Saxon Math, Course 2 (Student Edition)

919 Pages·2007·40.58 MB·english

by  Stephen Hake

Course 2
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 1-5914-1835-6
© 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.
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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
Lessons 11–20, Investigation 2
Section 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
Lessons 21–30, Investigation 3
Section 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
Lessons 31–40, Investigation 4
Section 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296
Lessons 41–50, Investigation 5
Section 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363
Lessons 51–60, Investigation 6
Section 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432
Lessons 61–70, Investigation 7
Section 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 502
Lessons 71–80, Investigation 8
Section 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 562
Lessons 81–90, Investigation 9
Section 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 631
Lessons 91–100, Investigation 10
Section 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 704
Lessons 101–110, Investigation 11
Section 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 778
Lessons 111–120, Investigation 12
Glossary with Spanish Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 847
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 881
iv Saxon Math Course 2
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TA B L E O F C O N T E N T S
B
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Integrated and Distributed Units of Instruction
O
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C
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Section 1 Lessons 1–10, Investigation 1 N
T
Math Focus: E
N
Number & Operations • Algebra
T
Distributed Strands: S
Number & Operations • Algebra • Geometry • Measurement • Problem Solving
Lesson 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Maintaining & Extending
• Arithmetic with Whole Numbers and Money
Power Up
• Variables and Evaluation
Facts pp. 6, 13, 20, 26, 34,
Lesson 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 40, 45, 53, 60, 66
• Properties of Operations
Mental Math Strategies
Lesson 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 pp. 6, 13, 20, 26, 34, 40, 45,
• Unknown Numbers in Addition, Subtraction, 53, 60, 66
Multiplication, and Division Problem Solving Strategies
pp. 6, 13, 20, 26, 34, 40, 45,
Lesson 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
53, 60, 66
• Number Line
• Sequences Enrichment
Early Finishers pp. 12, 25,
Lesson 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
33, 52
• Place Value Through Hundred Trillions
Extensions p. 74
• Reading and Writing Whole Numbers
Lesson 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
• Factors
• Divisibility
Lesson 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
• Lines, Angles and Planes
Lesson 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
• Fractions and Percents
• Inch Ruler
Lesson 9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
• Adding, Subtracting, and Multiplying Fractions
• Reciprocals
Lesson 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
• Writing Division Answers as Mixed Numbers
• Improper Fractions
Investigation 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
• Investigating Fractions and Percents with Manipulatives
Activity Using Fraction Manipulatives
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 • Problem Solving
Distributed Strands:
Number & Operations • Algebra • Geometry • Measurement • Problem Solving
Lesson 11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
Maintaining & Extending
• Problems About Combining
Power Up
• Problems About Separating
Facts pp. 75, 82, 88, 93,
Lesson 12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 100, 107, 114, 120, 128, 134
• Problems About Comparing
Mental Math Strategies
• Elapsed-Time Problems pp. 75, 82, 88, 93, 100, 107,
Lesson 13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 114, 120, 128, 134
• Problems About Equal Groups Problem Solving Strategies
pp. 75, 82, 88, 93, 100, 107,
Lesson 14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
114, 120, 128, 134
• Problems About Parts of a Whole
Enrichment
• Simple Probability
Early Finishers pp. 81, 87,
Lesson 15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
92, 113, 127, 133, 142
• Equivalent Fractions
• Reducing Fractions, Part 1
Lesson 16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
• U.S. Customary System
• Function Tables
Lesson 17 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
• Measuring Angles with a Protractor
Lesson 18 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
• Polygons
• Similar and Congruent
Lesson 19 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
• Perimeter
Activity Creating Formulas for Perimeters of Polygons
Lesson 20 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
• Exponents
• Rectangular Area, Part 1
• Square Root
Activity Creating Formulas for the Areas of Rectangles
and Squares
Investigation 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
• Using a Compass and Straightedge, Part 1
Activity Drawing Concentric Circles
vi Saxon Math Course 2
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O
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C
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Section 3 Lessons 21–30, Investigation 3 N
T
E
Math Focus:
N
Number & Operations • Problem Solving
T
Distributed Strands: S
Number & Operations • Geometry • Problem Solving
Lesson 21 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
Maintaining & Extending
• Prime and Composite Numbers
Power Up
• Prime Factorization
Facts pp. 149, 157, 163, 169,
Lesson 22 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 175, 182, 188, 194, 200, 208
• Problems About a Fraction of a Group
Mental Math Strategies
Lesson 23 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 pp. 149, 157, 163, 169, 175,
• Subtracting Mixed Numbers with Regrouping 182, 188, 194, 200, 208
Problem Solving Strategies
Lesson 24 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
pp. 149, 157, 163, 169, 175,
• Reducing Fractions, Part 2
182, 188, 194, 200, 208
Lesson 25 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
Enrichment
• Dividing Fractions
Early Finishers pp. 162,
Lesson 26 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 168, 187, 199, 207, 215
• Multiplying and Dividing Mixed Numbers
Lesson 27 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
• Multiples
• Least Common Multiple
• Equivalent Division Problems
Lesson 28 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
• Two-Step Word Problems
• Average, Part 1
Lesson 29 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
• Rounding Whole Numbers
• Rounding Mixed Numbers
• Estimating Answers
Lesson 30 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
• Common Denominators
• Adding and Subtracting Fractions with Different
Denominators
Investigation 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
• Coordinate Plane
Activity Coordinate Plane
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:
Number & Operations • Data Analysis & Probability
Distributed Strands:
Number & Operations • Geometry • Measurement • Data Analysis & Probability
Lesson 31 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
Maintaining & Extending
• Reading and Writing Decimal Numbers
Power Up
Lesson 32 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228 Facts pp. 221, 228, 235, 241,
• Metric System 247, 255, 264, 273, 280, 285
Lesson 33 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 Mental Math Strategies
pp. 221, 228, 235, 241, 247,
• Comparing Decimals
255, 264, 273, 280, 285
• Rounding Decimals
Problem Solving Strategies
Lesson 34 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241
pp. 221, 228, 235, 241, 247,
• Decimal Numbers on the Number Line
255, 264, 273, 280, 285
Activity Decimal Numbers on a Meterstick
Enrichment
Lesson 35 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247
Early Finishers pp. 234,
• Adding, Subtracting, Multiplying, and Dividing 246, 254, 263, 292
Decimal Numbers
Extensions p. 295
Lesson 36 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255
• Ratio
• Sample Space
Lesson 37 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264
• Area of a Triangle
• Rectangular Area, Part 2
Activity Area of a Triangle
Lesson 38 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273
• Interpreting Graphs
Lesson 39 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280
• Proportions
Lesson 40 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285
• Sum of the Angle Measures of a Triangle
• Angle Pairs
Activity Sum of the Angle Measures of a Triangle
Investigation 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
• Stem-and-Leaf Plots, Box-and-Whisker Plots
viii Saxon Math Course 2
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A
B
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O
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C
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Section 5 Lessons 41–50, Investigation 5 N
T
E
Math Focus:
N
Number & Operations
T
Distributed Strands: S
Number & Operations • Measurement • Data Analysis & Probability
Lesson 41 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296
Maintaining & Extending
• Using Formulas
Power Up
• Distributive Property
Facts pp. 296, 302, 309, 317,
Activity Perimeter Formulas 323, 329, 336, 342, 347, 352
Lesson 42 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302
Mental Math Strategies
• Repeating Decimals pp. 296, 302, 309, 317, 323,
Lesson 43 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309 329, 336, 342, 347, 352
• Converting Decimals to Fractions Problem Solving Strategies
• Converting Fractions to Decimals pp. 296, 302, 309, 317, 323,
329, 336, 342, 347, 352
• Converting Percents to Decimals
Enrichment
Lesson 44 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317
Early Finishers pp. 301,
• Division Answers
308, 335, 358
Lesson 45 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323
Extensions p. 362
• Dividing by a Decimal Number
Lesson 46 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329
• Rates
Lesson 47 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336
• Powers of 10
Lesson 48 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342
• Fraction-Decimal-Percent Equivalents
Lesson 49 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347
• Adding and Subtracting Mixed Measures
Lesson 50 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352
• Unit Multipliers and Unit Conversion
Investigation 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359
• Creating Graphs
Table of Contents ix