i-xvi SB MS1 SE FMsbdasset.evo-text.com/ebook/public/documents/Grade.6.SB...Embedded Assessment 2 Expressions and Equations—The School Book Fair 211 UNIT 4 RATIOS Unit 4 Overview

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UNIT 1 NUMBER CONCEPTS Unit 1 Overview 1 Getting Ready 2

Activity 1 Whole Numbers and Decimals—Science, Shopping, and Society 3 Lesson 1-1 Comparing and Ordering Whole Numbers and Decimals 3 Lesson 1-2 Adding and Subtracting Decimals 6 Lesson 1-3 Multiplying Decimals 11 Lesson 1-4 Dividing Whole Numbers 15 Lesson 1-5 Dividing Decimals 19 Activity 1 Practice 23

Embedded Assessment 1 Comparing and Computing with Whole Numbers and Decimals—For the Birds 25

Activity 2 Prime Factorization and Exponents—The Primes of Your Life 27 Lesson 2-1 Prime Factorization 27 Lesson 2-2 Exponents 30 Activity 2 Practice 33

Activity 3 Greatest Common Factor and Least Common Multiple—Parties and Pups 35 Lesson 3-1 Greatest Common Factor 35 Lesson 3-2 Least Common Multiple 38 Activity 3 Practice 41

Embedded Assessment 2 Prime Factorization, Exponents, GCF, and LCM— Winter Sports 43

Activity 4 Fractions and Mixed Numbers—The Choice Is Yours 45 Lesson 4-1 Meaning of Fractions 45 Lesson 4-2 Comparing and Ordering Fractions 50 Lesson 4-3 Mixed Numbers 56 Lesson 4-4 Comparing and Ordering Mixed Numbers 60 Activity 4 Practice 62

Activity 5 Multiplying Fractions and Mixed Numbers—Skateboarding Fun! 63 Lesson 5-1 Multiplying by Fractions 63 Lesson 5-2 Multiplying Mixed Numbers 67 Activity 5 Practice 69

Activity 6 Dividing Fractions and Mixed Numbers—How Many Sandwiches? 71 Lesson 6-1 Dividing by Fractions 71 Lesson 6-2 Dividing Mixed Numbers 76 Activity 6 Practice 77

Embedded Assessment 3 Multiplying and Dividing Fractions and Mixed Numbers— Juan’s Bookcase 79

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UNIT 2 INTEGERS Unit 2 Overview 81 Getting Ready 82

Activity 7 Introduction to Integers—Get the Point? 83 Lesson 7-1 Integers and the Number Line 83 Lesson 7-2 Comparing and Ordering Integers 87 Activity 7 Practice 91

Activity 8 Adding and Subtracting Integers—What’s the Temperature? 93 Lesson 8-1 Using Models to Add Integers 93 Lesson 8-2 Using Rules to Add Integers 97 Lesson 8-3 Subtracting Integers 100 Activity 8 Practice 105

Embedded Assessment 1 Integer Sums and Differences—Hot and Cold 107

Activity 9 The Coordinate Plane—Map It Out! 109 Lesson 9-1 Integers in the Coordinate Plane 109 Lesson 9-2 Distance and Reflections in the Coordinate Plane 112 Activity 9 Practice 116

Activity 10 Multiplying and Dividing Integers—Temperature Ups and Downs 117 Lesson 10-1 Multiplying Integers 117 Lesson 10-2 Dividing Integers 122 Activity 10 Practice 125

Embedded Assessment 2 Coordinate Plane and Multiplying and Dividing Integers— Scavenger Hunt 127

UNIT 3 EXPRESSIONS AND EQUATIONS Unit 3 Overview 129 Getting Ready 130

Activity 11 Expressions—A Fairly Ordered Operation 131 Lesson 11-1 Order of Operations 131 Lesson 11-2 Evaluating Algebraic Expressions 136 Lesson 11-3 Writing Expressions 139 Lesson 11-4 Properties of Operations 143 Activity 11 Practice 147

Activity 12 Equations—Dog Gone 149 Lesson 12-1 Representing Situations with Equations 149 Lesson 12-2 Solutions of Equations 152 Activity 12 Practice 155

Embedded Assessment 1 Order of Operations and Expressions—The Cost of After-School Activities 157

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Activity 13 Solving Addition and Subtraction Equations—Music to My Ears 159 Lesson 13-1 Modeling and Solving Addition Equations 159 Lesson 13-2 Solving Addition Equations 162 Lesson 13-3 Modeling and Solving Subtraction Equations 166 Lesson 13-4 Solving Subtraction Equations 169

Activity 13 Practice 173

Activity 14 Solving Multiplication and Division Equations—Trash Talk 175 Lesson 14-1 Modeling and Solving Multiplication Equations 175 Lesson 14-2 Solving Multiplication Equations 178 Lesson 14-3 Solving Division Equations 182


Activity 15 Inequalities—Up in the Air 187 Lesson 15-1 Representing Situations with Inequalities 187 Lesson 15-2 Solving One-Step Inequalities 193


Activity 16 Expressions and Equations—Moving Right Along 199 Lesson 16-1 Representing Relationships 199 Lesson 16-2 Dependent and Independent Variables 204


Embedded Assessment 2 Expressions and Equations—The School Book Fair 211

UNIT 4 RATIOS Unit 4 Overview 213 Getting Ready 214

Activity 17 Understanding Ratios—All About Pets 215 Lesson 17-1 Understanding Ratios 215 Lesson 17-2 Ratios in Proportional Relationships 218


Activity 18 Reasoning with Ratios—A Picture Is Worth 223 Lesson 18-1 Solve Problems Using Ratios 223 Lesson 18-2 Converting Between Measurements Using Ratios 227

Lesson 18 Practice 231

Activity 19 Rates and Unit Rates—Zooming! 233 Lesson 19-1 Understanding Rates and Unit Rates 233 Lesson 19-2 Calculating Unit Rates 236 Lesson 19-3 Calculating Rates of Speed 240


Embedded Assessment 1 Ratios and Rates—A Summer Job 245

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Activity 20 Modeling and Understanding Percents—A “Cent” for Your Thoughts 247 Lesson 20-1 Using Models to Understand Percents 247 Lesson 20-2 Percents, Fractions, and Decimals 251 Lesson 20-3 More Percents, Decimals, and Fractions 256 Activity 20 Practice 259

Activity 21 Applying Percents—Feel the Beat 261 Lesson 21-1 Using Models to Understand Percents 261 Lesson 21-2 Find the Part Given a Percent and a Whole 264 Lesson 21-3 Find the Whole Given a Part and the Percent 268 Activity 21 Practice 271

Embedded Assessment 2 Understanding and Applying Percents—An Ice Cream Treat 273

UNIT 5 GEOMETRIC CONCEPTS Unit 5 Overview 275 Getting Ready 276

Activity 22 Angles and Triangles—Triangle Trivia 277 Lesson 22-1 Properties of Triangles and Side Lengths 277 Lesson 22-2 Properties of Triangles and Angle Measures 281 Activity 22 Practice 287

Activity 23 Area and Perimeter of Polygons—Play Area 289 Lesson 23-1 Recalling Quadrilaterals 289 Lesson 23-2 Perimeter and Area of Composite Figures 293 Lesson 23-3 Area of Triangles, Trapezoids, and Polygons 297 Activity 23 Practice 301

Activity 24 Polygons on the Coordinate Plane—Wall Art 305 Lesson 24-1 Defining Polygons on the Coordinate Plane 305 Lesson 24-2 Area of Polygons on a Coordinate Plane 309 Activity 24 Practice 313

Embedded Assessment 1 Geometric Concepts—Astronomy Logo 315

Activity 25 Nets and Surface Area—All Boxed Up 317 Lesson 25-1 Nets and Surface Area of Cubes 317 Lesson 25-2 Nets and Surface Area of Prisms 321 Activity 25 Practice 325

Activity 26 Volume—Crystal Collections 331 Lesson 26-1 Volume of Cubes 331 Lesson 26-2 Volume of Rectangular Prisms 335 Activity 26 Practice 339

Embedded Assessment 2 Surface Area and Volume of Prisms—Coloring Creations 343

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UNIT 6 DATA ANALYSIS Unit 6 Overview 345 Getting Ready 346

Activity 27 Summarizing Data Graphically—Making a Survey 347 Lesson 27-1 Survey Questions and Variability 347 Lesson 27-2 Types of Variables and Graphs 351 Lesson 27-3 Shapes of Distributions 357 Activity 27 Practice 362

Activity 28 Measures of Center—Bull’s Eye 363 Lesson 28-1 Mean and Outliers 363 Lesson 28-2 Median 367 Lesson 28-3 Summarize the Center of a Distribution 370 Activity 28 Practice 375

Embedded Assessment 1 Types of Variables and Measures of Center—Dribble, Shoot, Score! 377

Activity 29 Measures of Variability—Making the Grade 379 Lesson 29-1 Range 379 Lesson 29-2 Mean Absolute Deviation 382 Lesson 29-3 Interquartile Range (IQR) 386 Activity 29 Practice 390

Activity 30 Summarizing Numerical Data Graphically—Batter Up! 391 Lesson 30-1 Box Plots 391 Lesson 30-2 Histograms 397 Lesson 30-3 More on Histograms 401 Activity 30 Practice 405

Embedded Assessment 2 Measures of Variability and Numerical Graphs— “Take a Snapshot” Revisited 407

UNIT 7 PERSONAL FINANCIAL LITERACY Unit 7 Overview 409 Getting Ready 410

Activity 31 Using Financial Services—You Can Bank on It 411 Lesson 31-1 Understanding Bank Accounts 411 Lesson 31-2 Using Credit 414 Lesson 31-3 Planning for the Future 416 Activity 31 Practice 420

RESOURCES 421 Formulas 422 Learning Strategies 426 Glossary 429 Academic Vocabulary Graphic Organizers 439

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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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i-xvi SB MS1 SE FMsbdasset.evo-text.com/ebook/public/documents/Grade.6.SB...Embedded Assessment 2 Expressions and Equations—The School Book Fair 211 UNIT 4 RATIOS Unit 4 Overview