of black marbles to red marbles?

What is the ratio of to ?

11%

5%

3/100

SUBTRACTION

operations with mixed numbers

ADDITION

MULTIPLICATION DIVISION

VOCABULARYaddition

dividend

division

divisor

equivalent fraction

factor

fraction

improper fraction

least common denominator (LCD)

mixed number

multiplication

numerator

product

quotient

reciprocalsubtraction

Add 22/3 + 3 1/6 Add 22/3 + 3 1/6

Multiply 21/4 x 2/3 = m Multiply 12/3 x 1 3/7 = n

21/4 =

21/4 x 2/3 =

5/3 x 7/10 =

7/6 =

Step 1: Find the least common denominator (LCD) of 2/3 and 1/6.

Step 1: Write the mixed number as an improper fraction. Step 1: Write the mixed number as improper fractions.

Step 2: Rewrite as multiplication using the reciprocal of the divisor.

Step 3: Multiply the numerators and denominators and simplify.

Step 4: Write as a mixed number.

Step 2: Multiply the numerators and then denominators of the two factors.

Step 3: Simplify the product.

Step 4: Write the product as a mixed number if it is an improper fraction.

Step 2: Write the equivalent fractions with a denominator of 6.

Step 3: Add the fraction. Then add the whole numbers. Simplify the sum, if necessary.

Step 1: Find the LCD and write equivalent factions. LCD of 3/4 and 5/8 is .

Step 2: Subtract the fractionsfirst, then the whole numbers. Simplify the difference if necessary.

=

=

2 2/3

35/30

+3 1/6

=4 3/4

-2 5/8

12/3 = 13/7 =

=

+ -

2/3 multiples of 3: _,_,_,_,_,... 1/6 multiples of 6: _,_,_,_,_,...

=

=x

=

factor dividend

improper fraction

improper fraction

mixed number

mixed number

factor divisorproduct quotient

48

operations with mixed numbersNAME:_____________________ DATE :______________ CLASS:______________

A. 7 9/27B. 8 20/27C. 6 18/27D. 8 2/27

A. 17 11/12B. 18 11/13C. 17 11/24D. 18 22/24

A. trueB. false

A. 6 4/8B. 2 4/8C. 6 2/8D. 2 2/8

A. 5 35/55B. 3 35/55C. 1 100/105D. 2 20/21

A. 7 1/9B. 8 1/9C. 7 10/9D. 8 5/9

A. 10

B. 3 3/5C. 16

D. 9 3/5

A. 2 1/2

B. 21 3/4C. 2 5/12D. 2 7/12

Add 711/27 + 1 9/27 =

Add 9 10/12 + 8 1/12 = True or false?

Subtract 4 3/8 - 2 1/8 =

Subtract 12 4/5 - 3 1/5 =

7 1/4 ÷ 3 = 29/4 ÷ 3/1 = 29/4 x 1/3 =

6 1/5 ÷ 2 1/10 = 31/5 ÷ 21/10 = 31/5 x 10/21 =

5 5/9 + 2 5/9 =

2 2/5 x 4 1/6 = 12/5 x 25/6 = 300/30 = 10

introduction to algebra

ALGEBRAIC EXPRESSIONS

TRANSLATING WORD PHRASES INTO ALGEBRAIC EXPRESSIONS

SOLVING EQUATIONS

EVALUATING ALGEBRAIC EXPRESSIONS

An algebraic expression is a mathematical phrase consisting of variables, numbers and operations.

To evaluate algebraic expressions, replace the variable with a number.

An equation is a mathematical sentence which shows that two expressions or values are equal.

Think of an equation as a balance scale.

Solve the equation to find the value of the variable that makes the equation true. The value of the variable is called the solution.

What number plus 16 equals 28?

Replace m with in the expression.

The letter m is a _____________ which represents an unknown number.

3 x 2m = is an _______ ________

evaluate m + 5 for m = 4

solve 16 + m = 28

+ 16 = 28 = 28

solution m =

+ 5 =

m + 16 28=

m + 5

Examples of Algebraic ExpressionsAddition:Subtraction:

Multiplication:

Division:

Operation Word Phrase Algebraic Expression

Addition

Subtraction

Multiplication

Division

A number plus 9The sum of m and 99 more than a numbera number increased by 9The difference between a number and 9

A number minus 99 less than a numberA number decreased by 9

9 more than twice a number2 x a numberA number multiplied by 2The product of 2 and a number

A number divided by 99 divided by a numberThe quotient of a number and 9

expression expressionequal sign

28m 16

VOCABULARYalgebra

algebraic expressions

difference

equation

increase

more

plus

product

quotient

solution

sum

variable

50

Introduction to algebraNAME:_____________________ DATE :______________ CLASS:______________

Evaluate the following equation then choose the answer that best completes the equation.





A. 7B. 8C. 9D. 10

A. 2B. 3C. 4D. 5

A. 9B. 8C. 7D. 6

A. 1B. 5C. 7D. 9

A. 2B. 3C. 4D. 5

11 - x = 4; x = 5 x r = 25; r =

16 - 9 = x; x =

t x 2 = 14; t =

9 = 3 x y; y =




A. 10B. 8C. 3D. 9

A. 8B. 9C. 10D. 11

A. 5B. 10C. 15D. 20

15 + y = 23; y =

x - 7 = 3; x =

30 = c + 15; c =

It is __________that the spinner

will land on a green section;

and ___________ that it will land

on a yellow section.

There is an ______ ______

that the spinner will land on a green

or

yellow section.

It is ______ ______that the

spinner will land on a green section;

and ______ ______that it will

land on a yellow section.

On which color is the spinner more likely to land?

probability concepts

ALGEBRAIC EXPRESSIONS

FINDING PROBABILITIES

The probability of an event shows the __________ that some event will occur. An event is all the possible __________.An impossible event has a probability of __________.A certain event has a probability of ___.

You can determine the probability of an event by comparing the number of favorable outcomes with the total number of possible outcomes.

If you pick 2 balls from the bag, what is the probability that they will be red and green?

probability of picking a red ball

probability of picking a green ball

probability of picking a red & a green ball

When we toss a number cube, there are possible different outcomes. It can show either __,__,__,__,__ or __.

probablity of an eventnumber of favorable outcomes

number of possible outcomes=

What is the probability that you will pick a red ball?

Step 1: Count the number of red balls. Step 2: Count the total number of balls. Step 3: Write a fraction.

probability of picking a red ball

number of red balls.

total number of balls=

probablity of picking a red ball =

= =

= =

= =

= + =

VOCABULARYcertain

chance

even chance

event

favorable outcome

impossible

less likely

more likely

possible outcome

probability

52

probability conceptsNAME:_____________________ DATE :______________ CLASS:______________

On the spinner, what is the probability of spinning the letter F?

A bag contains 4 red marbles, 16 yellow marbles, 5 purple marbles, 16 blue marbles, and 10 green marbles. What is the probability of pulling out a red or green marble?

On this spinner, what is the probability of spinning the letter G?

If one is chosen at random from the work knickknack, the probability that the letter “a” is chosen is 1 out of ______.

A bag contains 3 yellow marbles, 18 blue marbles, 5 purple marbles, 8 red marbles, and 10 green marbles. The probability of pulling out a green marble is _____ out of 44.

A. 7 out of 1B. 1 out of 7C. 7 out of 7D. 4 out of 7



A. 9B. 8C. 10D. 11

A. 3B. 5C. 18D. 10

On this spinner, what is the probability of spinning the letter H?

A bag contains 10 red marbles, 3 purple marbles, 11 yellow marbles, 3 green marbles, and 3 blue marbles. What is the probability of pulling out a red or a green marble?

A number cube has 6 sides. The sides are numbered 1 to 6. If the cube is thrown once, what is the probability of rolling the number 6?




A C

E

GF

B

D

H F

G

GC

G

B

FJ

H

KJ

H

K

L

CIRCLES & RELATED FIGURES

lines, angles & circles LINES

ANGLES

MEASURING ANGLES DRAWING ANGLES

POINT LINE LINE SEGMENT RAY ANGLEdefine define

center

define define define

example example example example example

FD

E

A

H

G I

VOCABULARYacute angle point

angle protractor

circle radius

cord ray

diameter right angle

line straight angle

line segment straight line

obtuse angle vertex

A

B

C

Measure BAC

Step 1: Place the center point of the protractor over the vertex (corner) of the angle.

Step 2: Place the protractor so that ray AC is over the base line of the protractor and passes through the 0˚ mark.

Step 3: Read the measure where the other ray AB crosses the projector.

FD

CBA

E

AB is a ______________.

AC is a ______________.

EF is a ______________.

DBC is a _____________.

Step 1

Step2

Step 3

Step 4

Step 5

54

lines, angles & circlesNAME:_____________________ DATE :______________ CLASS:______________

You may use a protractor to measure the following angle.

You may use a protractor to measure the indicated angle for the geometric shape.

The radius is one-half the diameter. True or false?

The PNO equals 5 degrees, what is the measure of MNP?

If the measure of LOM equals 135 degrees, what is the measure of MON?.

A. 360 degrees

B. 180 degrees

C. 90 degrees

D. 45 degrees

A. 120˚

B. 360˚

C. 90˚

D. 60˚

A. True

B. False

A. 5˚

B. 75˚

C. 85˚

D. 175˚

A. 55˚

B. 45˚

C. 315˚

D. 225˚

The measure of the following angle is less than 90 degrees. True or false?

Identify the angle as right, straight, obtuse, or acute.

You may use a protractor to measure the indicated angle for the geometric shape?

A. True

B. False

A. obtuse

B. right

C. acute

D. straight

A. 108˚

B. 90˚

C. 120˚

D. 60˚

Y

H

P

M

O

N

N

O

M

L

diam

eter

radius

slope

GRAPHING LINEAR FUNCTIONS IDENTIFYING SLOPE & Y-INTERCEPT OF A LINE

Slope is used to describe _______________________________________________________________________________________________.

The slope of a line can be found by dividing the _________ by the __________.

A horizontal line has a slope of ___________.

A vertical line has ____ _______.

A line with a __________ slope resembles a line going uphill.

A line with a __________slope resembles a line going downhill.

The graphs of linear equations are straight lines.

Slope is ________. The y-intercept is _____. From the y-intercept,

move ____ unit up (rise) and _____ units left (run) to find another line

coordinate. Draw a line to connect these points.

The slope-intercept form of a linear equation is:

The y-intercept is the y-value at which the line

crosses the __________.

=Slope

=rise=run

VOCABULARYcoordinate

function

incline

linear equation

rise

run

slope

x-axis

y-axis

y-intercept

y = mx + bslope y-intercept

run:

rise:Graph: y = -1/4x + 3

( , )

( , )

y

y

y-axis

x-axis

x

x

= =Slope

56

slopeNAME:_____________________ DATE :______________ CLASS:______________

What is the slope of the line shown? What is the equation of a line that has a slope of -7 and crosses the y-axis at the point (0,5)?

What is the slope of the line shown?

According to the graph shown, what are the y-values for the x-values of 5,6, and 7?

A. positiveB. negativeC. zeroD. undefined

A. y = -2x + 5B. y = -5x + 2C. y = 5x - 2D. y = 5x +2

A. y = 3x + 9B. y = -9x - 3C. y = 9x - 3D. y = -3x + 9

A. y = 5x - 7B. y = 5x + 7C. y = -7x + 5D. y = -7x - 5

A. -2,-4,-6B. 2.4.6C. 0,2,4D. 0,-2,-4

A. positiveB. negativeC. zeroD. undefined

A. 4B. 3C. -3D. -4

What is the equation of the line with a slope of 5 and a y-intercept of -2?

What is the equation of the line with a slope of -3 and a y-intercept of 9?

What is the equation of a line that has a slope of 4 and crosses the y-axis at the point (0, -1)?

The equation of a line -3x + y =-4. What is the slope of the line?

A. y = -x + 4B. y + 4x - 1C. y = 4x +1D. y = x + 4

The Pythagorean theorem

A right triangle is a triangle with an __________ or

__________. The two sides that from the right triangle are

called __________. The side opposite of the right triangle is the

___________.

__________was one of the first mathematicians to recognize the

relationship between the sides of a right triangle. The special relationship

forms the __________ ____________ .

The Pythagorean Theorem states ____________

__________________________________

______________________________.

According to the Pythagorean Theorem, the sum of

the two green squares, is equal to the area of the

blue square.

Therefore in algebraic terms, the

Pythagorean Theorem is stated as:

Find the length of the hypotenuse (C).

VOCABULARYangle

hypotenuse

leg

Pythagorean Theorem

right triangle

side

THE PYTHAGOREAN THEOREM

USING THE PYTHAGOREAN THEOREM

SQUARE A

SQUARE C

SQUARE B

a c

b

=Area of square A=Area of square B

=Area of square C

=+

=+=+

=+

===

C3cm

4cm

C

a2 b2 c2

Substitute for the known variables.

Take the square root of both sides.

The length of the hypotenuse.

58

The Pythagorean TheoremNAME:_____________________ DATE :______________ CLASS:______________

In the figure shown, CB is one of the legs. True or false?

In the figure shown, JLK is right angle. True or false?

Based on the figure shown, how long is the hypotenuse?

Based on the figure shown, how long is the hypotenuse?

A. trueB. false

A. 6 mB. 8 mC. 10 mD. 100 m

A. 5 cmB. 12 cmC. 13 cmD. 17 cm

A. trueB. false

A. 3.600 cmB. 1,296 cmC. 60 cmD. 36 cm

A. 20 cmB. 26 cmC. √635 cmD. √685 cm

A. 17 ftB. 15 ftC. 14 ftD. 13 ft

How long is the hypotenuse in the triangle shown?

What is the measure of the longer leg of the triangle shown?

In a right triangle, one leg measures 3 inches and the other leg measures 4 inches. What is the length of the hypotenuse?

A ladder leans against a house as shown in the angle below. It is 5 feet away from the house. The ladder reaches the house 12 feet from the gound. What is the length of the ladder?

A. 3 in.B. 4 in.C. 5 in.D. 14 in.

C

A B

36cm

20cm

48cm

15cm

c

c

L

KJ

8m

5cm 12cm

13m

10m

5ft

12ft

6m

a2 + b2 = c2

a2 + b2 = c2

a2 + b2 = c2a2 + b2 = c2

Introduction to probability

Probability is the possibility that

a _______ ________will

occur. An event that is certain to

occur has a probability of ___.

An event that cannot occur has

a probability of ___. Therefore,

the probability of an event

occurring is always between

___ and ___.

EXPERIMENTAL PROBABILITY

INDEPENDENT EVENTS

COMBINATIONS

THEORETICAL PROBABILITY

DEPENDENT EVENTS

PERMUTATIONS

WHAT IS PROBABILITY?VOCABULARY

certain

combination

dependent event

event

experimental probability

favorable outcome

impossible

independent eventlikelyoutcome

permutation

possible outcome

probability

theoretical probability

unlikely

Experimental probability is ______________________________

__________________________________.

Theoretical probability is _______________________________

__________________________________.

Probability is _________________________________________

___________________________________.

A combination is ______________________________________

___________________________________.

The number of ways that an event can occur depends on the

order. A permutation is _________________________________

_____________________.

The dependent event is _________________________________

__________________________________.

experimentalProbability

P (a and b) = P (a) • P (b) P (a and b) = P (a) • P (b after a)

Probability of two independent variables.

Example: How many different combinations can be made when picking 2 letters out of the word DOG?

Example: Arrange 3 students in 3 chairs.

Probability of two dependent variables.

theoretical probability

number of times an event occurs

number of favorable outcomes

total number of trials

total number of possible outcomes

≈ ≈

probability of both events

There are ___ possible letter combinations:DG, OD, GO

Cross out the duplicates.

probability of both events

probability of first event

probability of first event

probability of second event

Probability of second event

DOG

321

• •• •• •• •• •• •

3 • 2 • 1 or 3! =

Impossible

Unlikely

fraction

decimal

percent

Likely

As likely as not Certain

0

0

0%

11/4 1/2 3/4

60

Introduction to probability NAME:_____________________ DATE :______________ CLASS:______________

Probability is a fraction, decimal,or percent that represents how likely a favorable event is to occur based on the total number of times the event occurs. It is always between 0 and 2. True or false?

There are 52 cards in a standard deck of cards, what is the probability of picking a 3?

A letter is picked from the word MISSISSIPPI. What is the probability of picking an “S”?

Ashley flips a penny 15 times and keeps track of the results. She thinks heads will land up the most. Her results are H, T, T, H,T,H,T,T,T,H,H,H,T,T, and H. What is the experimental probability that heads landed up?

A die is rolled and a coin is flipped. What is the probability of getting a 2 or a head?

A. TrueB. False

A. 1/52B. 2/52C. 3/52D. 4/52

A. 1/2B. 1/4C. 4/11D. 4/12

A. 8%B. 50%C. 58%D. 67%

A. 54%B. 53%C. 47%D. 50%

If an event is most likely to happen, the probability gets closer to___________.

The probability that 14-year old Joe did not have a birthday last year is _______.

The Angels soccer team has a 75% chance of making the playoffs. What does that mean?

A. 0B. 0.25C. 0.50D. 1

A. 0

B. 1/12C. 1/2D. 1

A. They certainly will not make the playoffs.B. They most likely will not make the playoffs. C. They most likely will make the playoffs. D. They certainly will make the playoffs.

all about percents

The percent means _________.

It is the ratio of a number to 100.

The symbol ___ is then added after a

number to indicate that it is a percent.

Write percent as a fraction

with a denominator of 100.

Simplify, in needed.

Write the percent as a fraction


Convert the fraction to a

decimal.

Write an equivalent fraction


Write the fraction as a percent.

Write the decimal as a fraction.

Write the decimal as a percent

by moving the decimal point

two places to the right.

Percents can be written as

decimals or fractions. VOCABULARY

decimaldecimal pointdenominatorequationequivalent fractionfractionpercent proportion

Fraction Decimal Percent

0. 10%

0. 25%

0. 33.3%

0. 50%

0. 75%

0. 100%

PERCENTS AS FRACTIONS

PERCENTS AS DECIMALS

DECIMALS AS PERCENTS

FRACTIONS AS PERCENTS

= = =

=

=

= = =

=

20%

What is 57% of 80?

57100 m

10036 = 15% • m=

= = == = =

= ==

=m80

m mm

3570

35 is what percent of 70? 36 is 15% of what number?

23% 0.09••

• •

• •

• • ••

3/5

SOLVING PROBLEMS USING PERCENTSDETERMINING THE PERCENT OF A NUMBER USING PROPORTIONS USING EQUATIONS

57% of 80 is ___ 35 is ___ of 70 36 is 15% of ___

62

all about percents NAME:_____________________ DATE :______________ CLASS:______________

What is the fraction 2/3 as a percent? One hundred twenty-five is what percent of 500?

What is 150% of 280?

In the month of July, the temperature was above 90˚ about 26% of the time. How many days was the temperature above 90˚?

A. 5B. 6C. 7D. 8

A. 84.0B. 88.2C. 840D. 882

What is the decimal 0.84 as a percent?

What is 30% of 20? What is 280% of 315?

What is 42.5% as a fraction?

A. 4.8%B. 8.4%C. 48%D. 84%

A. 450B. 420C. 45D. 42

A. 33.3%B. 66.7%C. 75%D. 80%

A. 20%B. 25%C. 27%D. 303%

A. 4B. 5C. 6D. 8

A. 17/40B. 18/40C. 21/50D. 22/50

a/b = p/100

finding volumeVOLUME OF PRISMS

VOLUME OF PRISMS VOLUME OF PRISMS VOLUME OF PRISMS

VOCABULARYcone

cylinder

diameterpi (π)prismpyramid

radius

rectangular prism

spheretrianglevolume

V ≈ 3.14•__•__V ≈ 3.14•__•__V ≈ ________

(l)

VOLUME OF CYLINDERS

v = π r2hπ ≈ 3.14diameter (d) = ____

radius (r) = ____

radius (r) = ____

r = ____

V = l x w x hV = __ •__•__V = __

5 cm

3 cm

3 cm

(w)

(h )

Rectangular Prism

4 cm12 cm

Prism

7 cm

Since the bases are triangles, the area

of each triangle is:

B = 1/2b • h, or 1/2•__•__=__

V = base area (b)•height (h)

V = __V = __•__

V = 1/3 π r2 h

V ≈ 1/3 • 3.14•__ •__V ≈ 1/3 • 3.14•__ •__V ≈ __________

V = 4/3 π r3

V ≈ 4/3 • 3.14 •__V ≈ 4/3 • 3.14 •__V ≈ __________

V = 1/3B • hB= l • h

V ≈ 1/3 • __•__V ≈ __________

3 cm

3 cm8 cm

8 cm

4 cm6 cm

(h)(h)

(r)

(r)

64

12 in24 in

10 in

finding volume NAME:_____________________ DATE :______________ CLASS:______________

In the figure shown, each cube equals 1 unit. What is the volume of the figure?

The volume of a can of paint is 265.33 inches. If the diameter of the can is 6.5 inches, what is the height?

What is the volume of the pyramid shown?

If the volume of a sphere is 38,772.72 cm3, what is it’s approximate diameter.

A. 21 cmB. 33 cmC. 42 cmD. 66 cm

A. 329 in3

B. 1,236.4 in3

C. 1,854.6 in3

D. 3,461.9 in3

What is the volume of the prism shown?

What is the volume of the prism shown? What is the volume of the cone shown?

The volume of the cylinder shown is 5,836.26 cm3. The height is 11 cm. What is the radius of the cylinder?

A. 5,400 cm3

B. 8,100 cm3

C. 12,150 cm3

D. 40,500 cm3

A. 1,372 cm

B. 2,058 cm3

C. 3,087 cm3

D. 4,116 cm3

A. 14 units3

B. 22 units3

C. 25 units3

D. 40 units3

A. 2 inB. 6.5 inC. 8 inD. 13 in

A. 360 in3

B. 720 in3

C. 1,440 in3

D. 2,880 in3

A. 13 cmB. 15 cmC. 26 cmD. 169 cm

V = l x w x h

V = l x w x h V = 1/3Bh, where B is the area of the base.

V = (1/2) x l x w x h

45 cm

30 cm

6 cm

h = ?

h = 21 cm

h = 21 in

d = x

V = 38,772.72 cm3

7.5 in

14 cm

6.5 in

v = π r2h v = π r2h

v = π r2h

v = π r2h

π ≈ 3.14 π ≈ 3.14

π ≈ 3.14

π ≈ 3.14

11 cm

v = 5,837,26 cm3

numerical & Geometric Proportions

Numerical Proportions compare two ___________

_______________.

Geometric proportions compare two ______

____________.

Similar figures have equal corresponding ________

and corresponding ___________ that are in

__________________.

Identify the corresponding sides in the two triangles.

Use ratios of the corresponding sides to determine whether

the triangles ∆GHI and ∆JKL are similar.

The triangles are _________ since their corresponding

sides are _____________.

An equation with two equal

ratios is called a proportion.

A cross product is the product of the

________ in one ratio and the _______

in the other ratio.

Cross Product Rule

Ratios are used to compare quantities with the

___________ _______________.

_______ are used to compare quantities measured with

different units.

_______ __________ are used to find a missing

quantity in a proportion.

NUMERICAL PROPORTIONS

GEOMETRIC PROPORTIONS

Determining whether two triangles are similar.

m5

ab

36

35=

=

=

===

=

= ==? =?

124

c4

12

610

m

•

•

•Cross multiply.

Divide each side by __ to isolate the variable.

When two ratios are equal, then the cross product, a • d and b • c are ________.

corresponds to

corresponds to

corresponds to

VOCABULARYcorresponding angle

corresponding side

cross multiply

cross product

denominator

equation

equivalent

geometric proportion

numerator

numerical proportion

proportion

rate

ratiosimilar figuretriangle

variable

H K

L JG I

24 cm

12 cm

16 ft6 cm

3 cm

4 cm

B

CA E

DF

66

B

D

F E C

A B

A

CF

ED

Numerical & geographic proportionsNAME:_____________________ DATE :______________ CLASS:______________

What is x is to 45 as 9 is to 90 written in a proportion? The figure shown is of similar triangles. True or false?

In the figure shown, the triangles are similar. True or false?

Given the similar polygons show, which side corre-sponds to side DF?

A. EF

B. AC

C. AB

D. BC

A. 27˚

B. 42˚

C. 53˚

D. 95˚

A. true

B. false

Lindsey is building a model of her house. She wants to use the ratio of 1 inch for every 5 feet. If her house is 35 feet tall, which proportion should she use to get the height of her house?

Mariah is making a batch of cookies. A batch needs 3 cups of flour and 2 cups of oatmeal to make enough cookies for 16 people. If Mariah wants to make enough cookies for 80 people, much flour is needed?

The triangles shown are similar. What is the measure of DFE?

The quotient of 2 yards / 8 feet is a ratio. True or false?

A. 1/35 = x/5B. x/5 = 35/1C. 1/5 = x/35D. 35/5 = 1/x

A. x/9 = 90/45B. x/45 = 90/9C. x/45 = 9/90D. 45/x = 9/90

A. 2 cups / 3 cups = 16 people / x

B. 2 cups / 16 people = x / 80 people

C. 3 cups / 16 people = 80 people/x

D. 3 cups / 16 people = x / 80 people

A. true

B. false

12 m

4 m

2 m

6 m

30 cm

41˚110˚

29˚

20 cm

10 cm

15 cm

10 cm

5 cm 110˚30˚

40˚A. true

B. false

28 ft

18 ft

12 ft21 ft

24 ft

16 ft

95˚

65˚ 58˚

58˚ 65˚

57˚57˚

95˚

32˚

exponents, factors & multiples

An exponent tells how many times to multiply a number,

called base, by itself.

Move the decimal point ___ places to get a number that is greater

than or equal to ___ and less than ___.

The _____________ is equal to the number of decimal places you

moved the point.

The Prime Factorization of 120 is

Powerof ten

standard form scientific notation

A number written with a base and an exponent is in

exponential form.

Prime factorization is ________________________

_______________________________________

___________________.

A prime number has exactly two factors: ______ and

____________.

A _________ __________ has more than two factors.

EXPONENTS

PRIME FACTORIZATION

PRIME FACTORIZATION OF 120

POWER OF TENS & SCIENTIFIC NOTATION

VOCABULARYbase multiple

composite number power of ten

exponent prime factorization

exponential form prime number

factor scientific notation

greatest common factor standard form

least common factor

GREATEST COMMON FACTOR LEAST COMMON FACTOR

43 = __ x __ x __ = ___ 104 = __ x __ x __ = ___

36 = __,__,__,__,__,__,__,__,__ 5 = __,__,__,__,__,__,...

54 = __,__,__,__,__,__,__,__ 6 = __,__,__,__,__,__,...

2,380,000 = _____ x _____

• •

• • •

• •

• • • • = • •

120

The greatest common factor (GCF) of two or more numbers is

_________________________________________

_________________________________________

____________.

The least common multiple (LCM) of two or more numbers is

_________________________________________

_________________________________________

____________.

GREATEST COMMON FACTOR OF 36 & 54 LEAST COMMON FACTOR OF 5 & 6

The GCF is ________ The LCM is ________

68

exponents, factors & multiples NAME:_____________________ DATE :______________ CLASS:______________

Numbers that have only two factors are_______? What is the prime factorization of 1,440?

To simplify a fraction, divide the numerator and denominator by their _______.

17 = 1 x 1 x 1 x 1 x 1 x 1 x 1 = ___

A. 7B. 1C. 100D. 8

A. 1,728B. 144C. 1,600D. 360

Writing a number as a product of prime numbers is called _______.

What is the prime factorization of 72? 123 = 12 x 12 x 12 =

What is the prime factorization of 368?

A. compositeB. factoringC. prime factorizationD. distributing

A. Greatest Common FactorB. Least Common MultipleC. productD. sum

A. compositeB. primeC. evenD. factors

A. 5 x 4 x 32 x 2B. 5 x 42 x 3 x 2C. 5 x 4 x 32 x 2D. 52 x 42 x 3 x 2

A. 23 x 32

B. 22 x 33

C. 2 x 33

D. 23 x 3

A. 23 x 21B. 25 x 23C. 24 x 21D. 24 x 23

INEQUALITIESAn _____________ is a mathematical sentence that

does not have an exact solution. Instead, a range of

solutions will satisfy the inequality.

All the solutions of an inequality with more than one solution

are called ___________ _____.

________________ are used in many real-world

situations. An example is a driving speed sign with a

number which tells you that your speed must be ≤65 mph.

An ______ ______ is used when

the variable is > or < a number. Graph each inequality separately.

Solve an addition or subtraction inequality

the same way as you would solve an

__________.

When you multiply or divide both sides of an

inequality by a negative integer, _______ the

direction of the ______ _________.

A ______ ______ is used when

the variable is ≥ or ≤ a number. Combine both graphs.

An inequality uses one of the following symbols, instead of

an equal sign:

VOCABULARYclosed circle open circlecompound inequal-ity simple inequality

greater than solutiongreater than or equal to solution set

less than variable

less than or equal to

negative integer

SYMBOL MEANING EXAMPLEGreater thanMore than above

less than fewer thanbelow

greater than or equal tono less thanat least

less than or equal tono more thanat most

GRAPHIC SIMPLE INEQUALITIES

SOLVING INEQUALITIES BY ADDING OR SUBTRACTING

SOLVING INEQUALITIES BY MULTIPLYING OR DIVIDING

GRAPHIC COMPOUND INEQUALITIES

x > -4

x + 3 ≥ 5 -2x > 6-2x < 6

x ≥x

x ≥ 1 x < -2

y ≤ 1

-6 -4 -2 0 2 4 6

-6 -4 -2 0 2 4 6 -6 -4 -2 0 2 4 6

-2 0 2 4 -4 -2 0 2

-6 -4 -2 0 2 4 6 -6 -4 -2 0 2 4 6

70

Inequalities NAME:_____________________ DATE :______________ CLASS:______________

According to the number line, which inequality is shown?


A number, x, is less than 7. Which inequality represents this?

A number, x, is less than or equal to 6. Which inequality represents this?

A number, x, is greater than -1. Which inequality represents this?


Solve the inequality for x.-3x < 42

Solve the inequality for x.x - 8 > -29

A. X < -3

B. X ≤ -3

C. X > -3

D. X ≥ -3

A. X ≤ -7

B. X < -7

C. X < 7

D. X ≤ 7

A. X ≥ 6

B. X ≤ 6

C. X < 6

D. X > 6

A. X > 1

B. X < -2

C. X < -1

D. X > -1

A. X ≥ -2

B. X ≤ -2

C. X > -2

D. X < -2

A. X ≥ 4

B. X > 4

C. X < 4

D. X ≤ 4

A. X < -14

B. X < 14

C. X > 14

D. X > -14

A. X > -37

B. X > -21

C. X > 21

D. X > 37

-3 -2 -1 0 1 2 3

-4 -3 -2 -1 0 1 2

3 4 5 6 7 8 9

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