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UNIT 1 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 Lesson 4-1 Sets of Rational Numbers 33 Lesson 4-2 Adding Rational Numbers 36 Lesson 4-3 Subtracting Rational Numbers 39 Lesson 4-4 Multiplying and Dividing Rational Numbers 41 Activity 4 Practice 44

Embedded Assessment 2 Rational Number Operations and Multiplying and Dividing Integers—Top to Bottom 47

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

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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 Pays 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

UNIT 3 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

Activity 10 Proportional Relationships and Scale—Patriotic Proportions 101 Lesson 10-1 Using Scale Drawings 101 Lesson 10-2 Using Maps 105 Lesson 10-3 Make Scale Drawings 108 Activity 10 Practice 111

Embedded Assessment 2 Proportional Relationships and Scale—Soccer Sense 113

Activity 11 Problems—Well, There Is More Than One Way 115 Lesson 11-1 Basic Percent Problems 115 Lesson 11-2 Sales Tax, Tips, and Commission 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

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Embedded Assessment 3 Percents and Proportions—Socializing and Selling 133

UNIT 4 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 Measurement 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 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 Lesson 17-2 More Area of Composite Figures 183 Activity 17 Practice 186

Embedded Assessment 2 Circumference and Area—In the Paint 188

Activity 18 Sketching Solids—Putt-Putt Perspective 191 Lesson 18-1 Shapes that Result from Slicing Solids 191 Lesson 18-2 Lateral and Total Surface Area of Prisms 199 Lesson 18-3 Lateral and Total Surface Area of Pyramids 205 Activity 18 Practice 211

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

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UNIT 5 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 Estimating Probabilities—Simulations 297 Lesson 23-1 What is Simulation? 297 Lesson 23-2 Using Random Numbers to Simulate Events 302 Lesson 23-3 Simulating a Compound Event 306 Lesson 23-4 Finding Probabilities Using Simulation 310 Activity 23 Practice 316

Embedded Assessment 2 Probability and Simulation—Flipping Coins and Random Choices 320

UNIT 6 STATISTICS 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

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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

UNIT 7 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

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To the StudentTo the StudentWelcome 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 LearningKnowledge 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 process standards• Number and operations• Proportionality• Expressions, equations, and relationships• Measurement and data• Personal financial literacy

Mathematical process standards guide your study of mathematics. They are actions you take to help you understand math rather than mathematical concepts. For example, the mathematical process standards suggest the following:

• Connect mathematics concepts to everyday life and situations around you.• Use models to solve problems and to justify solutions and their

reasonableness.• Choose tools, such as number lines, protractors, technology, or paper and

pencil to help you solve problems.• Communicate what you are learning both orally and in writing.• Create and use representations to communicate mathematical ideas.• Analyze mathematical relationships to connect ideas.• Learn and use precise mathematical language in both written and oral

communication.

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 understanding of addition, subtraction, and multiplication with rational numbers, along with computational fluency with whole-number operations.

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As you continue your studies, you will examine ratios and rates, which will allow you to make comparisons between numbers. Ratio and rates represent proportionality. Understanding the concept of proportionality is critical to future success in your study of algebra and the rest of the high school mathematics curriculum.

See pages xiii–xvi for a complete list of the Texas Essential Knowledge and Skills for this course.

Strategies for Learning MathematicsSome tools to help you learn are built into every activity. At the beginning of each activity, you will see suggested learning strategies. Each of these strategies is explained in full in the Resources section of your book. As you learn to use each strategy, you’ll have the opportunity to decide which strategies work best for you. Suggested learning strategies include:

• Reading strategies, which help you learn to look at problem descriptions in different ways, from marking the text to highlight key information to turning problem information into questions that help you break the problem down into its separate parts.

• Writing strategies, which help you focus on your purpose for writing and what you’re writing about.

• Problem-solving strategies, which give you multiple ways to approach the problem, from learning to identify the tasks within a problem to looking for patterns or working backward to see how the problem is set up.

• Collaborative strategies, which you’ll use with your classmates to explore concepts and problems in group discussions and working with partners.

Building Mathematics Knowledge and SkillsWhether it is mathematics or sports or cooking, one way we learn something really well is by practice and repetition. To help you learn mathematics, the SpringBoard program is built around problem solving, reasoning and justification, communication, connections between concepts and ideas, and visual representation of mathematical concepts.

Problem Solving Many of the problems in this book are based on real-life situations that require you to analyze the situation and the information in the problem, make decisions, determine the strategies you’ll use to solve the problem, and justify your solution. Having a real-world focus helps you see how mathematics is used in everyday life.

Reasoning and Justification One part of learning mathematics, or any subject, is learning not only how to solve problems but also why you solved them the way you did. You will have many opportunities to predict possible solutions and then to verify solutions. You will be asked to explain the reasoning behind how you solved the problem, the mathematics concepts involved, and why your approach was appropriate for solving the problem.

Communication When learning a language, saying words out loud helps you learn to pronounce the words and to remember them. Communicating about mathematics, orally and in writing, with your classmates and teachers helps

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you organize your learning and explain mathematics concepts and problem-solving strategies more precisely. Sharing your ideas and thoughts allows you and your classmates to build on each other’s ideas and expand your own understanding.

Mathematics Connections As you study mathematics, you will learn many different concepts and ways of solving problems. Reading the problem descriptions will take you into the real-life applications of mathematics. As you develop your mathematics knowledge, you will see the many connections between mathematics concepts and between mathematics and your own life.

Representations Artists create representations through drawings and paintings. In mathematics, representations can take many forms, such as numeric, verbal, graphic, or symbolic. In this course, you are encouraged to use representations to organize problem information, present possible solutions, and communicate your reasoning. Creating representations is a tool you can use to gain understanding of concepts and communicate that understanding to others.

We hope you enjoy your study of mathematics using the SpringBoard program. We, the writers, are all classroom teachers, and we created this program because we love mathematics. We wanted to inspire you to learn mathematics and build confidence that you can be successful in your math studies and in using mathematics in daily life.

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