Problem Solving PDF
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Course 3 Student Edition Stephen Hake A C K N O W L E D G E M E N T S This book was made possible by the signifi cant contributions of many individuals and the dedicated efforts of a talented team at Harcourt Achieve. Special thanks to: • Melody Simmons and Chris Braun for suggestions and explanations for problem solving in Courses 1–3, • Elizabeth Rivas and Bryon Hake for their extensive contributions to lessons and practice in Course 3, • Sue Ellen Fealko for suggested application problems in Course 3. The long hours and technical assistance of John and James Hake on Courses 1–3, Robert Hake on Course 3, Tom Curtis on Course 3, and Roger Phan on Course 3 were invaluable in meeting publishing deadlines. The saintly patience and unwavering support of Mary is most appreciated. – Stephen Hake Staff Credits Editorial: Jean Armstrong, Shelley Farrar-Coleman, Marc Connolly, Hirva Raj, Brooke Butner, Robin Adams, Roxanne Picou, Cecilia Colome, Michael Ota Design: Alison Klassen, Joan Cunningham, Deborah Diver, Alan Klemp, Andy Hendrix, Rhonda Holcomb Production: Mychael Ferris-Pacheco, Heather Jernt, Greg Gaspard, Donna Brawley, John-Paxton Gremillion Manufacturing: Cathy Voltaggio Marketing: Marilyn Trow, Kimberly Sadler E-Learning: Layne Hedrick, Karen Stitt ISBN 1-5914-1884-4 © 2007 Harcourt Achieve Inc. and Stephen Hake All rights reserved. No part of the material protected by this copyright may be reproduced or utilized in any form or by any means, in whole or in part, without permission in writing from the copyright owner. Requests for permission should be mailed to: Paralegal Department, 6277 Sea Harbor Drive, Orlando, FL 32887. Saxon is a trademark of Harcourt Achieve Inc. 1 2 3 4 5 6 7 8 9 048 12 11 10 09 08 07 06 ABOUT THE AUTHOR Stephen Hake has authored five books in the Saxon Math series. He writes from 17 years of classroom experience as a teacher in grades 5 through 12 and as a math specialist in El Monte, California. As a math coach, his students won honors and recognition in local, regional, and statewide competitions. Stephen has been writing math curriculum since 1975 and for Saxon since 1985. He has also authored several math contests including Los Angeles County’s first Math Field Day contest. Stephen contributed to the 1999 National Academy of Science publication on the Nature and Teaching of Algebra in the Middle Grades. Stephen is a member of the National Council of Teachers of Mathematics and the California Mathematics Council. He earned his BA from United States International University and his MA from Chapman College. EDUCATIONAL CONSULTANTS Nicole Hamilton Heidi Graviette Melody Simmons Consultant Manager Stockton, CA Nogales, AZ Richardson, TX Brenda Halulka Benjamin Swagerty Joquita McKibben Atlanta, GA Moore, OK Consultant Manager Pensacola, FL Marilyn Lance Kristyn Warren East Greenbush, NY Macedonia, OH John Anderson Lowell, IN Ann Norris Mary Warrington Wichita Falls, TX East Wenatchee, WA Beckie Fulcher Gulf Breeze, FL iii C O N T E N T S O V E R V I E W Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v Letter from the Author . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii How to Use Your Textbook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xviii Introduction to Problem Solving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Section 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Lessons 1–10, Investigation 1 Section 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 Lessons 11–20, Investigation 2 Section 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 Lessons 21–30, Investigation 3 Section 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202 Lessons 31–40, Investigation 4 Section 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277 Lessons 41–50, Investigation 5 Section 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346 Lessons 51–60, Investigation 6 Section 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415 Lessons 61–70, Investigation 7 Section 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479 Lessons 71–80, Investigation 8 Section 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545 Lessons 81–90, Investigation 9 Section 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 610 Lessons 91–100, Investigation 10 Section 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675 Lessons 101–110, Investigation 11 Section 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 731 Lessons 111–120, Investigation 12 Appendix: Additional Topics in Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 785 Glossary with Spanish Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 859 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 897 iv Saxon Math Course 3 T A TA B L E O F C O N T E N T S B L E Integrated and Distributed Units of Instruction O F C O Section 1 Lessons 1–10, Investigation 1 N T Math Focus: E N Number & Operations • Measurement T Distributed Strands: S Number & Operations • Algebra • Geometry • Measurement • Data Analysis & Probability • Problem Solving Lesson 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Maintaining & Extending • Number Line: Comparing and Ordering Integers Power Up Lesson 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Facts pp. 6, 12, 19, 26, 31, • Operations of Arithmetic 36, 41, 47, 54, 60 Lesson 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Mental Math Strategies • Addition and Subtraction Word Problems pp. 6, 12, 19, 26, 31, 36, 41, Lesson 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 47, 54, 60 • Multiplication and Division Word Problems Problem Solving Strategies pp. 6, 12, 19, 26, 31, 36, 41, Lesson 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 47, 54, 60 • Fractional Parts Enrichment Lesson 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 Early Finishers pp. 11, 25, • Converting Measures 40, 53 Lesson 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 • Rates and Average • Measures of Central Tendency Lesson 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 • Perimeter and Area Lesson 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 • Prime Numbers Lesson 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 • Rational Numbers • Equivalent Fractions Investigation 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 • The Coordinate Plane Activity Coordinate Plane Table of Contents v TA B L E O F C O N T E N T S Section 2 Lessons 11–20, Investigation 2 Math Focus: Number & Operations • Geometry Distributed Strands: Number & Operations • Algebra • Measurement • Geometry • Problem Solving Lesson 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 Maintaining & Extending • Percents Power Up Lesson 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 Facts pp. 72, 78, 85, 92, 97, • Decimal Numbers 103, 108, 114, 120, 126 Lesson 13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 Mental Math Strategies • Adding and Subtracting Fractions and pp. 72, 78, 85, 92, 97, 103, Mixed Numbers 108, 114, 120, 126 Problem Solving Strategies Lesson 14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 pp. 72, 78, 85, 92, 97, 103, • Evaluation 108, 114, 120, 126 • Solving Equations by Inspection Enrichment Lesson 15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 Early Finishers pp. 107, • Powers and Roots 119, 125 Lesson 16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 • Irrational Numbers Lesson 17 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 • Rounding and Estimating Lesson 18 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 • Lines and Angles Lesson 19 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 • Polygons Lesson 20 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 • Triangles Investigation 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 • Pythagorean Theorem Activity Pythagorean Puzzle vi Saxon Math Course 3 T A B L E O F C O Section 3 Lessons 21–30, Investigation 3 N T E Math Focus: N Number & Operations T Distributed Strands: S Number & Operations • Algebra • Geometry • Problem Solving Lesson 21 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 Maintaining & Extending • Distributive Property Power Up • Order of Operations Facts pp. 139, 146, 153, 159, Lesson 22 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 163, 169, 176, 181, 186, 192 • Multiplying and Dividing Fractions Mental Math Strategies Lesson 23 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 pp. 139, 146, 153, 159, 163, • Multiplying and Dividing Mixed Numbers 169, 176, 181, 186, 192 Problem Solving Strategies Lesson 24 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 pp. 139, 146, 153, 159, 163, • Adding and Subtracting Decimal Numbers 169, 176, 181, 186, 192 Lesson 25 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 Enrichment • Multiplying and Dividing Decimal Numbers Early Finishers pp. 158, Lesson 26 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 180, 185, 191 • Transformations Activity Describing Transformations Lesson 27 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176 • Laws of Exponents Lesson 28 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 • Scientific Notation for Large Numbers Lesson 29 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 • Ratio Lesson 30 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 • Repeating Decimals Investigation 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 • Classifying Quadrilaterals Table of Contents vii TA B L E O F C O N T E N T S Section 4 Lessons 31–40, Investigation 4 Math Focus: Algebra • Measurement Distributed Strands: Number & Operations • Algebra • Geometry • Measurement • Data Analysis & Probability • Problem Solving Lesson 31 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202 Maintaining & Extending • Adding Integers Power Up • Collecting Like Terms Facts pp. 202, 210, 218, 223, Lesson 32 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 229, 237, 245, 250, 257, 264 • Probability Mental Math Strategies Lesson 33 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218 pp. 202, 210, 218, 223, 229, • Subtracting Integers 237, 245, 250, 257, 264 Lesson 34 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 Problem Solving Strategies • Proportions pp. 202, 210, 218, 223, 229, 237, 245, 250, 257, 264 • Ratio Word Problems Enrichment Lesson 35 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 Early Finishers pp. 217, • Similar and Congruent Polygons 222, 244, 263, 270 Lesson 36 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 Extensions p. 275 • Multiplying and Dividing Integers • Multiplying and Dividing Terms Lesson 37 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245 • Areas of Combined Polygons Lesson 38 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250 • Using Properties of Equality to Solve Equations Lesson 39 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 • Circumference of a Circle Lesson 40 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264 • Area of a Circle Investigation 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271 • Drawing Geometric Solids Activity 1 Sketching Prisms and Cylinders Using Parallel Projection Activity 2 Sketching Pyramids and Cones Activity 3 Create a Multiview Drawing Activity 4 One-Point Perspective Drawing viii Saxon Math Course 3 T A B L E O F C O Section 5 Lessons 41–50, Investigation 5 N T E Math Focus: N Number & Operations • Algebra T Distributed Strands: S Number & Operations • Algebra • Geometry • Measurement • Problem Solving Lesson 41 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277 Maintaining & Extending • Functions Power Up Lesson 42 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287 Facts pp. 277, 287, 294, 300, • Volume 308, 313, 319, 326, 330, 336 Lesson 43 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294 Mental Math Strategies • Surface Area pp. 277, 287, 294, 300, 308, Activity Surface Area of a Box 313, 319, 326, 330, 336 Problem Solving Strategies Lesson 44 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300 pp. 277, 287, 294, 300, 308, • Solving Proportions Using Cross Products 313, 319, 326, 330, 336 • Slope of a Line Enrichment Lesson 45 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308 Early Finishers pp. 307, 341 • Ratio Problems Involving Totals Lesson 46 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313 • Solving Problems Using Scientific Notation Lesson 47 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319 • Graphing Functions Lesson 48 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326 • Percent of a Whole Lesson 49 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330 • Solving Rate Problems with Proportions and Equations Lesson 50 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336 • Solving Multi-Step Equations Investigation 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342 • Graphing Transformations Table of Contents ix
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