Springboard Mathematics: Course 2

420 Pages·26.341 MB·English

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