Prentice Hall Algebra 1, Geometry, Algebra 2, Foundations Series is a great
option for low-level and inclusion classrooms, delivering comprehensive content
in ...
Change the way
students see math
Prentice Hall
Algebra 1 Geometry Algebra 2
FOUNDAT IONS SER IE S
A New Perspective on Math Prentice Hall Algebra 1, Geometry, Algebra 2 ©2011, Foundations Series is changing the way students see math! By delivering instruction through a blend of digital and print components, we are helping you reach today’s digital natives.
Hi, my name is Anya. I’m one of the six peer coaches you’ll find throughout the program— in print and online.
Make Math Meaningful For many students, math shows up as a collection of rules, formulas, and properties that they learn temporarily, forget quickly, and never use again. Students find mathematics meaningless if they don’t see the connections. Prentice Hall Algebra 1, Geometry, Algebra 2, Foundations Series teaches for understanding by incorporating an interwoven strand of thinking and reasoning into problem solving. This connects the math that students learn, from the first lesson to the last. By focusing on thinking, reasoning, and problem solving, students will become more prepared for success in school, in their careers, and in life.
2
Distinguished Authorship Series Authors Randall I. Charles, Ph.D., is Professor Emeritus in the Department of Mathematics and Computer Science at San Jose State University in California. He was a high school mathematics teacher and supervisor for five years. Dr. Charles has been a member of several NCTM committees and is the former vice president of the National Council of Supervisors of Mathematics. Much of his writing and research has been in the area of problem solving. He has authored more than 75 mathematics textbooks for kindergarten through college.
Dan Kennedy, Ph.D., is a classroom teacher and the Lupton Distinguished Professor of Mathematics at the Baylor School in Chattanooga, Tennessee. Dr. Kennedy is a frequent speaker on the subject of mathematics education reform. He is coauthor of textbooks in calculus and precalculus, and he chaired the College Board’s AP* Calculus Development Committee. He is a 1992 Tandy Technology Scholar and a 1995 Presidential Award winner.
Basia Hall currently serves as Manager of Instructional Programs for the Houston Independent School District. With 33 years of teaching experience, Ms. Hall has served as a department chair, instructional supervisor, school improvement facilitator, and professional development trainer. She has developed curriculum for Algebra 1, Geometry, and Algebra 2 and codeveloped the Texas state mathematics standards. A 1992 Presidential Award winner, Ms. Hall is past president of the Texas Association of Supervisors of Mathematics, and a state representative for the National Council of Supervisors of Mathematics (NCSM).
Consulting Authors Stuart J. Murphy is a visual learning author and consultant. He is a champion of developing visual learning skills to help children become more successful students. He is the author of Math Start, a series of children's books that present mathematical concepts in the context of stories. A graduate of the Rhode Island School of Design, he has worked in educational publishing and has been on the authorship teams of a number of elementary and high school mathematics programs. He presents at meetings of the National Council of Teachers of Mathematics and the International Reading Association.
Grant Wiggins, Ed.D., is the President of Authentic Education in Hopewell, New Jersey. He earned his Ed.D. from Harvard University and his B.A. from St. John's College in Annapolis, Maryland. Dr. Wiggins consults with schools, districts, and state education departments on a variety of reform matters. He is perhaps best known for being the coauthor, with Jay McTighe, of Understanding by Design® and The Understanding by Design Handbook, the award-winning and highly successful materials on curriculum reform published by ASCD. His work has been supported by the Pew Charitable Trusts, the Geraldine R. Dodge Foundation, and the National Science Foundation. *
3
Advanced Placement, Advanced Placement Program, AP, and Pre-AP are registered trademarks of the College Board, which was not involved in the production of, and does not endorse, these products.
Classroom Solutions
Complete Online Program
Foundations Program Prentice Hall Algebra 1, Geometry, Algebra 2, Foundations Series is a great option for low-level and inclusion classrooms, delivering comprehensive content in an accessible manner to all students. Simpler problems allow easier access to concepts and skills. Shorter lessons and shorter chapters allow for more frequent assessments. More scaffolding in problems and exercises support students at every step.
PowerAlgebra.com and PowerGeometry.com is the digital component for the series that can be used as part of the blended model with print or as a stand-alone digital course. The digital component includes a wealth of assets, including the Student and Teacher’s Editions, instruction and presentation tools, student-generated videos, classroom management tools and editable resources, and online assessment with remediation.
Contents Algebra 1
Geometry
Algebra 2
1. Foundations for Algebra
1. Tools of Geometry
1. Expressions, Equations, and Inequalities
2. Solving Equations
2. Reasoning and Proof
2. Functions, Equations, and Graphs
3. Solving Inequalities
3. Parallel and Perpendicular Lines
3. Linear Systems
4. An Introduction to Functions
4. Congruent Triangles
4. Quadratic Functions and Equations
5. Linear Functions
5. Relationships Within Triangles
5. Polynomials and Polynomial Functions
6. Systems of Equations and Inequalities
6. Polygons and Quadrilaterals
6. Radical Functions and Rational Exponents
7. Exponents and Exponential Functions
7. Similarity
7. Exponential and Logarithmic Functions
8. Polynomials and Factoring
8. Right Triangles and Trigonometry
8. Rational Functions
9. Quadratic Functions and Equations
9. Transformations
9. Sequences and Series
10. Radical Expressions and Equations
10. Area
10. Quadratic Relations and Conic Sections
11. Rational Expressions and Functions
11. Surface Area and Volume
11. Probability and Statistics
12. Data Analysis and Probability
12. Circles
12. Matrices T. Trigonometry Concepts
4
Engage Today’s Students Introducing PowerAlgebra.com and PowerGeometry.com—the gateway for students and teachers to all the digital components available for the series. This includes access to the online Student Edition with audio, Teacher’s Edition, student-generated videos, animations, presentation tools, online assessment with remediation, as well as lesson planning, editable worksheets, and a sophisticated classroom management system. Lights, Camera…Math! My Math Videos, found at the beginning of each chapter, are student-produced videos that engage students in math concepts that are relevant to their lives. Through the Pearson Video Challenge, students can demonstrate their understanding and creativity by generating their own videos to be included on PowerAlgebra.com and PowerGeometry.com. Try it for yourself! Go to PowerAlgebra.com or PowerGeometry.com Username: PHHSMath2011 Password: 123456
5
Learning by Doing Dynamic Activities provide an interactive way for students to explore lesson concepts. Additionally, math tools enable you and your students to utilize the functionality of tools such as a graphing calculator, algebra tiles, and geometry software.
Practice Makes Perfect MathXL® for School tutorial exercises provide interactive practice at the midpoint and end of each chapter. Each exercise provides learning aids—including an interactive guided solution— sample problems, and similar problems that refresh with new numbers so students can retry exercises.
{
}
“Today’s students are digital natives. These students are not merely technology-savvy; they are approaching their lives differently as they integrate digital technologies seamlessly throughout their daily activities. Let’s not have them power-down when they get to math class.”
–Laurie Bass, program author 6
Build Conceptual Understanding Math proficiency is developed through fluency, reasoning, and application. By teaching for understanding, you are enabling your students to demonstrate their ability to transfer their knowledge from one situation or problem to another, particularly on high-stakes exams. Students are also able to make critical connections between concepts, making math meaningful.
Big Ideas This program incorporates the groundbreaking Understanding by Design® framework. Co-developed by consulting author Grant Wiggins, UbD changes the way students approach math by introducing them first to the Big Idea of each chapter. Within each chapter, students will develop answers to the Essential Questions posed and make connections around the Big Ideas. Pull It All Together, at the end of each chapter, enables students to demonstrate their understanding of the concepts and skills they studied in the chapter lessons and in previous chapters. In doing so, they apply their reasoning strategies and growth as independent problem solvers.
{
}
”A Big Idea is a way of seeing better and working smarter, not just another piece of knowledge.”
–Grant Wiggins, consulting author 7
{
}
“The visual models in the Student Edition allow students to interact with mathematical concepts, process the information, observe change, reflect on their experiences, modify their thinking, and draw conclusions. They learn.”
–Stuart J. Murphy, visual instruction consulting author
Visual Learning Visual Instruction is about acquiring and communicating information. Visuals support students as they analyze complex word problems. They clarify important concepts, and they engage students and encourage them to make connections with real-life situations. Visual learning strategies are a powerful teaching tool for a student’s depth of understanding about mathematics.
Connect to What You Know Visual Instruction increases the learning potential of all students. The Solve It! at the start of each lesson makes use of engaging visuals and real-world examples to help students tap into their prior knowledge and connect it to important concepts in the lesson.
8
Develop Problem Solving Problem-solving strategies are an integral part of the program and are embedded throughout each lesson. The worked-out problems model effective thinking and reasoning strategies and can help foster students’ mathematical reasoning.
Reasoning Call-outs “Think” and “Plan” call-outs model mathematical reasoning and problem solving for every problem in a lesson. Some reveal “Step Zero,” or the reasoning that goes on before the first step of the solution. Some worked-out problems provide even more support as they model the thinking behind each step of a problem-solving plan.
{
}
“Research shows that understanding develops during the process of solving problems in which important math concepts and skills are embedded…”
–Randy Charles, program author
9
Now It’s Your Turn Got It?, following each problem, checks for understanding. Students can find additional support for each Got It? in the Student Companion worktext.
Online Problems Each problem in the Student Edition is also modeled online at PowerAlgebra.com and PowerGeometry.com. Step-by-step instruction, with guided support from one of six avatars, enables students to follow along at their own pace.
10
Differentiate Instruction Students learn in different ways and at different paces. Unique, built-in resources differentiate instruction to support all levels of learners in becoming successful problem solvers. Differentiating instruction helps all students develop conceptual understanding, foster mathematical reasoning, and refine problem-solving strategies. Options are available to differentiate instruction at the start of each chapter and throughout the lessons.
ive Zero and Negat s Exponent
7-1
Proper
11. Com plete th e table. Expone nt
Vocabulary n.
ent exp
19 ? 19 ? 19 5 ? 19 ? 19 ? 19 ? 5. 19 ? 19 ? 19
5 4. 35 ? 35 ? 35 43 , identify
exponent. the base and the
ve) negative (adjecti
NEG
42
a value less than
e numbers. Reserve
, Inc. or its affili
Pearson Education
or its aff
e in Column B.
A to its opposit
Column B
Educati
17
Pearson
1 2
Copyrig
ht © by
3 35
194 Chapter 7
â
1 (Ľ3) 5 â
â 1
343 1
1
14. 9 21 5 21 9
the sim
15. 9 23 5 1
ing Po wer
27
s
plified 16. Com form of 23 plete ea 4 ? ch step to simpl ify 4 23. 4 23 5 1
iliates. Al
pay A worker’s hourly . increases by $.50
on, Inc.
ber in Column
h negative num
13. (29) 0 5 21
m1 S implify
Got It? What is
l Rights
lar y
Use Your Vocabu
t each situation. ber to represen ther 7. Write a num You owe your bro is 4 degrees The temperature eight dollars. . below zero eac Draw a line from Column A
81
Proble
d.
1 and 2p are all negativ , Examples: 2 3,2 2
ź
zero.
(Ľ3) Ľ5 â
for true or F for false. 12. 9 22 5 1
is
uh tiv
ative quantity has Definition: A neg
10. 217
4 Ľ2 â 1
Write T
The symbol for negative
lder
3
73
an
Vocabular y Bui
9. 23 5
7 Ľ3 â 1
exponent =
base =
1 8. 22
es
6 0 â1
For ever y nonzer o number a and in teger n, (a) Ľn â 1
Negative
Reserved.
ion 6. In the express
Exampl
For ever y nonzer o number a,
(Ľ24) 0 â
exponent. ression using an
Write an equival
nents
7 3. 2 5 128
2 2. 7 5 49
5 243
ates. All Rights
1.
35
ive Expo
(a) 0 â1
nt in each equatio
Circle the expone
d Negat
Property
Zero
Move th e power to the de make th nominat e expone or and nt positiv e. Evaluate the pow er to sim plify the expressi on.
4
5
1
Proble m2 Simplif ying Ex Got It? ponen tial Ex What is pressio the sim pl x 29
Copyright © by
Review
ties Ze ro an
ified fo
1 n 23
rm of ea
ch expr ession?
ns
Underlin 4c 3b e the co 2 rrect w ord to co 17. To a 23 n 25 mplete simplify each se a ba m2 se ntence. in the nu the deno minator merator and writ that has 18. To e a posi a negativ simplify tive / ne gative ex e exponent, m to the nu a base in the de ove the ponent nominat merator base to . or that ha and writ e a posi s a negativ tive / ne e ex po ga nent, m tive expo 0 AM 2/14/09 5:56:3 ove the nent. base 2
1.indd 194
HSM11A1MC_070
HSM11A
195
1MC_070
1.indd
195
Lesson
Support for Students Each lesson offers multiple options for differentiating instruction to reach all students. As one of these options, the Student Companion worktext provides daily support for each lesson, targeting Vocabulary, Got It?, and Lesson Checks. With the Student Companion, students find the support they need to fill in the gaps and find success with problem solving and mathematics.
11
7-1
2/14/09
5:56:36
AM
{
}
“Differentiated instruction does not change what is taught; it changes how it is taught.”
–Basia Hall, program author
Differentiat
ed Remed
iation continu
ed
On-Level
• Practice (2 pag for each less es) Provides extra pr actice on. For simp ler practice exercises, u se t found in the he Form K Practice p ages All-in-One T eaching Reso and online. urces
Practice and Problem Solv All-in-One ing Wkbk/ Resources/ Online Practice pag e1 Class
7-1
Solutions may vary. Sample: For w 5 1: 5 0: Negative Exponents 1 w and Zero w Properties For 0 For w 522: 5400 ? 3 5 5400 ? 3 w 22 5400 ? 3 5 5400 ? 3 w 5 5400 ? 3 5400 ? 3 5 5400 ? 3table. the1 5 5400 ? 1 11. Complete 5 5400 ? 9 Examples 5 16,200 Property Exponent 5 5400 5 600 60 â1 For every nonzero a, Zero represent? number 0 (Ľ24)0 â 1 1, the value 16,200 24. What does each value (a) â1 For w 5 5400 For w 5 0, the value 600 represents the number For w 5 2 2, the value 1 represents the number 1 â 343 9. 7Ľ3 âof insects represents the number 73 of insects 9. of insects 9. Review 11 week1 after the every nonzero For when the population 4Ľ2 â 2 â the before each equation. 2 weeksin 4 number a and integer n, Circle the exponent 16 Review Negative 3. 27 5 128 population was measured Ľn â 1n 2. 72 5 49was(a)measured a was measured 243 in each equation. 1. 35 5 Circle population 1 the exponent 1 27 5 128 (Ľ3)Ľ5 â (Ľ3)3.5 â expression using an exponent. 2. 72 5 49 9 Ľ243 Write an equivalent 19 5 19 1. 35 5 243 19 ? 19 ? 19 ? 19 ? 19 ? 19 ? 19 ?exponent. 3 5. 19 ?using an ? 35 5 35 4. 35 ? 35 9 Write an equivalent expression ? 19 ? 19 ? 19 5 19 UNDERSTAND? you • Doand ? 19 ? 19 ? 19 ? 19 ? 19 19exponent. 3, identify 3 5.the Lesson Check 5 35the base false. 4. 35 ? 35 ?4T35 6. In the expression 1 Write for true or F for xn as F 15. 923 5 27 n 21 0 exponent. 3 ed n = base simplifi 921 F x14. exponent an x5 the 9 anda02n A student incorrectly 5b 21 4In the expression (29) F 13. 413, identify the = 6.Analysis = 0 Error base T 12. 922 5 81 b a-n b0 student’s error. Find and correct the an xn undefined exponent = 3 shown at the right. for =The symbol base = 4 0 23. Now solve the problem.
Vocabulary
HSM11A1MC_0701.indd
195 194
Chapter 7
All Rights Reserved.
All Rights Reserved.
11xv 3 y
v 23
20.
© by Pearson
5m 21 9(ab) 24 c 7
Education,
• Teaching
2n
a and
7-1
exponent is negative, raise exponent.
Inc., or its
affiliates.
Understanding0, the expression the Problem 1 9
b. 922 51. 2What is the
1 5 2. 81 How do you
so raise the reciprocal of 9, The exponent is negative, exponent 2(22), or 2.
target diameter Simplify.
know if a rod
for the metal
1
or 9 , to the
1.5 mm
is acceptab
le?
within 10 23 of 1.5
negative exponent by raising Rewrite the factor with the exponent.
1
7
mm
the reciprocal of
the Solutiothe base to a positive n
the word “within” Simplify by multiplying. tell you
5 2 3
about the acceptab diameter a b s? The diameter le range of may not be 1.5 2 0.001 greater than mm. 1.50 1 0.001 mm or less 5. What does
this tell you
The inequalit
y will use
about the type the symbols
than
of inequalit
y that you should
R and S.
use?
Getting an Answer 6. Write 10 23
as a fraction
7. Find the acceptab
Resources Algebra 1 • Teaching All Rights Reserved.
between
single inequalit
14.999 and
15.001 mm
y. ne All-in-One Resources/Onli Support English Language Learner
2/14/09 5:56:30 AM 194
Prentice Hall
Name
n the Lesson Quiz to Use the student work o d review assignment. prescribe a differentiate
Points 0–2 3 4
Differentiated Remediation Intervention 0419A_hsm11a1te_FL_07_01_lr.indd On-level Extension
Copyright
7-1
REmEdiAtioN PREScRiPtioN foR
Complete
© by Pearson
2
affiliates.
base
420
zero as an exponent
negative exponent
simplest form
7-1
Personalized Assessment Success Tracker™ online assessment system provides instant analysis of class and student performance. Measure student progress through the year with lesson quizzes, benchmark tests, and more. Success Tracker diagnoses student success, prescribes automatic remediation, and reports on student and class progress.
12
affiliates.
Standardized
© by Pearson
a,
For every nonzero1number 2n integer n, a 5 an .
a0
Resources All Rights
7-1
D.
1 25
I.
D.
3a 4c 3 b2
the Power
Zero and Negativ e Exponen ts
Reserved.
Date
of 2
Answer each of the out the numbers 12 clues below. Each time you fi in the figure nd an answer, below. use
2 22 and its 2 25 and 1
reciprocal
10 22 and 11 22
4 34
1 4 2 25 and 1
3 4 and 3 21
4 3 22
7 2 and 1 62
2 23 and 2 26
1 4 2 and 1 4 2 21
1 4 24
an X to cross
2 and 1 16 4
1 4 5 21 and 1
8 2 and 1 72 4 5 22
1 128
z y7
I. 2
1 16
3 2
D. 24 1 2
125a 3 27
4
49
36
1 36
I. 2
6 2 and 1 3 21
1 121
1 32
64
32
81
1 9
5
25 1 3 1 49
1 100
9
16
1 8
1 4
1 81
1 64
affiliates.
Resources All Rights
Reserved.
Algebra 1
© by Pearson
• Activities,
Education,
Inc., or its
61
Games, and
affiliates.
All Rights
Puzzles Reserved.
Lesson Res
ources 419 B
50 5 1
1
5x
3/2/09 1:47:4 6 PM
1 x3 , x3 2 3 3, 2
is in simplest An algebraic expression like terms, form when it is has no parentheses. negative exponents, or
4
4b4
4a22b 5 a2 3a2 1 2a 2 5ab
1 • Teaching Resources
Education, Inc., or its
affiliates.
622 5 62
a and
A number and its reciprocal have a product of 1.
Prentice Hall Algebra
• Teaching
Inc., or its
Class
Puzzle: Find
Prentice Hall
The exponent is 3.
A mathematical expression raised to consisting of a constant a power.
Copyright © by Pearson
as
answer
Algebra 1
Education,
8 Online Tea cher Resour ce Center Activities, Games, and Puzzles
Copyright
63 5 6 3 6 3 6
5 1.
• Teaching
Inc., or its
7
63 5 6 3 6 3 6
factor.
45p 14q 22r 23
. The correct
© by Pearson
After you follow you rearrange all the clues, only two fractions should the digits of (Hint: Every their denomin remain. Circle power of 2 ators, you will these fractions has an even find a positive . When digit as its Puzzle answer: power of 2. ones digit.) 8192 or 2 13 What is it? ________ ___________ Algebra 1
Education,
Picture or Example
how many The number that tells used as a times a base is to be repeated factor.
simplified 14
Prentice Hall
at 4:00 A.M.
Prentice Hall
Copyright
A number used as a repeated
25a 6
14
The student
instead of 45pq 2r 3
Copyright
of bacteria in a culture 65,536 bacteria quadruples in the culture every hour. the number There were at 8:00 a.m. of bacteria The expressio in the culture n 65,536 ? h a. What is h hours after 4 models the value of 8:00 a.m. the expressio b. What does n for h 5 24? the value of the expressio 256; the number n in part a of bacteria represent? in the culture
Reserved.
information.
simplified as 5 22a 29 (5a 3) 22 instead of 22 26 5 a . The correct answer is 2 1
5 2r 23
45p 14q 22 r 23
Name
s 1–6, choose
Date
All Rights
Definition
For every nonzero number
Date
The student
45pq 22r 23
is
Reserved.
Test Prep
the correct letter. simplified form of 3a 4 22 3 81a 4c 3 b c ? D A. 81a 4 b2 B. 3a 4 b 2c 3 C. 2. What is2a 22 b 2c 3 if a 5 25 ? H F. 225 G. 25 H. 2 1 3. Which 25 of the following simplifies to a negative A. 24 24 number? A B. (24) 24 C. 4 24 4. What is the simplifi ed form of 2(14x) 0 y 27 14z z? I F. 2 14z G. y7 z y7 H. 5. What is y7 (2m) 23n if m 5 2 and A. 3 n 5 224? A B. 23 C. 4 6. What is the simplifi 5a 23 ed form of a2 b ? G 3 27 F. 125a 3 G. 2 27 125a 3 125a 3 H. 27
45pq 22r 23 14 45pq 2r 3 . 14
Resources
All Rights
Zero and Negativ e Exponen ts
affiliates. All Rights Reserved.
1
3/2/09 1:47:25 PM
_01_lr.indd 419
1 • Teaching
Inc., or its
Multiple Choice
Lesson Resources
0419A_hsm11a1te_FL_07
Education,
Class
The base is 6.
exponent
Gold Algebra
© by Pearson
Resources
filling in the missing the vocabulary chart by
reciprocal
Assign the Lesson Quiz. practice, Appropriate intervention, tically or enrichment is automa generated based on student performance.
• Teaching
Inc., or its
Zero and Negative Exponents
exponential expression
5 Assess & Remediate
14.99 R d R 15.001
Class
Algebra 1
Education,
ELL Support
Word or Word Phrase
Prentice Hall
Copyright
7. The number
0.1
Prentice Hall le range affiliates. for Pearson Education, Inc., or its diameter Copyright © by the s of 9 the rods.
answer as a
5 incorrect;
Practice and Problem4 Solv All-in-One ing Wkbk/ Resources/ Online Standardiz ed Test Prep
se
1 10 ,
5
27
Short Respon and as a decimal.
9p 2r 23 7q 22 4 5 . 9p 2r 23 9p 7q 22 4 5 5 7q 22 ?
c. Find the
5 3 , R c 23 27 2 5 , 3 8 8 c 5
1. What is the
rods?
Problem
4. What does 7
c 5 2 , c 21 3
For Exercise
3. What is 7b23 the problem using only positive exponents? of 2asking you to determin What is the simplified form a e? an inequalitypositive exponents and range of diameter a product of factors with for the acceptable 7 7b23 23 s Rewrite the expression as 5 2?b factors with negative exponents. a a2
5 2? 3 Plannin b a g
vary. Sample:
.
25 22 a 29
52 1 25a 9
5. Simplify
ded Choose a fraction to values of c 21 23 use as a value , c , and 3 for the variable c .
Answers may
Name
Manufacturing A company 1.5 mm. A rod is acceptab is making metal rods Problem with a target le when diameter. Write expression? its diameter is within 23 diameter of an inequalit of each y for the acceptab 10 mm of which is not What is the simplified form is 3.9, the target le range of the expression the base of diameter Since the exponent is 0 but 0 s. a. 3.9 5 1 has a value of 1.
)
2(5a 3) 22 5
incorrect;
4
Reserved.
Date
; The student simplified 24 cd as 1 instead of c . cd 4 d 4 The correct answer is 240c 4. Simplify b 8d 4 . 2(5a 3 22
.
xy 4 5 correct 3z 3
Resources
All Rights
a Plan
Zero and Negativ e Exponen ts
3x 3
6xy 4 18z 3
5
33. Open-En
5a 4b 4 9mc 7
Class an to the opposite of the
the base ThinkofAbout the reciprocal
3z 23 ? y 24 18 2x 3z 23 2x(3z 23) ? y 24 18 5 y 24 (18)
d R 16
4
is
3. Simplify 2x
makes large pizzas with is acceptab a target diameter le if its diameter of 16 inches. d represen t the diameter is within 3 ? 2 22 in. A pizza of the of a pizza. acceptable Write an inequalit target diameter. Let large pizza diameters y for the range in inches. of 15 1 R 3
21 10,000a 4
0
Name
For every nonzero number
1 21 10 10
as a decimal.
Date
Algebra 1
4
exponents.
32. A pizza shop
27n 3 8m 3
18. 2(10a) 24 0 b
10 using negative
30. 8 ? 10 24 of people who 0.0008 election. Th vote early doubles is week 1200 every week people voted the number early. The expressio leading up to an of people who expression will vote early for w w weeks after n 1200 ? 2 w models in the situation 5 23. Describe what this week. the value Evaluate .
5 2a 4c
23
a power of
28.
expression
For each exercise exercise whether below, a student’s answer is below shown. indicate where each answer is correct Indicate below or the each write the correct student made an error, incorrect. For each incorrect and describe answer. how to correct answer, it. Then 1. Simplify 1 ? (2y) 0 x 23 . 3 28 2. Simplify 1 25 ? 8b cd 24 (2)(1)x 23 ? (2y) 0x 23 . 5 3 12 0 3 28 25 ? 8b cd 24 240b 28cd 24 5 2 12 0 5 1 3x 3 incorrect; The student 240 simplified 5 instead of (2y) 0 as 2 1. correct b 8cd 4 answer incorrect 1
26. (2c) 22 1
the of the expressio 150; The expressio n represen ts n 1200 ? 2 early three represents weeks ago. the number of people who voted
24
16.
Class Prentice Hall Gold
8. Write your
ELL Support
419A
k3
number as
29. 10 23 0.001
23p 8m 3n 3
q3 64r 5
Copyright
Lesson 7-1
195
HSM11A1MC_0701.indd
11xy 21z 0
19.
3
28
22 3 25 r
24. 9a 0 c 4 144
Date
Enrichment Zero and Negativ e Exponen ts
27
1 23 1000 10
Write each
Class
7-1
c 5 2.
22. b 23 1
31. The number
20 1
ne All-in-One Resources/Onli ing Reteach Practice and Problem3 Solv Reteaching ing Wkbk/ 7-1All-Zeroin-O and Negative ne Exponents Resources/ Online Thin 1. 5 k a a, For every nonzero number About a 1Planwords, when the other integer n, a 5 . In
3. 12 0,600 people 4. 10,600; 2,650; About 1 ay. About 2,650 visited the website in M te in March. people visited the websi
2/14/09 5:56:45 AM
1 2 144 x2
6b
22
14.
b. 5y3
2/14/09 5:56:36 AM 194
HSM11A1MC_0701.indd
0
21
3 m8
23
17.
Lesson 7-1
Have students Focus on Communication le. Label one column make a two-column tab other “Negative “Zero Exponent” and the n example s write a student Exponent.” Have sk volunteers for of each in the columns. A the board. Repeat the their examples to put on mplify the power. For property each time you si ith a zero exponent example, say: A value w 0 5 1. Continue with always equals 1 so 29 ents a chance to examples, allowing stud d to simplify the explain the property use ric and algebraic bases. powers. Use both nume
0
4
b. 1
26a2 2. a. b
Education, Inc. or its affiliates.
Education, Inc. or its affiliates.
1
1. a. 8
2/20/09 12:23:27 PM
197
HSM11A1MC_0701.indd
Copyright © by Pearson
All Rights Reserved.
Education, Inc. or its affiliates.
Education, Inc. or its affiliates.
Copyright © by Pearson
197 194
Chapter 7
10.
quiz ANSWERS to lESSoN
negative
with — for work Builder studentNEG is The symbol Simplifying Powers theProblem 1uhcorrectly tiv 25. Did Vocabulary base b? Yes / No negative (adjective) negative Yes / No base a? zero. ź No thanof 423 ? Yes / quantity a value lessform baseAx?negative has simplified is correctly. What is the NEG uh tiv Got It?(adjective) Definition: negative 27. Now simplify the expression the student make? ź 423. 26. What error to simplify than zero. may vary. Sample: 1 did step negative a value lessSolutions are all hasnumbers. and 2peach 3,2Complete 216. Examples:Definition: 2 , A negative quantity and b0 as the power to the denominator 1 simplified n n xnan The student _______ Move xnan xn 423 5 1 ______________________ 5 0 5 1 5x a 2p are all negative numbers. positive. b Examples: 2 3,2 23, and make the exponent a 2n b0 of as 41. 0 instead Vocabulary _______ Use Your ______________________ the expression. 1 each situation. Evaluate the power to simplify 5 7. Write a number to represent A worker’s hourly pay Use Your Vocabulary 64 You owe your brother increases by $.50. The temperature is 4 degrees each situation. 7. Write a number to representeight dollars. A worker’s hourly pay below zero. You owe your brother $.50 is 4 degrees2$ 8 increases by $.50. temperature Expressions The Success Exponential dollars. 24 Math 2 Simplifying eight its opposite in Column B. Problem zero. below in Column A to $.50 each negative number that you understand. 2$of8 each expression? a line from Draw Check the vocabulary words simplified form off24 B. exponent B Column Got It? What is theColumn negative in n25 A to its opposite 2 in Column zero exponent Column A number from each negative m2 1 a line29 exponent 4c 23b Draw a 23 x exponents. 1 n 23 17and Column negative B 8. 22 well youAcan simplify zero Rate howColumn each sentence. 1 to complete 17 10 the correct word Now I 1 to 8 3 8. 2Underline 62 4 exponent, move the base 2 it! negative 9. 23Need to 2 0 that has aget 5 a base in the numerator 1 review 17. To simplify / negative exponent. 3 a positive 3 the denominator and3write 2 5 move the base 10. 217 9. 235 that has a negative exponent, in the denominator 3 18. To simplify a base / negative exponent. 35 write a positive 10. 217 to the numerator and
Copyright © by Pearson
All Rights Reserved.
Vocabulary Builder
Re
22
0 1
28 0
Name
a23b2 for a 5 22 3. What is the value of 26 and b 5 4? The number of 4. Do you unDERStAnD? every month. hits on a website doubles ited the website About 10,600 people vis t n 10,600 • 2 xpressio during May. The e sitors after models the number of vi pression for t 5 0 t months. Evaluate the ex at each value of and t 5 22. Describe wh in the situation. the expression represents
Differentiat ed Remedia and Negative Intervention 7-1 Zerotion Zero and Negative Exponents 7-1 Exponents On-level Extension Vocabulary
mediate Assign the Lesson Qui z. Appropriate intervention , practice, or enrichm ent is auto matically generated based on stud performanc ent e.
5 y23
27.
Name
Form G
for a 5 24, b 5 3, and
9
16
46
8.
9.
15.
2 21 a. 26a b
b.
25. 2a 22 21
Write each
2(12x) ovides reteaching 1 • Reteaching (2 pages) Pr 8 r the key lesson 6bc and practice exercises fo 2(11x) gling students or concepts. Use with strug 2 a b 9 absent students. 3m p Suppor5at Helps • English Language Learner 2c 23k (mn) inforce mathematical students develop and re p 2m a b cepts. 3n vocabulary and key con 8 q 13.
)
Zero and Negativ e Exponen ts
expression
23. 4a 2 b 22 3 512 c
6. 46 21 1 7. 26 0 1
Date
Practice (continued
Evaluate each 21. 3a 21 3 24
2 1
All-in-One Resources/ Online Enrichment
Class
7-1
1 125
2 4 21 8
12.
a. 223 0 b. (5.5) orm of each 2. What is the simplified f expression?
Name
Form G
49
Intervention
1. What is expression?
• Got It for each Problem • Lesson Check
5 Assess &
5. 2(7) 22
11.
• New Vocabulary • Key Concepts
Points
3 3 24 243 4.
ach the simplified form of e
Students can use the Al u teach the lesson. worktext (4 pages) as yo support Use the Companion to
Copyright © by Pearson
Lesson Resources provide a detailed blueprint for instruction, assessment, and remediation that includes prescriptions for all levels of students, from intervention to extension.
2. 5 23
Lesson Quiz
anion Algebra 1 Compgebra 1 Companion
Data-Driven Differentiation
1. 13 0 1
3.
5 Assess & Remediate
Additional Instructional Support
tion
Differentiated Remedia
Lesson Resources
7-1
Date
Practice Zero and Negativ e Exponen ts
expression.
Extension
• Enrichm ent Provide s students w interesting ith problems an d activities t extend the c hat oncepts of t he lesson. • Activities, Games, and Worksheets Puzzles that can be used for con developmen cepts t, enrichmen t, and for fu n!
Practice and Problem Solv All-in-One ing Wkbk/ Resources/ Online Practice pag e2
Name
Simplify each
• Think Abo ut a Plan Hel ps students develop spe cific problem -solving skil strategies b ls and y providing scaffolded g questions. uiding • Standardiz ed Test Prep major exerc Focuses on ises, all ma jor question all and helps s type tudents prep s, are for the high-stakes assessments .
Help Every Student Master Mathematics
5
My Math Video PART A 5-1 Rate of Change and Slope 5-2 Direct Variation Concept Byte: Inve stigating y 5 mx 5-3 1b Slope-Intercept Form Part 1 329–333, Part 2 334–337 5-4 Point-Slope Form Part 1 338–340, Part 2 341–344 Chapter 5A Review and Test PART B 5-5 Standard Form 5-6 Parallel and Perpend icular Lines 5-7 Scatter Plots and Trend Lines Concept Byte: Coll ecting Linear Data Assessment and Test Prep Pull It All Together Chapter 5B Review and Test Cumulative Test Prep
Prentice Hall Algebra 1, Geometry, Algebra 2, Foundations Series provides the support students need to achieve mathematics success.
Linear Functions
CHAPTER
5
Linear Functions
Get Ready!
xxvi
311 313 314 321 328 329 338 345 349 357 364 371 372 373 376
Contents
PART A
R022_hsm11a1se_
fmtoc_LLNA.indd
Your place to get all things digital
E VID O
Some lessons and chapters are divided into parts to help students who might be overwhelmed by denser content. This also allows for more frequent assessment.
Vocabulary for Part A
AM YN I
C
Audio Online: English/Spanish Vocabulary Spanish English variación directa direct variation, p. 321 ecuación lineal linear equation, p. 329 función elemental parent function, p. 329 forma punto-pendiente point-slope form, p. 338 tasa de cambio rate of change, p. 314 pendiente slope, p. 315 forma pendiente-intercepto slope-intercept form, p. 329 intercepto en y y-intercept, p. 329
ES
AC
T I V I TI
S
NLINE
HO
NLINE
ME
WO
FO R
athX
®
Extra practice and review online
L
M
Get and view your assignments online.
OL
O
O B LE M
RK
R
P
Download Step-by-Step Problems with Instant Replay.
O
Interactive! Vary numbers, graphs, and figures to explore math concepts.
are lots Did you know that there They’re of ways to describe lines? d. In this not just straight or slante algebra chapter, you’ll learn to use to describe lines.
VE OL I
D
S
A BUL
T!
The online Solve It will get you in gear for each lesson.
Chapter Organization
lines?
Y AR
Math definitions in English and Spanish
VOC
Download videos connecting math to your world.
SCHO
2/24/09 5:49:58 PM
0311_hsm11a1ls_05co.indd
xxvi
ed in These performers are arrang think they parallel lines. How do you make the decided where to stand to
312
Reading Support Improve student comprehension with additional reading level and vocabulary support.
13
4/27/09 11:49:45 AM
More Scaffolded Support More support in problems and exercises helps students connect to what they already know, break down complex steps, and model the thinking before the math.
riation a Direct Va Graphing rs y varies Mars ight on Ma Weight on We of the on ts ati igh lor e we Space Exp Earth x. Th rs 50 lb h weight on Phoenix Ma the directly wit ard bo truments on wn. science ins Mars are sho Earth and Earth Lander on s weight, in Weight on n that relate tio ua eq an y? A What is d on Mars 130 lb y 5 kx Earth x an on. iati var pounds, on ct of a dire function form 50 5 k(130) Start with the for y. for x and 50 0.38 < k Substitute 130 for k. e solv to y 5 0.38x side by 130 Divide each k in y 5 kx. ute 0.38 for ation. Substit Write an equ on y weight 8x gives the on y 5 0.3 weighs The equati object that unds, of an Mars, in po . rth Ea ? x pounds on n in part (A) the equatio the graph of ph. B What is draw the gra values. Then of le tab a Make y a linear The points form line 60 y wa x pattern. Dra h them. )50 40 oug 8(0 thr 0.3 0 0) 5 19 20 50 0.38(5 x 00) 5 38 100 0.38(1 50 100 150 57 O 5 50) A person 150 0.38(1 t on Earth x. with weigh . What is an ies directly on the moon moon y var lb 6 the 16. on on y? What s t a. Weigh t on the mo Earth weigh Got It? 3. s 100 lb on x and weigh who weigh ight on Earth t relates we blem 3? Pro in ? equation tha ation y 5 0.38x of this equ the graph of is the graph the slope of g What is equation? the to b. Reasonin d slope relate How is the
3 Problem
graphed
Have you like equations before? y 5 0.38x r 4, you Yes. In Chapte ar functions line graphed table of by making a tting values and plo points.
Concept
Summary
Graphs of
Lesson 5-2
ls_0502.indd
0321_hsm11a1
tions
y x
k0
tion
Direct Varia
323
336
and Prob lem
Graph each
-Solving
equation.
Exercise
s
Guided Practice
To start, fin
d the y-inte
rcept.
4. y 5 x 1 5 7. y 5 2x 24 10. y 5 7x 13. Retail
5. y 5 22 x11 8. y 5 6x 23 11. y 5 5x 11
Sales Supp ose yo
See Problem
3. y 5 3x 14 The y-inte rcept is 4. So plot a po int at (0, 4).
5.
6. y 5 24 x21 9. y 5 23 x13 12. y 5 2x 1 10
Guided Practice
To start, ide
r Function
s
0334_hsm
11a1ls_0503-
2.indd 336
Standardized Assessment Support Students find daily test-taking support and practice in the Practice and Problem Solving pages combined with the Student Companion. Teachers may choose additional test taking practice from the Progress Monitoring Assessments.
y Suppor t
QBSBUJPO
Practice Practice
u have a $5 that costs $7.50 per ya -off coupon rd. Write an at money yo equation tha a fabric store. You bu u pay if yo u buy x ya y fabric t models the rds of fabric total amou See Problem . What is the ntify the slo nt of 6. pe and the graph of the y-intercept. equation? The slope is the cost per ya rd, $7.50 per ya rd. The y-inte rcept is the y amou nt of 14. Tempera coupon, 2$ the 5.00. ture The temperature 58F. Write at sunrise an equatio is 658F. Ea n that mode x x hours. Wh ch hour, the tem ls the tem at is the gra pe pe rature y, in rature rises ph of the eq B Apply degrees Fa uation? 15. Think hrenheit, after About a Pla n Polar be were abou k0 ars are list t 25,000 po ed as a thr lar bears in the eatened sp 1000 each ec year, in wh wo ies rld . In 2005, the . If the numb at year will • What eq re er of polar polar bears uation mo bears decli become ext dels the nu • How ca nes by 323 inct? mber of po n graphing lar bears? the equatio n help you 16. Error An solve the pro alysis A stu blem? dent drew y 5 22x 1 the graph 1. What err at the right or did the for the equa student ma 17. Comp tion ke? Draw the uters A co mp co PM rrect graph :29 ute r repair ser $35 per ho 3/11/09 3:25 . vice charg ur for repair es $50 for s. Let x be computer. dia y the gn osis and Let y be the number of hours it tak total cost of a. Write an es to repair the repair. equation in 2 a slope-inter b. Graph the equatio cept form that relate n. c. Reasonin x s x and y. g Explain 2 0 why you sh 2 ould draw Use the slo the line on 2 ly in Quad pe and y-i rant I. ntercept to graph each 18. y 5 7 equation. 2 3x 19. 2y 1 21. y 1 2 4x 5 0 5 5x 2 4 20. 3y 1 22. 4x 1 6 5 22x 3y 5 2x 2 1 23. 22(3x 1 4) 1 y 50 Chapter 5 Linea
Direct Varia
is on y 5 kx iation equati of a direct var perties. The graph following pro the h wit e 0). , a lin gh (0 passes throu • The line is k. e of the line • The slop
A
2/24/09 5:57 :50 PM
Date
Class Name
3-2
Standardized
Test Prep
Subtraction Addition or alities Using Solving Inequ
e
Multiple Choic
ter. the correct let s 1–6, choose For Exercise 8? 21 . 12 2 solution of p 1. What is the B. p , 26 A. p , 230 1 5 # 29? solution of x 2. What is the G. x # 24 F. x , 24 ph 3. Which gra A.
25
Name
C. p . 26
H. x . 24
utions of z s all of the sol
represent
C.
D. B.
25
5
0
7-2
I. x $ 24
23
0 For3Exer
Class
Standardiz
Scientific
Multiple Ch 2 7 # 23 ? oice
5
0
D. p . 230
ed Test Prep
Date
Notation
7
cises 1–6,
choose th e correct let ter. e following expressions is written in scientifi B. 0.09 3 c notation 10 7 ?
1. Which of th
213
28A. 73.4 23 3 10 5
C. 80 3 10 3
D. 4.22 3 2 . 0?2. Which of the 10 25 following utions of n 2 is 0.00000 F. 7.08 3 6 28 00708 writt H. 2 4 10 en in scien 4. G. 7.8 3 4 2 0 tific notation 10 28 ? H. 708 3 F. 2 4 6 10 210 4 2 0 3. Which I. 70.8 3 6 I. 4 essio 10 29 2expr n represen 4 2A. 0 ts the large 40.1 3 10 26 st number? G. 6 B. 4 4.1 3 10 27 2 4 2 0 C. 0.411 3 10 26 $ m 1 4? D. m # 3 D. 0.04001 ivalent to 21 3 10 25 Which expr C. m $4.25 quality is equ ession is eq 25 1 5. Which ine # m ua B. l to 25 wr , itt m en A. F. 8.0 3 in scientifi 8000 3week. So far 10 per c les no mi tation? n 50 G.? 1.25 3 run more tha 10 24 s the situation the race is to 50 H. 125 3 ality represent l in training for I. d 1 32 . 10 25 . Which inequ 6. Your goa 32hic$h 50 I. 1.25 3 1W e run 32 miles d 5. hav H. of th you 10 4 e ek fol 50 lowing sta this we in scientifi tements is G. d 2 32 . c notation not true reg F. d $ 18 in the form arding an A. The va a 3 10 n? lue of a mu expression st be greate written B. The va r than or eq lue of n mu ual to 1 an st be an int C. Doublin d smaller . On eger. g n res st s92% than 10. leault se in a doublin rage at D.stDo ave mu ub Shor t Respon res on ling a neult g of the va r test sco edstoinget lue of the do you res a doubling in a class, you expression. . What score of the value to earn an A 7. In order average of 91% of the expr ession. ts, you have an r work. 6. Which you the first 6 tes ow Sh number is n an A? ear to t eq tes t ua l to 7(3.5 3 4 the las F. 24.5 10 4
s all of the sol
represent Which graph
14
Program Components
Prentice Hall
Algebra 1 Geometry Algebra 2
Foundations Series Student Edition
Go Digital!
Teacher’s Edition with Teaching Resources DVD
Check out PowerAlgebra.com and PowerGeometry.com for all of your online resources for instruction, assessment, and classroom management.
Student Companion with Practice and Problem Solving Student Companion with Practice and Problem Solving, Teacher’s Edition Practice and Problem Solving Workbook Practice and Problem Solving Workbook, Teacher’s Edition
PowerGeometry.com
+
On-Level Student Edition
Shared Resources
Teacher’s Edition with Teaching Resources DVD
All-in-One Teaching Resources
Student Companion
Teaching with TI Technology
Student Companion, Teacher’s Edition
Solve It! and Lesson Quiz on Transparencies
Student Companion, Spanish Teacher’s Edition
Progress Monitoring Assessments
Practice and Problem Solving Workbook
ExamView Assessment Suite CD-ROM Answers and Solutions CD-ROM
Practice and Problem Solving Workbook, Teacher’s Edition
TI-Nspire™* Lesson Support CD-ROM
Pearson eText CD-ROM
®
PowerAlgebra.com PowerGeometry.com An on-level series is also available. Please contact your Pearson sales representative for more details.
+
* T his resource/activity has been designed for use with
Texas Instruments TI-Nspire™ technology.
Spanish Resources Spanish Student Edition (Algebra 1 only) Spanish Student Companion Spanish Student Companion, Teacher’s Edition Spanish Practice and Problem Solving Workbook, Teacher’s Edition
PearsonSchool.com 800-848-9500 International customers: visit PearsonGlobalSchools.com Copyright Pearson Education, Inc., or its affiliates. All rights reserved.
PDF.0410.v1.DM.KW.LS
PowerAlgebra.com
Mat100402
Pearson eText CD-ROM
