Book Saxon Math Course 3 pdf - Web Education

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(2) Course 3. Student Edition. Stephen Hake.

(3) ACKNOWLEDGEMENTS. This book was made possible by the significant 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.

(4) 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 Richardson, TX. Stockton, CA. Nogales, AZ. Brenda Halulka. Benjamin Swagerty. Joquita McKibben. Atlanta, GA. Moore, OK. Consultant Manager Pensacola, FL. Marilyn Lance. Kristyn Warren. East Greenbush, NY. Macedonia, OH. Ann Norris. Mary Warrington. Wichita Falls, TX. East Wenatchee, WA. John Anderson Lowell, IN. Beckie Fulcher Gulf Breeze, FL. iii.

(5) CONTENTS OVERVIEW. 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.

(6) TA B LE O F CO NTE NT S. TA B LE O F CO N T E N T S Integrated and Distributed Units of Instruction. Section 1. Lessons 1–10, Investigation 1. Math Focus: Number & Operations • Measurement Distributed Strands: Number & Operations • Algebra • Geometry • Measurement • Data Analysis & Probability • Problem Solving Lesson 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 • Number Line: Comparing and Ordering Integers. Maintaining & Extending. Lesson 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 • Operations of Arithmetic. Facts pp. 6, 12, 19, 26, 31, 36, 41, 47, 54, 60. Lesson 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 • Addition and Subtraction Word Problems Lesson 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 • Multiplication and Division Word Problems Lesson 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 • Fractional Parts Lesson 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 • Converting Measures. Power Up. Mental Math Strategies pp. 6, 12, 19, 26, 31, 36, 41, 47, 54, 60 Problem Solving Strategies pp. 6, 12, 19, 26, 31, 36, 41, 47, 54, 60. Enrichment Early Finishers pp. 11, 25, 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.

(7) TA B LE O F CO 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 • Percents. Maintaining & Extending. Lesson 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 • Decimal Numbers. Facts pp. 72, 78, 85, 92, 97, 103, 108, 114, 120, 126. Lesson 13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 • Adding and Subtracting Fractions and Mixed Numbers. Mental Math Strategies pp. 72, 78, 85, 92, 97, 103, 108, 114, 120, 126. Lesson 14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 • Evaluation • Solving Equations by Inspection. Problem Solving Strategies pp. 72, 78, 85, 92, 97, 103, 108, 114, 120, 126. Lesson 15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 • Powers and Roots 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. Power Up. Enrichment Early Finishers pp. 107, 119, 125.

(8) TA B LE O F CO NTE NT S. Section 3. Lessons 21–30, Investigation 3. Math Focus: Number & Operations Distributed Strands: Number & Operations • Algebra • Geometry • Problem Solving Lesson 21 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 • Distributive Property • Order of Operations Lesson 22 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 • Multiplying and Dividing Fractions Lesson 23 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 • Multiplying and Dividing Mixed Numbers. Maintaining & Extending. Power Up Facts pp. 139, 146, 153, 159, 163, 169, 176, 181, 186, 192 Mental Math Strategies pp. 139, 146, 153, 159, 163, 169, 176, 181, 186, 192. Lesson 24 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 • Adding and Subtracting Decimal Numbers. Problem Solving Strategies pp. 139, 146, 153, 159, 163, 169, 176, 181, 186, 192. Lesson 25 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 • Multiplying and Dividing Decimal Numbers. Enrichment. Lesson 26 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 • Transformations Activity Describing Transformations. Early Finishers pp. 158, 180, 185, 191. 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.

(9) TA B LE O F CO 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 • Adding Integers • Collecting Like Terms Lesson 32 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210 • Probability. Power Up Facts pp. 202, 210, 218, 223, 229, 237, 245, 250, 257, 264. Lesson 33 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218 • Subtracting Integers. Mental Math Strategies pp. 202, 210, 218, 223, 229, 237, 245, 250, 257, 264. Lesson 34 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 • Proportions • Ratio Word Problems. Problem Solving Strategies pp. 202, 210, 218, 223, 229, 237, 245, 250, 257, 264. Lesson 35 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 • Similar and Congruent Polygons Lesson 36 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 • 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. Maintaining & Extending. Saxon Math Course 3. Enrichment Early Finishers pp. 217, 222, 244, 263, 270 Extensions p. 275.

(10) TA B LE O F CO NTE NT S. Section 5. Lessons 41–50, Investigation 5. Math Focus: Number & Operations • Algebra Distributed Strands: Number & Operations • Algebra • Geometry • Measurement • Problem Solving Lesson 41 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277 • Functions. Maintaining & Extending. Lesson 42 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287 • Volume. Facts pp. 277, 287, 294, 300, 308, 313, 319, 326, 330, 336. Lesson 43 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294 • Surface Area Activity Surface Area of a Box. Mental Math Strategies pp. 277, 287, 294, 300, 308, 313, 319, 326, 330, 336. Lesson 44 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300 • Solving Proportions Using Cross Products • Slope of a Line. Problem Solving Strategies pp. 277, 287, 294, 300, 308, 313, 319, 326, 330, 336. Lesson 45 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308 • Ratio Problems Involving Totals. Power Up. Enrichment Early Finishers pp. 307, 341. 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.

(11) TA B LE O F CO N T E N T S. Section 6. Lessons 51–60, Investigation 6. Math Focus: Number & Operations • Data Analysis & Probability Distributed Strands: Number & Operations • Algebra • Geometry • Measurement • Data Analysis & Probability • Problem Solving Lesson 51 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346 • Negative Exponents • Scientific Notation for Small Numbers Lesson 52 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354 • Using Unit Multipliers to Convert Measures • Converting Mixed-Unit to Single-Unit Measures Lesson 53 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360 • Solving Problems Using Measures of Central Tendency Lesson 54 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367 • Angle Relationships Lesson 55 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375 • Nets of Prisms, Cylinders, Pyramids, and Cones Activity Net of a Cone Lesson 56 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382 • The Slope-Intercept Equation of a Line Lesson 57 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389 • Operations with Small Numbers in Scientific Notation Lesson 58 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394 • Solving Percent Problems with Equations Lesson 59 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400 • Experimental Probability Lesson 60 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406 • Area of a Parallelogram Activity Area of a Parallelogram Investigation 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412 • Collect, Display, and Interpret Data. x. Saxon Math Course 3. Maintaining & Extending. Power Up Facts pp. 346, 354, 360, 367, 375, 382, 389, 394, 400, 406 Mental Math Strategies pp. 346, 354, 360, 367, 375, 382, 389, 394, 400, 406 Problem Solving Strategies pp. 346, 354, 360, 367, 375, 382, 389, 394, 400, 406. Enrichment Early Finishers pp. 353, 366, 374, 381, 399.

(12) TA B LE O F CO NTE NT S. Section 7. Lessons 61–70, Investigation 7. Math Focus: Algebra Distributed Strands: Number & Operations • Algebra • Geometry • Measurement • Data Analysis & Probability • Problem Solving Lesson 61 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415 • Sequences. Maintaining & Extending. Lesson 62 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422 • Graphing Solutions to Inequalities on a Number Line. Facts pp. 415, 422, 429, 435, 440, 446, 452, 457, 463, 470. Lesson 63 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429 • Rational Numbers, Non-Terminating Decimals, and Percents • Fractions with Negative Exponents Lesson 64 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435 • Using a Unit Multiplier to Convert a Rate Lesson 65 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 440 • Applications Using Similar Triangles. Power Up. Mental Math Strategies pp. 415, 422, 429, 435, 440, 446, 452, 457, 463, 470 Problem Solving Strategies pp. 415, 422, 429, 435, 440, 446, 452, 457, 463, 470. Enrichment Early Finishers pp. 462, 475. Lesson 66 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 446 • Special Right Triangles Lesson 67 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 452 • Percent of Change Lesson 68 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 457 • Probability Multiplication Rule Lesson 69 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463 • Direct Variation Lesson 70 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 470 • Solving Direct Variation Problems Investigation 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 476 • Probability Simulation Activity 1 Probability Simulation Activity 2 Design and Conduct a Simulation. Table of Contents. xi.

(13) TA B LE O F CO N T E N T S. Section 8. Lessons 71–80, Investigation 8. Math Focus: Algebra • Measurement Distributed Strands: Number & Operations • Algebra • Measurement • Data Analysis & Probability Lesson 71 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479 • Percent Change of Dimensions. Maintaining & Extending. Lesson 72 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 486 • Multiple Unit Multipliers. Facts pp. 479, 486, 491, 496, 502, 507, 514, 519, 525, 531. Lesson 73 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 491 • Formulas for Sequences. Mental Math Strategies pp. 479, 486, 491, 496, 502, 507, 514, 519, 525, 531. Lesson 74 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 496 • Simplifying Square Roots Lesson 75 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 502 • Area of a Trapezoid Lesson 76 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 507 • Volumes of Prisms and Cylinders Lesson 77 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514 • Inequalities with Negative Coefficients Lesson 78 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 519 • Products of Square Roots Lesson 79 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525 • Transforming Formulas Lesson 80 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 531 • Adding and Subtracting Mixed Measures • Polynomials Investigation 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 538 • Scatterplots Activity Make a Scatterplot and Graph a Best-fit Line. xii. Saxon Math Course 3. Power Up. Problem Solving Strategies pp. 479, 486, 491, 496, 502, 507, 514, 519, 525, 531. Enrichment Early Finishers pp. 485, 530.

(14) TA B LE O F CO NTE NT S. Section 9. Lessons 81–90, Investigation 9. Math Focus: Algebra • Measurement Distributed Strands: Number & Operations • Algebra • Geometry • Measurement • Data Analysis & Probability • Problem Solving Lesson 81 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545 • Central Angles and Arcs. Maintaining & Extending. Lesson 82 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 550 • Graphing Equations Using Intercepts. Facts pp. 545, 550, 557, 563, 568, 574, 580, 585, 593, 599. Lesson 83 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 557 • Probability of Dependent Events Lesson 84 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563 • Selecting an Appropriate Rational Number Lesson 85 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 568 • Surface Area of Cylinders and Prisms Lesson 86 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 574 • Volume of Pyramids and Cones. Power Up. Mental Math Strategies pp. 545, 550, 557, 563, 568, 574, 580, 585, 593, 599 Problem Solving Strategies pp. 545, 550, 557, 563, 568, 574, 580, 585, 593, 599. Enrichment Early Finishers pp. 567, 573, 584, 592, 598, 605. Lesson 87 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 580 • Scale Drawing Word Problems Lesson 88 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 585 • Review of Proportional and Non-Proportional Relationships Lesson 89 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 593 • Solving Problems with Two Unknowns by Graphing Lesson 90 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 599 • Sets Investigation 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 606 • Sampling Methods Activity Random Number Generators. Table of Contents. xiii.

(15) TA B LE O F CO N T E N T S. Section 10. Lessons 91–100, Investigation 10. Math Focus: Algebra • Measurement Distributed Strands: Algebra • Measurement • Geometry • Data Analysis & Probability Lesson 91 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 610 • Effect of Scaling on Perimeter, Area, and Volume. Maintaining & Extending. Lesson 92 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 617 • Areas of Rectangles with Variable Dimensions • Products of Binomials. Facts pp. 610, 617, 624, 629, 634, 640, 646, 651, 658, 664. Lesson 93 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 624 • Equations with Exponents. Mental Math Strategies pp. 610, 617, 624, 629, 634, 640, 646, 651, 658, 664. Lesson 94 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 629 • Graphing Pairs of Inequalities on a Number Line. Problem Solving Strategies pp. 610, 617, 624, 629, 634, 640, 646, 651, 658, 664. Lesson 95 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 634 • Slant Heights of Pyramids and Cones. Enrichment. Lesson 96 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 640 • Geometric Measures with Radicals Lesson 97 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 646 • Recursive Rules for Sequences Lesson 98 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 651 • Relations and Functions Lesson 99 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 658 • Inverse Variation Lesson 100 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 664 • Surface Areas of Right Pyramids and Cones Investigation 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 670 • Compound Interest Activity Calculating Interest and Growth. xiv. Power Up. Saxon Math Course 3. Early Finishers pp. 623, 645, 657, 669.

(16) TA B LE O F CO NTE NT S. Section 11. Lessons 101–110, Investigation 11. Math Focus: Algebra • Data Analysis & Probability Distributed Strands: Algebra • Data Analysis & Probability • Measurement • Geometry • Number & Operations • Problem Solving Lesson 101 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675 • Geometric Probability. Maintaining & Extending. Lesson 102 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 681 • Growth and Decay. Facts pp. 675, 681, 686, 691, 697, 702, 707, 712, 717, 722. Power Up. Lesson 103 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 686 • Line Plots • Box-and-Whisker Plots. Mental Math Strategies pp. 675, 681, 686, 691, 697, 702, 707, 712, 717, 722. Lesson 104 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 691 • Volume, Capacity, and Mass in the Metric System. Problem Solving Strategies pp. 675, 681, 686, 691, 697, 702, 707, 712, 717, 722. Lesson 105 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 697 • Compound Average and Rate Problems Lesson 106 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 702 • Reviewing the Effects of Scaling on Volume. Enrichment Early Finishers p. 690. Lesson 107 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 707 • Volume and Surface Area of Compound Solids Lesson 108 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 712 • Similar Solids Lesson 109 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 717 • Consumer Interest Lesson 110 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 722 • Converting Repeating Decimals to Fractions Investigation 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 727 • Non-Linear Functions Activity 1 Modeling Freefall Activity 2 Using the Graph of a Quadratic Function Activity 3 Maximization. Table of Contents. xv.

(17) TA B LE O F CO N T E N T S. Section 12. Lessons 111–120, Investigation 12. Math Focus: Geometry • Algebra Distributed Strands: Geometry • Algebra • Measurement • Number & Operations • Data Analysis & Probability Lesson 111 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 731 • Volume and Surface Area of a Sphere. Maintaining & Extending. Lesson 112 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 737 • Ratios of Side Lengths of Right Triangles. Facts pp. 731, 737, 742, 748, 754, 758, 763, 768, 773, 778. Lesson 113 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 742 • Using Scatterplots to Make Predictions Activity Using a Scatterplot to Make Predictions. Mental Math Strategies pp. 731, 737, 742, 748, 754, 758, 763, 768, 773, 778. Lesson 114 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 748 • Calculating Area as a Sweep. Problem Solving Strategies pp. 731, 737, 742, 748, 754, 758, 763, 768, 773, 778. Lesson 115 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 754 • Relative Sizes of Sides and Angles of a Triangle. Enrichment. Lesson 116 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 758 • Division by Zero Lesson 117 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 763 • Significant Digits Lesson 118 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 768 • Sine, Cosine, Tangent Lesson 119 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 773 • Complex Fractions Lesson 120 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 778 • Rationalizing a Denominator Investigation 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 782 • Proof of the Pythagorean Theorem. xvi. Saxon Math Course 3. Power Up. Early Finishers pp. 736, 741, 747, 781.

(18) LETTER FROM AUTHOR STEPHEN HAKE. Dear Student, We study mathematics because of its importance to our lives. Our school schedule, our trip to the store, the preparation of our meals, and many of the games we play involve mathematics. You will find that the word problems in this book are often drawn from everyday experiences. As you grow into adulthood, mathematics will become even more important. In fact, your future in the adult world may depend on the mathematics you have learned. This book was written to help you learn mathematics and to learn it well. For this to happen, you must use the book properly. As you work through the pages, you will see that similar problems are presented over and over again. Solving each problem day after day is the secret to success. Your book is made up of daily lessons and investigations. Each lesson has three parts. 1. The first part is a Power Up that includes practice of basic facts and mental math. These exercises improve your speed, accuracy, and ability to do math “in your head.” The Power Up also includes a problem-solving exercise to familiarize you with strategies for solving complicated problems. 2. The second part of the lesson is the New Concept. This section introduces a new mathematical concept and presents examples that use the concept. The Practice Set provides a chance to solve problems involving the new concept. The problems are lettered a, b, c, and so on. 3. The final part of the lesson is the Written Practice. This problem set reviews previously taught concepts and prepares you for concepts that will be taught in later lessons. Solving these problems helps you remember skills and concepts for a long time. Investigations are variations of the daily lesson. The investigations in this book often involve activities that fill an entire class period. Investigations contain their own set of questions instead of a problem set. Remember, solve every problem in every practice set, written practice set, and investigation. Do not skip problems. With honest effort, you will experience success and true learning that will stay with you and serve you well in the future.. Temple City, California. Letter from the Author. xvii.

(19) HOW TO USE YOUR TEXTBOOK Saxon Math Course 3 is unlike any math book you have used! It doesn’t have colorful photos to distract you from learning. The Saxon approach lets you see the beauty and structure within math itself. You will understand more mathematics, become more confident in doing math, and will be well prepared when you take high school math classes.. Power Yourself Up! Start off each lesson by practicing your basic skills and concepts, mental math, and problem solving. Make your math brain stronger by exercising it every day. Soon you’ll know these facts by memory!. --". xx. .ETSOF0RISMS

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(38) The front, top and right-side views are the three different rectangles that appear in the net. Each rectangle appears twice, because the front and back faces are congruent, as are the top and bottom faces and the left and right faces.. Top. Left. Front. Right. Bottom. Get Active!. Back. Dig into math with a hands-on activity. Explore a math concept with your friends as you work together and use manipulatives to see new connections in mathematics.. Activity. Net of a Cone Materials needed: unlined paper, compass, scissors, glue or tape, ruler. Using a compass, draw a circle with a radius of at least two inches. Cut out the circle and make one cut from the edge to the center of the circle. Form the lateral surface of a cone by overlapping the two sides of the cut. The greater the overlap, the narrower the cone. Glue or tape the overlapped paper so that the cone holds its shape.. cut. To make the circular base of the cone, measure the diameter of the open end of the cone and use a compass to draw a circle with the same diameter. (Remember, the radius is half the diameter.) Cut out the circle and tape it in place using two pieces of tape.. Thinking Skill. Now disassemble the cone to form a net. Cut open the cone by cutting the circular base free on one side. Unroll the lateral surface by making a straight cut to the point (apex) of the cone. The net of a cone has two parts, its circular base and a sector of a circle that forms the lateral surface of the cone.. Check It Out!. Connect. The formula for the surface area of a cone is s = π r l + π r 2. Which parts of the formula apply to which parts of the net? π r l applies to the lateral surface and π r 2 applies to the circular base.. base. lateral surface. Extend An alternate method for calculating the area of the lateral surface of a cone is to calculate central the area of the portion of a circle represented by angle the net of the lateral surface. Use a protractor to ra d measure the central angle of the lateral surface of iu s the cone you created. The measure of that angle is the fraction of a 360° circle represented by the lateral surface. Use a ruler to measure the radius. Find the area of a whole circle with that radius. Then find the area of the sector by multiplying the area of the whole circle by the central angle fraction . Answers will vary. 360. Lesson 55. The Practice Set lets you check to see if you understand today’s new concept.. Practice Set. 377. a. What is the lateral surface area of a tissue box with the dimensions shown? 112 in.2. 4 in.. b. What is the total surface area of a cube with edges 2 inches long? 24 in2. 5 in. 9 in.. c. Estimate the surface area of a cube with edges 4.9 cm long. 150 cm2 SXN_M8_SE_L055.indd 377. 2/28/06 1:01:21 PM. d.. Analyze. building.. Exercise Your Mind!. 8 ft. 20 ft 20 ft. e. Find a box at home (such as a cereal box) and measure its dimensions. Sketch the box on your paper and record its length, width, and height. Then estimate the number of square inches of cardboard used to construct the box. see student work. When you work the Written Practice exercises, you will review both today’s new concept and also math you learned in earlier lessons. Each exercise will be on a different concept — you never know what you’re going to get! It’s like a mystery game — unpredictable and challenging. As you review concepts from earlier in the book, you’ll be asked to use higherorder thinking skills to show what you know and why the math works.. Kwan is painting a garage. Find the lateral surface area of the 640 ft2. Written Practice. Strengthening Concepts. 1. Desiree drove north for 30 minutes at 50 miles per hour. Then, she drove (7) south for 60 minutes at 20 miles per hour. How far and in what direction is Desiree from where she started? 5 miles north 2. In the forest, the ratio of deciduous trees to evergreens is 2 to 7. If there are 400 deciduous trees in the forest, how many trees are in the forest? 1800 trees 3. Reginald left his house and rode his horse east for 3 hours at 9 miles (7) per hour. How fast and in which direction must he ride to get back to his house in an hour? 27 miles per hour west. (34). * 4. (42). Analyze What is the volume of a shipping box with dimensions 1 1 2 inches × 11 inches × 12 inches? 198 in.3. 5. How many square inches is the surface area of the shipping box described in problem 4? 333 in.2. (43). 7.. * 6. How many edges, faces, and vertices does a triangular pyramid have? 6 edges, 4 faces, 4 vertices. (Inv. 4). The mixed set of Written Practice is just like the mixed format of your state test. You’ll be practicing for the “big” test every day!. * 7. Graph y = −2x + 3. Is (4, −11) on the line?. no. (41). * 8. Find a the area and b circumference of the circle with a radius of 6 in. (39, 40) Express your answer in terms of π. a. 36π in.2 b. 12π in.. Lesson 43. SXN_M8_SE_L043.indd 297. 297. 2/28/06 5:31:27 PM. How to Use Your Textbook. xix.

(39) 6 -//" ÊÓ. ÊVÕÃÊ 0YTHAGOREAN4HEOREM. Become an Investigator!. 4HELONGESTSIDEOFARIGHTTRIANGLEISCALLEDTHEHYPOTENUSE4HEOTHERTWO SIDESARECALLEDLEGS.OTICETHATTHELEGSARETHESIDESTHATFORMTHERIGHT ANGLE4HEHYPOTENUSEISTHESIDEOPPOSITETHERIGHTANGLE. Dive into math concepts and explore the depths of math connections in the Investigations.. . . %VERYRIGHTTRIANGLEHASAPROPERTYTHATMAKESRIGHTTRIANGLESVERYIMPORTANT INMATHEMATICS4HEAREAOFASQUAREDRAWNONTHEHYPOTENUSEOFARIGHT TRIANGLEEQUALSTHESUMOFTHEAREASOFSQUARESDRAWNONTHELEGS. Continue to develop your mathematical thinking through applications, activities, and extensions.. . . . . . . !SMANYASYEARSAGOANCIENT%GYPTIANSKNEWOFTHISIMPORTANT ANDUSEFULRELATIONSHIPBETWEENTHESIDESOFARIGHTTRIANGLE4ODAYTHE RELATIONSHIPISNAMEDFORA'REEKMATHEMATICIANWHOLIVEDABOUT"# 4HE'REEKSNAMEWAS0YTHAGORASANDTHERELATIONSHIPISCALLEDTHE 0YTHAGOREAN4HEOREM. 4HE0 YTHAGOREAN4HEOREMISANEQUATIONTHATRELATESTHESIDESOFARIGHT TRIANGLEINTHISWAYTHESUMOFTHESQUARESOFTHELEGSEQUALSTHESQUAREOF THEHYPOTENUSE LEGàLEGâHYPOTENUSE )FWELETTHELETTERSAANDBREPRESENTTHELENGTHSOFTHELEGSANDCTHELENGTH OFTHEHYPOTENUSE

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(42) PROBLEM-SOLVING OVERVIEW. Problem Solving As we study mathematics we learn how to use tools that help us solve problems. We face mathematical problems in our daily lives, in our careers, and in our efforts to advance our technological society. We can become powerful problem solvers by improving our ability to use the tools we store in our minds. In this book we will practice solving problems every day.. four-step problemsolving process. Solving a problem is like arriving at a destination, so the process of solving a problem is similar to the process of taking a trip. Suppose we are on the mainland and want to reach a nearby island. Island Mainland. Problem-Solving Process. Taking a Trip. Step 1: Understand. Know where you are and where you want to go.. We are on the mainland and want to go to the island.. Step 2: Plan. Plan your route.. We might use the bridge, the boat, or swim.. Step 3: Solve. Follow the plan.. Take the journey to the island. Step 4: Check. Check that you have reached the right place.. Verify that you have reached your desired destination.. Problem-Solving Overview. 1.

(43) When we solve a problem, it helps to ask ourselves some questions along the way. Ask Yourself Questions. Follow the Process Step 1: Understand. What information am I given? What am I asked to find or do?. Step 2: Plan. How can I use the given information to solve the problem? What strategy can I use to solve the problem?. Step 3: Solve. Am I following the plan? Is my math correct?. Step 4: Check (Look Back). Does my solution answer the question that was asked? Is my answer reasonable?. Below we show how we follow these steps to solve a word problem.. Example Josh wants to buy a television. He has already saved $68.25. He earns $35 each Saturday stocking groceries in his father’s store. The sizes and prices of the televisions available are shown at right. If Josh works and saves for 5 more weekends, what is the largest television he could buy?. Televisions 15" $149.99 17" $199.99 20" $248.99. Solution Step 1: Understand the problem. We know that Josh has $68.25 saved. We know that he earns $35.00 every weekend. We are asked to decide which television he could buy if he works for 5 more weekends. Step 2: Make a plan. We cannot find the answer in one step. We make a plan that will lead us toward the solution. One way to solve the problem is to find out how much Josh will earn in 5 weekends, then add that amount to the money he has already saved, then determine the largest television he could buy with the total amount of money. Step 3: Solve the problem. (Follow the Plan.) First we multiply $35 by 5 to determine how much Josh will earn in 5 weekends. We could also find 5 multiples of $35 by making a table. Weekend Amount. 2. Saxon Math Course 3. 1. 2. 3. 4. 5. $35. $70. $105. $140. $175.

(44) $35 ×5 $175 Josh will earn $175 in 5 weekends. Now we add $175 to $68.25 to find the total amount he will have. +. $175 68.25 $243.25. We find that Josh will have $243.25 after working 5 more weekends. When we compare the total to the prices, we can see that Josh can buy the 17″ television. Step 4: Check your answer. (Look Back.) We read the problem again. The problem asked which television Josh could buy after working five weekends. We found that in five weekends Josh will earn $175.00, which combined with his $68.25 savings gives Josh $243.25. This is enough money to buy the 17″ television. 1. List in order the four steps in the problem-solving process. 2. What two questions do we answer to help us understand a problem? Refer to the text below to answer problems 3–8. Mary wants to put square tiles on the kitchen floor. The tile she has selected is 12 inches on each side and comes in boxes of 20 tiles for $54 per box. Her kitchen is 15 feet 8 inches long and 5 feet 9 inches wide. How many boxes of tile will she need and what will be the price of the tile, not including tax? 3. What information are we given? 4. What are we asked to find? 5. Which step of the four-step problem-solving process have you completed when you have answered problems 3 and 4? 6. Describe your plan for solving the problem. Besides the arithmetic, is there anything else you can draw or do that will help you solve the problem? 7. Solve the problem by following your plan. Show your work and any diagrams you used. Write your solution to the problem in a way someone else will understand. 8. Check your work and your answer. Look back to the problem. Be sure you used the information correctly. Be sure you found what you were asked to find. Is your answer reasonable?. Problem-Solving Overview. 3.

(45) problemsolving strategies. As we consider how to solve a problem we choose one or more strategies that seem to be helpful. Referring to the picture at the beginning of this lesson, we might choose to swim, to take the boat, or to cross the bridge to travel from the mainland to the island. Other strategies might not be as effective for the illustrated problem. For example, choosing to walk or bike across the water are strategies that are not reasonable for this situation. Problem-solving strategies are types of plans we can use to solve problems. Listed below are ten strategies we will practice in this book. You may refer to these descriptions as you solve problems throughout the year. Act it out or make a model. Moving objects or people can help us visualize the problem and lead us to the solution. Use logical reasoning. All problems require reasoning, but for some problems we use given information to eliminate choices so that we can close in on the solution. Usually a chart, diagram, or picture can be used to organize the given information and to make the solution more apparent. Draw a picture or diagram. Sketching a picture or a diagram can help us understand and solve problems, especially problems about graphs or maps or shapes. Write a number sentence or equation. We can solve many word problems by fitting the given numbers into equations or number sentences and then finding the unknown numbers. Make it simpler. We can make some complicated problem easier by using smaller numbers or fewer items. Solving the simpler problem might help us see a pattern or method that can help us solve the complex problem. Find a pattern. Identifying a pattern that helps you to predict what will come next as the pattern continues might lead to the solution. Make an organized list. Making a list can help us organize our thinking about a problem. Guess and check. Guessing a possible answer and trying the guess in the problem might start a process that leads to the answer. If the guess is not correct, use the information from the guess to make a better guess. Continue to improve your guesses until you find the answer. Make or use a table, chart, or graph. Arranging information in a table, chart, or graph can help us organize and keep track of data. This might reveal patterns or relationships that can help us solve the problem. Work backwards. Finding a route through a maze is often easier by beginning at the end and tracing a path back to the start. Likewise, some problems are easier to solve by working back from information that is given toward the end of the problem to information that is unknown near the beginning of the problem.. 4. Saxon Math Course 3.

(46) 9. Name some strategies used in this lesson. The chart below shows where each strategy is first introduced in this textbook. Strategy. writing and problem solving. Lesson. Act It Out or Make a Model. Lesson 1. Use Logical Reasoning. Lesson 15. Draw a Picture or Diagram. Lesson 1. Write a Number Sentence or Equation. Lesson 31. Make It Simpler. Lesson 4. Find a Pattern. Lesson 19. Make an Organized List. Lesson 38. Guess and Check. Lesson 8. Make or Use a Table, Chart, or Graph. Lesson 21. Work Backwards. Lesson 2. Sometimes a problem will ask us to explain our thinking. Writing about a problem solving can help us measure our understanding of math. For these types of problems, we use words to describe the steps we used to follow our plan. This is a description of the way we solved the problem about tiling a kitchen. First, we round the measurements of the floor to 6 ft by 16 ft. We multiply to find the approximate area: 6 × 16 = 96 sq. ft. Then we count by 20s to find a number close to but greater than 96: 20, 40, 60, 80, 100. There are 20 tiles in each box, so Mary needs to buy 5 boxes of tiles. We multiply to find the total cost: $54 × 5 = $270. 10. Write a description of how we solved the problem in the example. Other times, we will be asked to write a problem for a given equation. Be sure to include the correct numbers and operations to represent the equation. 11. Write a word problem for the equation b = (12 × 10) ÷ 4.. Problem-Solving Overview. 5.

(47) LESSON. 1. Number Line: Comparing and Ordering Integers. Power Up facts mental math. Building Power Power Up A a. Calculation: Danielle drives 60 miles per hour for 2 hours. How far does she drive in total? b. Number Sense: 100 × 100 c. Estimation: 4.034 × 8.1301 d. Measurement: How long is the key?. inches. 1. 2. 3. e. Number Sense: 98 + 37 f. Percent: 50% of 50 g. Geometry: This figure represents a A line. B line segment. C ray. h1. Calculation: 7 + 5, + 3, + 1, ÷ 8, × 2, × 4. problem solving. Some problems describe physical movement. To solve such problems, we might act out the situation to understand what is happening. We can also draw a diagram to represent the movement in the problem. We try to keep diagrams simple so they are easy to understand. Problem: A robot is programmed to take two steps forward, then one step back. The robot will repeat this until it reaches its charger unit, which is ten steps in front of the robot. How many steps back will the robot take before it reaches the charger unit? Understand. We are told a robot takes two steps forward and then one step back. We are asked to find how many steps back the robot will take before it reaches its charger unit, which is ten steps away. Plan We will draw a diagram to help us count the steps. Your teacher might also select a student to act out the robot’s movements for the class.. 1. 6. As a shorthand, we will use commas to separate operations to be performed sequentially from left to right. This is not a standard mathematical notation.. Saxon Math Course 3.

(48) Solve. We use a number line for our diagram. We count two spaces forward from zero and then one space back and write “1” above the tick mark for 1. From that point, we count two spaces forward and one space back and write “2” above the 2. We continue until we reach the tick mark for 10. The numbers we write represent the total number of backward steps by the robot. We reach 10 after having taken eight steps back. The robot reaches the charger unit after taking eight steps back. 1. 2. 3. 4. 0. 5. 6. 7. 8. 5. 10. Check. To check for reasonableness, we rethink the problem situation with our answer in mind. It makes sense that the robot takes eight steps back before reaching the charger unit. Two steps forward and one step back is the same as one step forward. After completing this pattern 8 times, we expect the robot to be able to take two steps forward and reach its destination.. New Concept. Increasing Knowledge. The numbers we use in this book can be represented by points on a number line. Number line ⫺5. ⫺4. ⫺3. ⫺2. ⫺1. 0. 1. 2. 3. 4. 5. Points to the right of zero (the origin) represent positive numbers. Points to the left of zero represent negative numbers. Zero is neither positive nor negative. The tick marks on the number line above indicate the locations of integers, which include counting numbers (1, 2, 3, . . .) and their opposites (. . . −3, −2, −1) as well as zero. Thus all whole numbers (0, 1, 2, . . .) are integers, but not all integers are whole numbers. We will study numbers represented by points between the tick marks later in the book. Classify. Give an example of an integer that is not a whole number.. Counting numbers, whole numbers, and integers are examples of different sets of numbers. A set is a collection of items, like numbers or polygons. We use braces to indicate a set of numbers, and we write the elements (members) of the set within the braces. Reading Math The three dots, called an ellipsis, mean that the sequence continues without end.. The set of integers {. . . , −3, −2, −1, 0, 1, 2, 3, . . .} The set of whole numbers {0, 1, 2, 3, . . .} Analyze. How are the sets of whole numbers and integers different?. Lesson 1. 7.

(49) The absolute value of a number is the distance between the number and the origin on a number line. Absolute value is always a positive number because it represents a distance. Thus, the absolute value of −5 (negative five) is 5, because −5 is 5 units from zero. Two vertical bars indicate absolute value. “The absolute value of negative five is five.” −5 = 5 We can order and compare numbers by noting their position on the number line. We use the equal sign and the greater than/less than symbols (> and <, respectively) to indicate a comparison. When properly placed between two numbers, the small end of the symbol points to the lesser number.. Example 1 Arrange these integers in order from least to greatest. −3, 3, 0, 1. Solution We write the integers in the same order as they appear on the number line. −3, 0, 1, 3. Example 2 Compare: a. −3. −1. b. ∣−3∣. ∣−1∣. Solution Thinking Skill Connect. When you move from left to right on a number line, do the numbers increase or decrease? What happens to the numbers when you move from right to left?. a. We replace the circle with the correct comparison symbol. Negative three is less than negative one. −3 ⬍ −1 b. The absolute value of −3 is 3 and the absolute value of −1 is 1, and 3 is greater than 1. ∣−3∣ ⬎ ∣−1∣ We graph a point on a number line by drawing a dot at its location. Below we graph the numbers −4, −2, 0, 2, and 4. ⫺5. ⫺4. ⫺3. ⫺2. ⫺1. 0. 1. 2. 3. 4. 5. These numbers are members of the set of even numbers. The set of even numbers can be expressed as a sequence, an ordered list of numbers that follows a rule. The set of even numbers {. . . −4, −2, 0, 2, 4, . . .}. 8. Saxon Math Course 3.

(50) Example 3 Graph the numbers in this sequence on a number line. {. . . , −3, −1, 1, 3, . . .}. Solution This is the sequence of odd numbers. We sketch a number line and draw dots at −3, −1, 1, and 3. The ellipses show that the sequence continues, so we darken the arrowheads to show that the pattern continues. ⫺3. ⫺2. ⫺1. 0. 1. 2. 3. Example 4 Graph two numbers that are four units from zero.. Solution Both 4 and −4 are four units from zero. –5 –4 –3 –2 –1 0 1 2 3 4 5. Practice Set. a. Arrange these integers in order from least to greatest. −4, 3, 2, −1, 0 b. Which number in problem a is an even number but not a whole number? c. Compare: −2 d.. Model. −4. Graph the numbers in this sequence on a number line. . . . , −4, −2, 0, 2, 4, . . .. Simplify. e. −3 g.. f. 3. Analyze. Write two numbers that are ten units from zero.. h. Write an example of a whole number that is not a counting number.. Written Practice. Strengthening Concepts. * 1. Graph these numbers on a number line. (1). −5, 3, −2, 1 * 2.. Analyze. ⫺5. Arrange these numbers from least to greatest.. (1). −5, 3, −2, 1. * Asterisks indicate exercises that should be completed in class with teacher support as needed.. Lesson 1. 9.

(51) * 3. Use braces and digits to indicate the set of whole numbers. (1). * 4. Use braces and digits to indicate the set of even numbers. (1). 5. Which number in problem 1 is an even number? (1). 6. Which whole number is not a counting number? (1). 7. Write the graphed numbers as a sequence of numbers. (Assume the pattern continues.). (1). ⫺5. 0. 5. * 8. The sequence of numbers in problem 7 is part of what set of (1) numbers? Analyze. Decide if the statements in 9 −11 are true or false, and explain why.. 9. All whole numbers are counting numbers. (1). 10. All counting numbers are whole numbers. (1). * 11. If a number is a counting number or the opposite of a counting number, (1) then it is an integer. 12. What is the absolute value of 21? (1). 13. What is the absolute value of −13? (1). 14. What is the absolute value of 0? (1). 15. Compare: 5 (1). 16. Compare: −3 (1). * 17.. Evaluate. −7 −2. Compare: |−3|. |−2|. (1). 18. Graph these numbers on a number line: −5, 0, 5 (1). * 19. If |n| = 5, then n can be which two numbers? (1). 20. Write two numbers that are five units from zero. (1). 21. Graph these numbers on a number line. (1). −3, 0, 3 22. Write two numbers that are 3 units from 0. (1). 23. Graph the numbers in this sequence on a number line. (1). . . . , −15, −10, −5, 0, 5, 10, 15, . . . 24. What number is the opposite of 10? (1). 10. Saxon Math Course 3.

(52) 25. What is the sum when you add 10 and its opposite? (1). * 26. What number is the opposite of −2? (1). * 27. (1). Conclude. What is the sum when you add −2 and its opposite?. For multiple choice problems 28−30, choose all correct answers from the list. A counting numbers (natural numbers) B whole numbers C integers D none of these * 28. Negative seven is a member of which set of numbers? (1). 29. Thirty is a member of which set of numbers? (1). 30. One third is a member of which set of numbers? (1). Early Finishers Real-World Application. A group of eight students wants to ride a roller coaster at the local fair. Each passenger must be at least 48 inches tall to ride. The list below represents the number of inches each student’s height differs from 48 inches. (A negative sign indicates a height less than 48 inches.) −4. −3. −1. 5. 0. −2. 1. 4. a. Write each student’s height in inches, then arrange the heights from least to greatest. b. How many of the students represented by the list may ride the roller coaster?. Lesson 1. 11.

(53) LESSON. 2 Power Up facts mental math. Operations of Arithmetic Building Power Power Up A a. Calculation: Kyle rides his bicycle 15 miles per hour for 2 hours. How far does he travel? b. Number Sense: 203 + 87 c. Measurement: How long would a row of 12 push pins be? d. Percent: 10% of 100. inches. 1. 2. e. Estimation: 25.032 + 49.994 f. Geometry: This figure represents a. A line. B line segment. C ray. g. Number Sense: 2 × 16 h. Calculation: 4 + 3, + 2, + 1, + 0. problem solving. A number of problems in this book will ask us to “fill in the missing digits” in an addition, subtraction, multiplication, or division problem. We can work backwards to solve such problems. Problem: Copy this problem and fill in the missing digits: $_0_8 − $432_ $4_07 Understand. We are shown a subtraction problem with missing digits. We are asked to fill in the missing digits. Plan. We will work backwards and use number sense to find the missing digits one-by-one. This is a subtraction problem, so we can look at each column and think of “adding up” to find missing digits. Solve. We look at the first column and think, “7 plus what number equals 8?” (1). We write a 1 in the blank. We move to the tens column and think, “0 plus 2 is what number?” We write a 2 in the tens place of the minuend (the top number). Then we move to the hundreds column and think, “What number plus 3 equals a number that ends in 0? We write a 7 in the difference and remember to regroup the 1 in the thousands column. We move to the thousands column and think, “4 plus 4 plus 1 (from regrouping) equals what number?” We write a 9 in the remaining blank.. 12. Saxon Math Course 3.

(54) Check. We filled in all the missing digits. Using estimation our answer seems reasonable, since $4700 + $4300 = $9000. We can check our answer by performing the subtraction or by adding. $9028 − $4321 $4707. New Concept. $4707 + $4321 $9028. Increasing Knowledge. The fundamental operations of arithmetic are addition, subtraction, multiplication, and division. Below we review some terms and symbols for these operations. Terminology addend + addend = sum minuend − subtrahend = difference factor × factor = product dividend ÷ divisor = quotient. Example 1 What is the quotient when the product of 3 and 6 is divided by the sum of 3 and 6?. Solution First we find the product and sum of 3 and 6. product of 3 and 6 = 18 sum of 3 and 6 = 9 Then we divide the product by the sum. 18 ÷ 9 = 2 Three numbers that form an addition fact also form a subtraction fact. 5+3=8 8−3=5 Likewise, three numbers that form a multiplication fact also form a division fact. 4 × 6 = 24 24 ÷ 6 = 4 We may use these relationships to help us check arithmetic answers.. Lesson 2. 13.

(55) Example 2 Simplify and check: a. 706 − 327. b. 450 ÷ 25. Solution Thinking Skill. We simplify by performing the indicated operation.. Represent. Form another addition fact and another subtraction fact using the numbers 706, 327, and 379.. a.. 18 b. 25 冄 450. 706 − 327 379. We can check subtraction by adding, and we can check division by multiplying. a.. b.. 379 + 327 706 ✓. 25 × 18 200 250 450 ✓. Symbols for Multiplication and Division. Math Language The term real numbers refers to the set of all numbers that can be represented by points on a number line.. “three times five”. 3 × 5, 3 ∙ 5, 3(5), (3)(5). “six divided by two”. 6 ÷ 2, 2 冄 6 , 2. 6. The table below lists important properties of addition and multiplication. In the second column we use letters, called variables to show that these properties apply to all real numbers. A variable can take on different values. Some Properties of Addition and Multiplication Name of Property. Representation. Example. Commutative Property of Addition. a+b=b+a. 3+4=4+3. Commutative Property of Multiplication. a∙b=b∙a. 3∙4=4∙3. Associative Property of Addition. (a + b) + c = a + (b + c). (3 + 4) + 5 = 3 + (4 + 5). Associative Property of Multiplication. (a ∙ b) ∙ c = a · (b · c). (3 ∙ 4) ∙ 5 = 3 ∙ (4 ∙ 5). Identity Property of Addition. a+0=a. 3+0=3. Identity Property of Multiplication. a∙1=a. 3∙1=3. Zero Property of Multiplication. a∙0=0. 3∙0=0. We will use these properties throughout the book to simplify expressions and solve equations.. 14. Saxon Math Course 3.

(56) Demonstrate the Associative Property of Addition using the numbers 3, 5, and 8. Represent. Example 3 Show two ways to simplify this expression, justifying each step. (25 ∙ 15) ∙ 4. Solution There are three factors, but we multiply only two numbers at a time. We multiply 25 and 15 first. Step: (25 ∙ 15) ∙ 4. Justification: Given. 375 ∙ 4. Multiplied 25 and 15. 1500. Multiplied 375 and 4. Instead of first multiplying 25 and 15, we can use properties of multiplication to rearrange and regroup the factors so that we first multiply 25 and 4. Changing the arrangement of factors can make the multiplication easier to perform. Step:. Justification:. (25 ∙ 15) ∙ 4. Given. (15 ∙ 25) ∙ 4. Commutative Property of Multiplication. 15 ∙ (25 · 4). Associative Property of Multiplication. 15 ∙ 100 1500. Multiplied 25 and 4 Multiplied 15 and 100. Notice that the properties of addition and multiplication do not apply to subtraction and division. Order matters when we subtract or divide. 5−3=2. but. 3 − 5 = −2. 8÷4=2. but. 4÷8=. 1 2. Example 4 Simplify 100 − 365.. Solution Reversing the order of the minuend and the subtrahend reverses the sign of the difference. 365 − 100 = 265 so 100 − 365 = −265. Example 5 Find the value of x and y in the equations below. a. 6 + x = 30. b. 6y = 30 Lesson 2. 15.

(57) Solution The letters x and y represent numbers and are unknowns in the equations. a. We can find an unknown addend by subtracting the known addend(s) from the sum. 30 − 6 = 24 Thus, x = 24. b. We can find an unknown factor by dividing the product by the known factor(s). 30 ÷ 6 = 5 Thus, y = 5.. Practice Set. Name each property illustrated in a–d. a. 4 ∙ 1 = 4. b. 4 + 5 = 5 + 4. c. (8 + 6) + 4 = 8 + (6 + 4) d. 0 ∙ 5 = 0 e. What is the difference when the sum of 5 and 7 is subtracted from the product of 5 and 7? f. Simplify: 36 − 87 g.. Justify Lee simplified the expression 5 · (7 · 8). His work is shown below. What properties of arithmetic did Lee use for steps 1 and 2 of his calculations?. 5 ∙ (7 ∙ 8). Given. 5 ∙ (8 ∙ 7) (5 ∙ 8) ∙ 7 40 ∙ 7 280. 5 ∙ 8 = 40 40 ∙ 7 = 280. h.. Explain. Explain how to check a subtraction answer.. i.. Explain. Explain how to check a division answer.. For j and k, find the unknown. j. 12 + m = 48. Written Practice * 1. (2). * 2. (2). 16. k. 12n = 48. Strengthening Concepts Analyze The product of 20 and 5 is how much greater than the sum of 20 and 5?. What is the quotient when the product of 20 and 5 is divided by the sum of 20 and 5? Analyze. Saxon Math Course 3.

(58) 3. The sum of 10 and 20 is 30. (2). 10 + 20 = 30 Write two subtraction facts using these three numbers. 4. The product of 10 and 20 is 200. (2). 10 ∙ 20 = 200 Write two division facts using the same three numbers. * 5. a. Using the properties of multiplication, how can we rearrange the (2) factors in this expression so that the multiplication is easier? (25 ∙ 17) ∙ 4 b. What is the product? c. Which properties did you use? 6. Use braces and digits to indicate the set of counting numbers. (1). 7. Use braces and digits to indicate the set of whole numbers. (1). 8. Use braces and digits to indicate the set of integers. (1). Justify. Decide if the statements in 9–10 are true or false, and explain why.. 9. All whole numbers are counting numbers. (1). 10. All counting numbers are integers. (1). 11. Arrange these integers from least to greatest: 0, 1, −2, −3, 4 (1). 12. a. What is the absolute value of –12? (1). b. What is the absolute value of 11? Analyze. In 13–17, name the property illustrated.. * 13. 100 ∙ 1 = 100 (2). * 14. a + 0 = a (2). * 15. (5)(0) = 0 (2). * 16. 5 + (10 + 15) = (5 + 10) + 15 (2). * 17. 10 ∙ 5 = 5 ∙ 10 (2). 18. a. Name the four operations of arithmetic identified in Lesson 2. (2). b. For which of the four operations of arithmetic do the Commutative and Associative Properties not apply? * 19. If |n| = 10, then n can be which two numbers? (1). * 20.. Analyze. (1). a. 0. Compare: −1. b. −2. −3. c. |−2|. |−3|. Lesson 2. 17.

(59) * 21. Graph the numbers in this sequence on a number line: (1). . . . , −4, −2, 0, 2, 4, . . . 22. What number is the opposite of 20? (1). 23. Which integer is neither positive nor negative? (1). For multiple choice problems 24–26, choose all correct answers. * 24. One hundred is a member of which set of numbers? (1). A counting numbers (natural numbers) B whole numbers C integers D none of these * 25. Negative five is a member of which set of numbers? (1). A counting numbers (natural numbers) B whole numbers C integers D none of these * 26. One half is a member of which of these set of numbers? (1). A counting numbers (natural numbers) B whole numbers C integers D none of these Generalize. Simplify. 27. 5010 − 846 (2). 29. 780(49) (2). 18. Saxon Math Course 3. * 28. 846 − 5010 (2). 30. 5075 (2) 25.

(60) LESSON. 3 Power Up facts. Addition and Subtraction Word Problems Building Power Power Up A. mental math. a. Calculation: Sophie drives 35 miles per hour for 3 hours. How far does she drive? b. Estimation: 21 + 79 + 28 c. Number Sense: 1108 + 42 A. d. Measurement: If object A weighs 7 pounds, how much does object B weigh?. B. 3 Ibs. e. Percent: 50% of 100 f. Geometry: This figure represents a A line. B line segment. C ray. g. Number Sense: Find the two missing digits: 9 ×. =. 1. h. Calculation: 3 dozen roses, minus 5 roses, plus a rose, minus a dozen roses, ÷ 2. problem solving. Thirty-eight cars are waiting to take a ferry across a lake. The ferry can carry six cars. If the ferry starts on the same side of the lake as the cars, how many times will the ferry cross the lake to deliver all 38 cars to the other side of the lake?. New Concept. Increasing Knowledge. When we read a novel or watch a movie we are aware of the characters, the setting, and the plot. The plot is the storyline. Although there are many different stories, plots are often similar. Many word problems we solve with mathematics also have plots. Recognizing the plot helps us solve the problem. In this lesson we will consider word problems that are solved using addition and subtraction. The problems are like stories that have plots about combining, separating, and comparing. Problems about combining have an addition thought pattern. We can express a combining plot with a formula, which is an equation used to calculate a desired result. some + more = total s+m=t. Lesson 3. 19.

(61) See how the numbers in this story fit the formula. In the first half of the game, Heidi scored 12 points. In the second half, she scored 15 points. In the whole game, Heidi scored 27 points. In this story, two numbers are combined to make a total. (In some stories, more than two numbers are combined.) s+m=t 12 + 15 = 27 A story becomes a word problem if one of the numbers is missing, as we see in the following example.. Example 1 In the first half of the game, Heidi scored 12 points. In the whole game, she scored 27 points. How many points did Heidi score in the second half?. Solution Heidi scored some in the first half and some more in the second half. We are given the total. s+m=t 12 + m = 27 The “more” number is missing in the equation. Recall that we can find an unknown addend by subtracting the known addend from the sum. Since 27 − 12 = 15, we find that Heidi scored 15 points in the second half. The answer is reasonable because 12 points in the first half of the game plus 15 points in the second half totals 27 points. Example 1 shows one problem that we can make from the story about Heidi’s game. We can use the same formula no matter which number is missing because the missing number does not change the plot. However, the number that is missing does determine whether we add or subtract to find the missing number. • If the sum is missing, we add the addends. • If an addend is missing, we subtract the known addend(s) from the sum. s+m=t Find by subtracting.. Find by adding.. Now we will consider word problems about separating. These problems have a subtraction thought pattern. We can express a separating plot with a formula. starting amount − some went away = what is left s−a=l Here is a story about separating. Alberto went to the store with a twenty dollar bill. He bought a loaf of bread and a half-gallon of milk for a total of $4.83. The clerk gave him $15.17 in change.. 20. Saxon Math Course 3.

(62) In this story some of Alberto’s money went away when he bought the bread and milk. The numbers fit the formula. s−a=l Math Language Recall that the minuend is the number in a subtraction problem from which another number is subtracted.. $20.00 − $4.83 = $15.17 We can make a problem from the story by omitting one of the numbers, as we show in example 2. If a number in a subtraction formula is missing, we add to find the minuend. Otherwise we subtract from the minuend. s−a=l Find by adding.. Find by subtracting.. Example 2 Alberto went to the store with a twenty dollar bill. He bought a loaf of bread and a half-gallon of milk. The clerk gave him $15.17 in change. How much money did Alberto spend on bread and milk? Explain why your answer is reasonable.. Solution This story has a separating plot. We want to find how much of Alberto’s money went away. We write the numbers in the formula and find the missing number. s−a=l $20.00 − a = $15.17 We find the amount Alberto spent by subtracting $15.17 from $20.00. We find that Alberto spent $4.83 on bread and milk. Since Alberto paid $20 and got back about $15, we know that he spent about $5. Therefore $4.83 is a reasonable answer. We can check the answer to the penny by subtracting $4.83 from $20. The result is $15.17, which is the amount Alberto received in change.. Example 3 The hike to the summit of Mt. Whitney began from the upper trailhead at 8365 ft. The elevation of Mt. Whitney’s summit is 14,496 ft. Which equation shows how to find the elevation gain from the trailhead to the summit? A 8365 + g = 14,496. B 8365 + 14,496 = g. C g − 14,496 = 8365. D 8365 − g = 14,496. Solution A 8365 + g = 14,496 One way of comparing numbers is by subtraction. The difference shows us how much greater or how much less one number is compared to another number. We can express a comparing plot with this formula. greater − lesser = difference g−l=d Lesson 3. 21.