Table Of Content

Authors Carter • Cuevas • Day • Malloy Kersaint • Luchin • McClain • Molix-Bailey • Price Reynosa • Silbey • Vielhaber • Willard i_FM_TP_895242.indd i 2/1/10 9:55 AM Copyright © 2012 The McGraw-Hill Companies, Inc. All rights reserved. No part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written consent of The McGraw-Hill Companies, Inc., including, but not limited to, network storage or transmission, or broadcast for distance learning. Send all inquiries to: Glencoe/McGraw-Hill 8787 Orion Place Columbus, OH 43240-4027 ISBN: 978-0-07-895242-5 MHID: 0-07-895242-5 Tennessee Math Connects, Course 2 Printed in the United States of America. 1 2 3 4 5 6 7 8 9 10 DOW/LEH 19 18 17 16 15 14 13 12 11 10 ii-ix_FM_895242.indd ii 2/1/10 10:53 AM Contents in Brief Master the Tennessee GLEs Start Smart A review of concepts from Course 1 1 Expressions and Patterns 2 Integers 3 Rational Numbers 4 Equations and Inequalities 5 Proportions and Similarity 6 Percent 7 Linear Functions 8 Probability and Predictions 9 Statistical Displays 10 Volume and Surface Area 11 Measurement and Proportional Reasoning End-of-Year Option Problem-Solving Projects Are We Similar? Turn Over a New Leaf Stand Up and Be Counted! Be True to Your School Math Genes C H A P TE R ii-ix_FM_895242.indd iii 2/1/10 10:53 AM iv connectED.mcgraw-hill.com Investigate Animations present an animation of a math concept or graphic novel. Vocabulary presents visual representations of math concepts. Multilingual eGlossary presents key vocabulary and formulas in 13 languages. iv iv iv iv iv iv iv iv “It’s easy to do my assignments online and quick to fi nd everything I need.” Online Guide tED hi Get ConnectED c G ii-ix_FM_895130.indd iv 1/13/10 11:25 AM D i g i t a l a n d P r i n t S o l u t i o n s v Learn Personal Tutor presents a teacher explaining step-by-step solutions to problems. Virtual Manipulatives provide digital ways to explore concepts. Graphing Calculator provides keystrokes other than the TI-83/84 Plus or TI-Nspire used in the textbook. Audio recordings provide an opportunity to build oral and listening fluency. Foldables provide a unique way to enhance students’ study skills. Practice Self-Check Practice allows students to assess their knowledge of foundational skills. Worksheets provide additional practice and reteach opportunities. Online Assessment checks understanding of concepts and terms. The icons found throughout Math Connects provide you with the opportunity to connect the print textbook with online interactive learning. ii-ix_FM_895130.indd v 1/13/10 11:25 AM vi Lead Authors Authors O ur lead authors ensure that the Macmillan/McGraw- Hill and Glencoe/McGraw-Hill mathematics programs are truly vertically aligned by beginning with the end in mind—success in Algebra 1 and beyond. By “backmapping” the content from the high school programs, all of our mathematics programs are well articulated in their scope and sequence. Get ConnectED Meet the Authors. Gilbert J. Cuevas, Ph.D. Professor of Mathematics Education Texas State University—San Marcos San Marcos, Texas Areas of Expertise: Applying concepts and skills in mathematically rich contexts; Mathematical Representations Carol Malloy, Ph.D. Associate Professor University of North Carolina at Chapel Hill Chapel Hill, North Carolina Areas of Expertise: Representations and critical thinking; Student Success in Algebra 1 John A. Carter, Ph.D. Assistant Principal for Teaching and Learning Adlai E. Stevenson High School Lincolnshire, Illinois Areas of Expertise: Using technology and manipulatives to visualize concepts; Mathematics Achievement of English-Language Learners Roger Day, Ph.D., NBCT Mathematics Department Chairperson Pontiac Township High School Pontiac, Illinois Areas of Expertise: Understanding and applying probability and statistics; Mathematics Teacher Education ii-ix_FM_895130.indd vi 1/15/10 8:52 AM A u t h o r s A vii Program Authors Gladis Kersaint, Ph.D. Associate Professor of Mathematics Education, K–12 University of South Florida Tampa, Florida Kay McClain, Ed.D. Research Professor Arizona State University Phoenix, Arizona Rhonda J. Molix-Bailey Mathematics Consultant Mathematics by Design DeSoto, Texas Beatrice Moore Luchin Mathematics Consultant Houston, Texas Jack Price, Ed.D. Professor Emeritus California State Polytechnic University Pomona, California Mary Esther Reynosa Instructional Specialist for Elementary Mathematics Northside Independent School District San Antonio, Texas Robyn Silbey Math Content Coach Montgomery County Public Schools Gaithersburg, Maryland Kathleen Vielhaber Mathematics Consultant St. Louis, Missouri Teri Willard, Ed.D. Associate Professor Central Washington University Ellensburg, Washington Contributing Author Dinah Zike Educational Consultant Dinah-Might Activities, Inc. San Antonio, Texas Lead Consultant Viken Hovsepian Professor of Mathematics Rio Hondo College Whittier, California ii-ix_FM_895242.indd vii 2/1/10 10:53 AM viii Consultants and Reviewers T hese professionals were instrumental in providing valuable input and suggestions for improving the effectiveness of the mathematics instruction. Mathematical Content Dr. Michaele Chappell Professor of Mathematics Education Middle Tennessee State University Murfreesboro, Tennessee Melissa D. Young Mathematics Specialist Differentiated Accountability Model, Region III Orlando, Florida Differentiated Instruction Jennifer Taylor-Cox, Ph.D. Educational Consultant Innovative Instruction: Connecting Research and Practice in Education Severna Park, Maryland Gifted and Talented Shelbi K. Cole Research Assistant University of Connecticut Storrs, Connecticut Problem Solving Dr. Stephen Krulik Professor Emeritus – Math Education Temple University Philadelphia, Pennsylvania Reading in the Content Areas Sue Z. Beers President / Consultant Tools for Learning, Inc. Jewell, Iowa Reading and Vocabulary Douglas Fisher Professor San Diego State University San Diego, California Consultants s Education ii-ix_FM_895242.indd viii 2/1/10 10:53 AM C o n s u l t a n t s a n d R e v i e w e r s C ix Lisa M. Baranoski Numeracy Coach Antioch High School Nashville, TN Tracy Benson Math Intervention Specialist (Grades 4-6)/Read 180 Catlettsburg Elementary School Sevierville, TN Stephen W. Blessing Director of Curriculum, 6-12 Coffee County Schools Manchester, TN Dr. Allison Clark Mathematics Curriculum Specialist Shelby County Schools Memphis, TN Dr. Brenda P. Dean Assistant Superintendent Morristown, TN Ashley Donoho 3rd Grade Teacher Dresden Elementary School Dresden, TN Jane Hudgins Assistant Principal/Literacy Leader Martin Elementary School Martin, TN Tamora L. Jackson, B.B.A., M.A.T., Ed.D. 6th/7th Grade Teacher Bellevue Middle School Memphis, TN Timothy Jones Exemplary Teacher Shelby County Schools Memphis, TN Randall B. Kincaid Supervisor of Instruction, PreK-3 Sevier County Board of Education Sevierville, TN Leslie Mattern Math Teacher Sevier County High School Sevierville, TN Gary A. Petko Mathematics Specialist Knox County Schools Knoxville, TN Stacey Roddy Director, Elementary Math and Science Hamilton County Department of Education Chattanooga, TN Sherleta Sanders 2nd Grade Teacher LaVergne Lake Elementary LaVergne, TN Ernestine Saville-Brock Math Coordinator Metro-Nashville Public Schools Nashville, TN Leah B. Tomlinson 8th Grade Math Teacher West Wilson Middle School Mt. Juliet, TN Jerry L. Whitaker Mathematics Curriculum Coordinator Washington County Jonesborough, TN Tennessee Advisory Board ii-ix_FM_895242.indd ix 2/1/10 10:53 AM Contents 1 A Plan for Problem Solving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4 2 Multiply Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7 3 Divide Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 4 Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 5 Perimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 6 Venn Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 x_001_FM_TOC_895130.indd x 1/13/10 11:34 AM C o n t e n t s xi C Every chapter and every lesson has a wealth of interactive learning opportunities. connectED.mcgraw-hill.com Investigate Learn Practice Are You Ready for the Chapter? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Expressions Multi-Part Lesson 1 A Powers and Exponents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 B Numerical Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 C Algebraic Expressions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 D Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 Patterns Multi-Part Lesson 2 A Problem-Solving Investigation: Look for a Pattern . . . . . . . . . . 42 B Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 C Exte tend Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 Mid-Chapter Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 Square Roots Multi-Part Lesson 3 A Expl plore Perfect Squares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 B Squares and Square Roots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 C Estimate Square Roots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 Problem Solving in Animal Conservation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 Chapter Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 Practice Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 Preparing for Standardized Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 Test Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 Expressions and Patterns 1 C H A P T E R tED hill Get ConnectED x_001_FM_TOC_895130.indd xi 1/13/10 11:34 AM xii 2 Integers C H A P T E R Are You Ready for the Chapter? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 Writing Math . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 Integers and the Coordinate Plane Multi-Part Lesson 1 A Exploree Absolute Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 B Integers and Absolute Value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 C The Coordinate Plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 Add and Subtract Integers Multi-Part Lesson 2 A Exploree Add Integers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 B Add Integers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 C Exploree Subtract Integers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 D Subtract Integers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 Mid-Chapter Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 Multiply and Divide Integers Multi-Part Lesson 3 A Problem-Solving Investigation: Look for a Pattern . . . . . . . . . 100 B Exploree Multiply and Divide Integers . . . . . . . . . . . . . . . . . . . . . . . 102 C Multiply Integers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 D Divide Integers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 Problem Solving in Astronomy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 Chapter Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 Practice Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 Preparing for Standardized Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 Test Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 x_001_FM_TOC_895130.indd xii 1/13/10 11:34 AM C o n t e n t s xiii C Every chapter and every lesson has a wealth of interactive learning opportunities. connectED.mcgraw-hill.com Investigate Learn Practice Are You Ready for the Chapter? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 Rational Numbers Multi-Part Lesson 1 A Explore The Number Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 B Terminating and Repeating Decimals . . . . . . . . . . . . . . . . . . . . . . 128 C Compare and Order Rational Numbers . . . . . . . . . . . . . . . . . . . . . 133 Add and Subtract Fractions Multi-Part Lesson 2 A Add and Subtract Like Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 B Explore Unlike Fractions with Models . . . . . . . . . . . . . . . . . . . . . . 144 C Add and Subtract Unlike Fractions . . . . . . . . . . . . . . . . . . . . . . . . . 146 D Add and Subtract Mixed Numbers . . . . . . . . . . . . . . . . . . . . . . . . . 152 Mid-Chapter Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 Multiply and Divide Fractions Multi-Part Lesson 3 A Explore Multiply Fractions with Models . . . . . . . . . . . . . . . . . . . . . 158 B Multiply Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 C Problem-Solving Investigation: Draw a Diagram . . . . . . . . . . . 166 D Divide Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 Problem Solving in Fashion Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 Monomials Multi-Part Lesson 4 A Multiply and Divide Monomials . . . . . . . . . . . . . . . . . . . . . . . . . . . 176 B Negative Exponents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 C Scientific Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 Chapter Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190 Practice Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194 Preparing for Standardized Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195 Test Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196 Rational Numbers 3 C H A P T E R tED hill Get ConnectED x_001_FM_TOC_895130.indd xiii 1/27/10 8:07 AM xiv 4 Equations and Inequalities C H A P T E R Are You Ready for the Chapter? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 Reading Math . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201 Addition and Subtraction Equations Multi-Part Lesson 1 A Problem-Solving Investigation: Work Backward . . . . . . . . . . . 202 B Exploree Solve Addition and Subtraction Equations with Bar Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204 C Exploree Solve Equations Using Algebra Tiles . . . . . . . . . . . . . . . . 206 D Solve One-Step Addition and Subtraction Equations . . . . . . . . . . 208 Multiplication and Division Equations Multi-Part Lesson 2 A Exploree Multiplication Equations with Bar Diagrams . . . . . . . . . . 214 B Solve One-Step Multiplication and Division Equations . . . . . . . . 215 C Exploree Solve Equations with Rational Coefficients . . . . . . . . . . . 220 D Solve Equations with Rational Coefficients . . . . . . . . . . . . . . . . . . 221 Mid-Chapter Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 Multi-Step Equations Multi-Part Lesson 3 A Exploree Two-Step Equations with Bar Diagrams . . . . . . . . . . . . . 228 B Solve Two-Step Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230 C Exploree Equations with Variables on Each Side . . . . . . . . . . . . . . 235 D Solve Equations with Variables on Each Side . . . . . . . . . . . . . . . . 236 Problem Solving in Veterinary Medicine . . . . . . . . . . . . . . . . . . . . . . . . . . . 240 Inequalities Multi-Part Lesson 4 A Exploree Solve Inequalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242 B Solve Inequalities by Addition or Subtraction . . . . . . . . . . . . . . . . 244 C Solve Inequalities by Multiplication or Division . . . . . . . . . . . . . . . 249 Chapter Study Guide and Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254 Practice Chapter Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258 Preparing for Standardized Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259 Test Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260 x_001_FM_TOC_895130.indd xiv 1/13/10 11:35 AM