Common Core Student Edition SpringBoard™ Mathematics Course 2 About the College Board The College Board is a mission-driven not-for-profit organization that connects students to college success and opportunity. Founded in 1900, the College Board was created to expand access to higher education. Today, the membership association is made up of more than 5,900 of the nation’s leading educational institutions and is dedicated to promoting excellence and equity in education. Each year, the College Board helps more than seven million students prepare for a successful transition to college through programs and services in college readiness and college success—including the SAT® and the Advanced Placement Program®. The organization also serves the education community through research and advocacy on behalf of students, educators, and schools. For further information, visit www.collegeboard.com. ISBN: 1-4573-0149-X ISBN: 0-978-1-4573-0149-0 Copyright © 2014 by the College Board. All rights reserved. College Board, Advanced Placement Program, AP, AP Central, AP Vertical Teams, CollegeEd, Pre-AP, SpringBoard, connect to college success, SAT, and the Acorn logo are registered trademarks of the College Board. College Board Standards for College Success, connect to college success, English Textual Power, and SpringBoard are trademarks owned by College Board. PSAT/NMSQT is a registered trademark of the College Board and the National Merit Scholarship Corporation. Microsoft and PowerPoint are registered trademarks of Microsoft Corporation. All other products and services may be trademarks of their respective owners. 1 2 3 4 5 6 7 8 13 14 15 16 17 18 Printed in the United States of America AAcckknnoowwlleeddggmmeennttss The College Board gratefully acknowledges the outstanding work of the classroom teachers and writers who have been integral to the development of this revised program. The end product is testimony to their expertise, understanding of student learning needs, and dedication to rigorous but accessible mathematics instruction. Michael Allwood Shawn Harris Dr. Roxy Peck Brunswick School Ronan Middle School California Polytechnic Institute Greenwich, Connecticut Ronan, Montana San Luis Obispo, California Floyd Bullard Marie Humphrey Katie Sheets North Carolina School of Science East Mecklenburg High School Harrisburg School and Mathematics Charlotte, North Carolina Harrisburg, South Dakota Durham, North Carolina Marcia Chumas Brian Kotz Andrea Sukow East Mecklenburg High School Montgomery College Mathematics Consultant Charlotte, North Carolina Monrovia, Maryland Nashville, Tennessee Kathy Fritz Chris Olsen Stephanie Tate Plano Independent School Prairie Lutheran School Hillsborough School District District Cedar Rapids, Iowa Tampa, Florida Plano, Texas Product Development Betty Barnett Robert Sheffield Executive Director, SpringBoard Sr. Director, SpringBoard Implementation Allen Dimacali Judy Windle d. ve Editorial Director, Mathematics Sr. Mathematics Instructional Specialist er es SpringBoard SpringBoard s r ht g All ri John Nelson Alex Chavarry d. Editor, SpringBoard Sr. Director, SpringBoard Strategic Accounts ar o B e g e oll C 4 1 0 2 © Acknowledgments iii AAcckknnoowwlleeddggmmeennttss ccoonnttiinnuueedd Research and Planning Advisors We also wish to thank the members of our SpringBoard Advisory Council and the many educators who gave generously of their time and their ideas as we conducted research for both the print and online programs. Your suggestions and reactions to ideas helped immeasurably as we planned the revisions. We gratefully acknowledge the teachers and administrators in the following districts. ABC Unified Hillsborough County Public Polk County Public Schools Cerritos, California Schools Bartow, Florida Tampa, Florida Albuquerque Public Schools Quakertown Community School Albuquerque, New Mexico Houston Independent School District District Quakertown, Pennsylvania Amarillo School District Houston, Texas Amarillo, Texas Rio Rancho Public Schools Hobbs Municipal Schools Rio Rancho, New Mexico Baltimore County Public Schools Hobbs, New Mexico Baltimore, Maryland Ronan School District Irving Independent School Ronan, Montana Bellevue School District 405 District Bellevue, Washington Irving, Texas St. Vrain Valley School District Longmont, Colorado Charlotte Mecklenburg Schools Kenton County School District Charlotte, North Carolina Fort Wright, Kentucky Scottsdale Public Schools Phoenix, Arizona Clark County School District Lee County Public Schools Las Vegas, Nevada Fort Myers, Florida Seminole County Public Schools Sanford, Florida Cypress Fairbanks ISD Newton County Schools d. Houston, Texas Covington, Georgia Southwest ISD ve er San Antonio, Texas es s r District School Board of Collier Noblesville Schools ht g County Noblesville, Indiana Spokane Public Schools All ri Collier County, Florida Spokane, Washington d. ar Oakland Unified School District Bo e Denver Public Schools Oakland, California Volusia County Schools eg oll Denver, Colorado DeLand, Florida C 4 1 Orange County Public Schools 0 2 © Frisco ISD Orlando, Florida Frisco, Texas School District of Palm Beach Gilbert Unified School District County Gilbert, Arizona Palm Beach, Florida Grand Prairie ISD Peninsula School District Grand Prairie, Texas Gig Harbor, Washington iv SpringBoard® Mathematics with Meaning™ Level 2 CCoonntteennttss To the Student x Instructional Units 1 UNIT NUMBER SYSTEMS Unit 1 Overview 1 Getting Ready 2 Activity 1 Operations on Positive Rational Numbers—Paper Clips, Airplanes, and Spiders 3 Lesson 1-1 Adding and Subtracting Decimals 3 Lesson 1-2 Multiplying and Dividing Decimals 5 Lesson 1-3 Operations with Fractions 7 Lesson 1-4 Converting Rational Numbers to Decimals 11 Activity 1 Practice 13 Activity 2 Addition and Subtraction of Integers—Elevation Ups and Downs 15 Lesson 2-1 Adding Integers 15 Lesson 2-2 Subtracting Integers 19 Activity 2 Practice 22 Embedded Assessment 1 Positive Rational Numbers and Adding and Subtracting Integers—Off to the Races 23 Activity 3 Multiplication and Division of Integers—What’s the Sign? 25 Lesson 3-1 Multiplying Integers 25 Lesson 3-2 Dividing Integers 29 Activity 3 Practice 31 Activity 4 Operations on Rational Numbers—Let’s Be Rational! 33 ed. Lesson 4-1 Sets of Rational Numbers 33 v er s Lesson 4-2 Adding Rational Numbers 36 e hts r Lesson 4-3 Subtracting Rational Numbers 39 g All ri Lesson 4-4 Multiplying and Dividing Rational Numbers 41 d. Activity 4 Practice 44 ar o B ge Embedded Assessment 2 Rational Number Operations and Multiplying and e Coll Dividing Integers—Top to Bottom 47 4 1 0 2 © UNIT 2 EXPRESSIONS AND EQUATIONS Unit 2 Overview 49 Getting Ready 50 Activity 5 Properties of Operations—What’s In a Name? 51 Lesson 5-1 Applying Properties of Operations 51 Lesson 5-2 Applying Properties to Factor and Expand 54 Activity 5 Practice 58 Contents v CCoonntteennttss ccoonnttiinnuueedd Activity 6 Writing and Solving Equations—Melody’s Music Solution 59 Lesson 6-1 Modeling and Writing Two-Step Equations 59 Lesson 6-2 Solving Two-Step Equations 61 Activity 6 Practice 64 Embedded Assessment 1 Writing and Solving Equations—Fundraising Fun 65 Activity 7 Solving and Graphing Inequalities—It Plays to Save 67 Lesson 7-1 Modeling and Writing Two-Step Inequalities 67 Lesson 7-2 Solving Two-Step Inequalities 70 Activity 7 Practice 74 Embedded Assessment 2 Solving Inequalities—A Gold Medal Appetite 75 3 UNIT RATIO AND PROPORTION Unit 3 Overview 77 Getting Ready 78 Activity 8 Ratio and Unit Rates—Strange, But True 79 Lesson 8-1 Ratio and Unit Rates 79 Lesson 8-2 Identifying and Solving Proportions 82 Lesson 8-3 Converting Measurements 85 Activity 8 Practice 87 Activity 9 Proportional Reasoning—Scrutinizing Coins 89 Lesson 9-1 Equations Representing Proportional Relationships 89 Lesson 9-2 Constants of Proportionality 94 Activity 9 Practice 97 Embedded Assessment 1 Ratios, Proportions, and Proportional Reasoning— Weighing in on Diamonds 99 d. e v Activity 10 Proportional Relationships and Scale—Patriotic Proportions 101 ser e Lesson 10-1 Using Scale Drawings 101 hts r g Lesson 10-2 Using Maps 105 All ri Lesson 10-3 Make Scale Drawings 108 d. ar o Activity 10 Practice 111 B e g e Embedded Assessment 2 Proportional Relationships and Scale—Soccer Sense 113 Coll 4 1 0 Activity 11 Percent Problems—Well, There Is More Than One Way 115 © 2 Lesson 11-1 Basic Percent Problems 115 Lesson 11-2 Sales Tax, Tips, and Commissions 119 Activity 11 Practice 121 Activity 12 More Percent Problems—Like Animals? Have I Got a Job for You! 123 Lesson 12-1 Percent Increase and Decrease 123 Lesson 12-2 Markups and Discounts 125 Lesson 12-3 Interest 127 Lesson 12-4 Percent Error 129 Activity 12 Practice 131 vi SpringBoard® Mathematics with Meaning™ Level 2 Embedded Assessment 3 Percents and Proportions—Socializing and Selling 133 4 UNIT GEOMETRY Unit 4 Overview 135 Getting Ready 136 Activity 13 Angle Pairs—Some of the Angles 137 Lesson 13-1 Complementary, Supplementary, and Adjacent Angles 137 Lesson 13-2 Vertical Angles and Angle Relationships in a Triangle 142 Activity 13 Practice 145 Activity 14 Triangle Measurements—Rigid Bridges 147 Lesson 14-1 Draw Triangles from Side Lengths 147 Lesson 14-2 Draw Triangles from Measures of Angles or Sides 151 Activity 14 Practice 155 Embedded Assessment 1 Angles and Triangles—Pool Angles 156 Activity 15 Similar Figures—The Same but Different 159 Lesson 15-1 Identify Similar Figures and Find Missing Lengths 159 Lesson 15-2 Indirect Measurement 164 Activity 15 Practice 167 Activity 16 Circles: Circumference and Area—Gardens Galore 169 Lesson 16-1 Circumference of a Circle 169 Lesson 16-2 Area of a Circle 173 Activity 16 Practice 177 Activity 17 Composite Area—Tile Designs 179 Lesson 17-1 Area of Composite Figures 179 d. Lesson 17-2 More Area of Composite Figures 183 e erv Activity 17 Practice 186 s e hts r Embedded Assessment 2 Circumference and Area—In the Paint 188 g d. All ri Activity 18 Sketching Solids—Putt-Putt Perspective 191 ar o Lesson 18-1 Shapes that Result from Slicing Solids 191 B e eg Lesson 18-2 Lateral and Total Surface Area of Prisms 199 oll C Lesson 18-3 Lateral and Total Surface Area of Pyramids 205 4 1 0 Activity 18 Practice 211 2 © Activity 19 Volume—Prisms and Pyramids—Berneen Wick’s Candles 213 Lesson 19-1 Find the Volume of Prisms 213 Lesson 19-2 Find the Volume of Pyramids 217 Activity 19 Practice 221 Embedded Assessment 3 Surface Area and Volume—Under the Sea 223 Contents vii CCoonntteennttss ccoonnttiinnuueedd 5 UNIT PROBABILITY Unit 5 Overview 225 Getting Ready 226 Activity 20 Exploring Probability—Spinner Games 227 Lesson 20-1 Making Predictions 227 Lesson 20-2 Investigating Chance Processes 231 Lesson 20-3 Estimating Probabilities 239 Lesson 20-4 Making Decisions 243 Activity 20 Practice 249 Activity 21 Probability—Probability Two Ways 251 Lesson 21-1 Equally Likely Outcomes 251 Lesson 21-2 Theoretical Probability 259 Lesson 21-3 Comparing Probabilities 265 Activity 21 Practice 268 Embedded Assessment 1 Finding Probabilities—Spinning Spinners and Random Picks 272 Activity 22 Games and Probability—Rock, Paper, Scissors…and Other Games 275 Lesson 22-1 Rock, Paper, Scissors 275 Lesson 22-2 More Rock, Paper, Scissors 279 Lesson 22-3 Boxes and Drawers 285 Lesson 22-4 More Boxes and Drawers 291 Activity 22 Practice 295 Activity 23 Probability—Estimating Probabilities Using Simulation 297 Lesson 23-1 What is Simulation? 297 d. Lesson 23-2 Using Random Numbers to Simulate Events 302 ve er s Lesson 23-3 Simulating a Compound Event 306 e s r Lesson 23-4 Finding Probabilities Using Simulation 310 ht g Activity 23 Practice 316 All ri d. ar Embedded Assessment 2 Probability and Simulation—Flipping Coins and Bo e g Random Choices 320 e oll C 4 6 1 UNIT STATISTICS 0 2 © Unit 6 Overview 323 Getting Ready 324 Activity 24 Statistics—Summer Reading Club 325 Lesson 24-1 Population and Census 325 Lesson 24-2 Sampling from a Population 328 Activity 24 Practice 336 viii SpringBoard® Mathematics with Meaning™ Level 2 Activity 25 Exploring Sampling Variability—Sample Speak 341 Lesson 25-1 Sample Statistic and Sampling Variability 341 Lesson 25-2 Predictions and Conclusions 346 Activity 25 Practice 353 Embedded Assessment 1 Random Sampling and Sampling Variability— School Populations 357 Activity 26 Comparative Statistics—Seventh-Grade Students 361 Lesson 26-1 Two Sample Means 361 Lesson 26-2 Difference in Terms of MAD 371 Lesson 26-3 Calculating MAD for a Sample 380 Activity 26 Practice 387 Embedded Assessment 2 Comparing Populations—One Mean Arm Span 391 7 UNIT PERSONAL FINANCIAL LITERACY Unit 7 Overview 393 Getting Ready 394 Activity 27 Budgeting and Money Management—How Much Is Too Much? 395 Lesson 27-1 Understanding Earnings and Budgets 395 Lesson 27-2 Financial Planning 400 Activity 27 Practice 404 RESOURCES 405 Formulas 406 Learning Strategies 410 Glossary 413 Academic Vocabulary Graphic Organizers 423 d. e v er s e s r ht g All ri d. ar o B e g e oll C 4 1 0 2 © Contents ix TToo tthhee SSttuuddeenntt Welcome to the SpringBoard program. We hope you will discover how SpringBoard can help you achieve high academic standards, reach your learning goals, and prepare for success in future mathematics studies. The program has been created with you in mind: the content you need to learn, the tools to help you learn, and the critical thinking skills that help you build confidence in your own knowledge of mathematics. The College Board publishes the SpringBoard program. It also publishes the PSAT/NMSQT, the SAT, and the Advanced Placement exams—all exams that you are likely to encounter in your student years. Preparing you to perform well on those exams and to develop the mathematics skills needed for high school success is the primary purpose of this program. Standards-Based Mathematics Learning Knowledge of mathematics helps prepare you for future success in college, in work, and in your personal life. We all encounter some form of mathematics daily, from calculating the cost of groceries to determining the cost of materials and labor needed to build a new road. The SpringBoard program is based on learning standards that identify the mathematics skills and knowledge that you should master to succeed in high school and in future college-level work. In this course, the standards follow these broad areas of mathematics knowledge: • Mathematical practices • Number and operations • Expressions, equations, and relationships • Ratio and proportionality • Geometry • Statistics and probability Mathematical practice standards guide your study of mathematics. They are actions you take to help you understand mathematical concepts rather than just mathematical procedures. For example, the mathematical practice d. e standards suggest the following: erv s e • Make sense of and connect mathematics concepts to everyday life and s r ht g situations around you. All ri • Model with mathematics to solve problems, justify solutions and their d. reasonableness, and communicate mathematical ideas. oar B • Use appropriate tools, such as number lines, protractors, technology, or ge e paper and pencil, strategically to help you solve problems. Coll 4 • Communicate abstract and quantitative reasoning both orally and in 01 2 writing through arguments and critiques. © • Analyze mathematical relationships through structure and repeated reasoning to connect ideas. • Attend to precision in both written and oral communication of your mathematical ideas. In the middle school years, your study of mathematics begins with a basic understanding of fractions and the operations performed with them. Your study continues with the development of a deep understanding of the rational numbers, their different representations, and the connections between these numbers and other number systems and operations. You will need a broad x SpringBoard® Mathematics with Meaning™ Level 2