Prentice Hall Algebra 1, Geometry, Algebra 2, Foundations Series is a great
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Change the way
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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.
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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. *
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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
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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
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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.
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“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.
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”A Big Idea is a way of seeing better and working smarter, not just another piece of knowledge.”
–Grant Wiggins, consulting author 7
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“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.
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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.
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“Research shows that understanding develops during the process of solving problems in which important math concepts and skills are embedded…”
–Randy Charles, program author
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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.
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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.
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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
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Differentiat ed Remedia and Negative Intervention 7-1 Zerotion Zero and Negative Exponents 7-1 Exponents On-level Extension Vocabulary
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Students can use the Al u teach the lesson. worktext (4 pages) as yo support Use the Companion to
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Data-Driven Differentiation
1. 13 0 1
3.
5 Assess & Remediate
Additional Instructional Support
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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
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• 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 .
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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
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Linear Functions
CHAPTER
5
Linear Functions
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311 313 314 321 328 329 338 345 349 357 364 371 372 373 376
Contents
PART A
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AM YN I
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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
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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.
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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
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Concept
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Lesson 5-2
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Direct Varia
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Guided Practice
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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
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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
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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.
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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
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2/24/09 5:57 :50 PM
Date
Class Name
3-2
Standardized
Test Prep
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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
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14
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