Student Edition SAXON MATH

1 HakeSaxonStudent Edition30%100%80%60%40%20%0%80%60%S AXON MATH 6/5 M65 Title Pages Page 1 Friday, March 28, 2003 12:51 PM Student Edition Stephen HakeJohn SAXON M65 Title Pages Page 2 Friday, March 28, 2003 12:51 PM SAXON Publishers gratefully acknowledges the contributions of the following individuals in the completion of this project: Authors: Stephen Hake, John SAXON Consultants: Diane Blank, Shirley McQuade Davis Editorial: Chris Braun, Brian E. Rice, Mary Burleson, Sherri Little, Rodney Clint Keele, Bo Bj rn Johnson, Brian Smith, Brooke Butner, Andrew Kershen, Dana Nixon, Sean G. Douglas Editorial Support Services: Christopher Davey, Jay Allman, Jean Van Vleck, Shelley Turner, Darlene C. Terry Production: Adriana Maxwell, Karen Hammond, Brenda Lopez, Debra Sullivan, Diane Readnour, Donna Jarrel, Ryan LaCroix, Alicia Britt, Nancy Rimassa, Cristi D. Whiddon Project Management: Angela Johnson, Becky Cavnar 2004 SAXON Publishers, Inc.

2 , and Stephen HakeAll rights reserved. No part of SAXON Math 6/5, Third Edition , Student Edition may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. Address inquiries to Editorial Support Services, SAXON Publishers, Inc., 2600 John SAXON Blvd., Norman, OK in the United States of AmericaISBN: 1-56577-505-8 Manufacturing Code: 02S0803 v CONTENTS Letter from Author Stephen Hake xi Acknowledgments xii LESSON 1 Sequences Digits 1 LESSON 2 Even and Odd Numbers 4 LESSON 3 Using Money to Illustrate Place Value 8 LESSON 4 Comparing Whole Numbers 12 LESSON 5 Naming Whole Numbers Through Hundreds 16 Dollars and Cents LESSON 6 Adding One-Digit Numbers 20 Using the Addition Algorithm LESSON 7 Writing and Comparing Numbers Through 25 Hundred Thousands Ordinal Numbers LESSON 8 Subtraction Facts Fact Families 30 LESSON 9 Practicing the Subtraction Algorithm 34 LESSON 10 Missing Addends 39 INVESTIGATION 1 Story Problems 43 LESSON 11 Story Problems About Combining 46 LESSON 12 Lines number Lines Tally Marks 52 LESSON 13 Multiplication as Repeated Addition 58 Adding and subtracting Dollars and Cents LESSON 14 Missing Numbers in Subtraction 62 LESSON 15 Making a Multiplication Table 67 LESSON 16 Story Problems About Separating 72

3 LESSON 17 Multiplying by One-Digit Numbers 77 LESSON 18 Multiplying Three Factors 82 Missing Numbers in Multiplication LESSON 19 Division Facts 87 LESSON 20 Three Ways to Show Division 91 INVESTIGATION 2 Fractions: Halves, Fourths, and Tenths 96 M65 Table of Contents Page v Friday, March 28, 2003 12:50 PM vi SAXON Math 6 / 5 LESSON 21 Problems About Equal Groups 101 LESSON 22 One-Digit Division with a Remainder 106 Divisibility by 2, 5, and 10 LESSON 23 Recognizing Halves 111 LESSON 24 Parentheses Associative Property 115 LESSON 25 Listing the Factors of Whole Numbers 119 LESSON 26 Division Algorithm 123 LESSON 27 Reading Scales 128 LESSON 28 Measuring Time 132 LESSON 29 Multiplying by Multiples of 10 and 100 137 LESSON 30 Interpreting Pictures of Fractions and Percents 142 INVESTIGATION 3 Fractions: Thirds, Fifths, and Eighths 147 LESSON 31 Pairs of Lines 151 LESSON 32 Angles Polygons 155 LESSON 33 Rounding Numbers Using a number Line 162 LESSON 34 Division with Zeros in the Quotient 166 LESSON 35 Problems About Comparing 170 Problems About Elapsed Time LESSON 36 Classifying Triangles 175 LESSON 37 Drawing Pictures of Fractions 180 LESSON 38 Fractions and mixed Numbers 184 on a number Line LESSON 39 Comparing Fractions by Drawing Pictures 189 LESSON 40 Pictures of mixed Numbers 193 Writing Quotients as mixed Numbers, Part 1 INVESTIGATION 4 Measuring Angles 198 LESSON 41 Adding and subtracting Fractions with 202 Common Denominators LESSON 42 Short Division Divisibility by 3, 6, and 9 207 LESSON 43 Writing Quotients as mixed Numbers, Part 2 212 Adding and subtracting Whole Numbers,Fractions, and mixed Numbers LESSON 44 Measuring Lengths with a Ruler 217 M65 Table of Contents Page vi Friday, March 28.

4 2003 12:50 PM Contents vii LESSON 45 Classifying Quadrilaterals 223 LESSON 46 Stories About a Fraction of a Group 230 LESSON 47 Simplifying mixed Measures234 LESSON48 Reading and Writing Whole Numbers238in Expanded NotationLESSON49 Solving Two-Step Word Problems242 LESSON50 Finding an Average246 INVESTIGATION5 Organizing and Analyzing Data251 LESSON51 Multiplying by Two-Digit Numbers258 LESSON52 Naming Numbers Through Hundred Billions263 LESSON53 Perimeter Measures of a Circle268 LESSON54 Dividing by Multiples of 10273 LESSON55 Multiplying by Three-Digit Numbers277 LESSON56 Multiplying by Three-Digit Numbers280 That Include ZeroLESSON57 Simple Probability284 LESSON58 Writing Quotients as mixed Numbers, Part 3289 LESSON59 Fractions Equal to 1 293 subtracting a Fraction from 1 LESSON60 Finding a Fraction to Complete a Whole298 INVESTIGATION6 Performing Probability Experiments302 LESSON61 Using Letters to Identify Geometric Figures307 LESSON62 Estimating Arithmetic Answers313 LESSON63 subtracting a Fraction from a Whole 317 number Greater than 1 LESSON64 Using Money to Model Decimal Numbers322 LESSON65 Decimal Parts of a Meter328 LESSON66 Reading a Centimeter Scale333 LESSON67 Writing Tenths and Hundredths as 338 Decimal NumbersLESSON68 Naming Decimal Numbers344M65 Table of Contents Page vii Friday, March 28, 2003 12.

5 50 PMviiiSaxon Math 6 / 5 LESSON69 Fractions of a Second 349 Comparing and Ordering Decimal NumbersLESSON70 Writing Equivalent Decimal Numbers 354 Writing Cents CorrectlyINVESTIGATION7 Pattern Recognition359 LESSON71 Fractions, Decimals, and Percents365 LESSON72 Area, Part 1371 LESSON73 Adding and subtracting Decimal Numbers377 LESSON74 Converting Units of Length382 LESSON75 Changing Improper Fractions to386 Whole or mixed NumbersLESSON76 Multiplying Fractions391 LESSON77 Converting Units of Weight and Mass397 LESSON78 Exponents and Powers 401 LESSON79 Finding Equivalent Fractions by Multiplying by 1407 LESSON80 Prime and Composite Numbers412 INVESTIGATION8 Displaying Data417 LESSON81 Reducing Fractions, Part 1425 LESSON82 Greatest Common Factor (GCF)431 LESSON83 Properties of Geometric Solids435 LESSON84 Mean, Median, Mode, and Range439 LESSON85 Converting Units of Capacity444 LESSON86 Multiplying Fractions and Whole Numbers448 LESSON87 Using Manipulatives and 453 Sketches to Divide FractionsLESSON88 Transformations458 LESSON89 Finding a Square Root463 LESSON90 Reducing Fractions, Part 2467 INVESTIGATION9 Line Graphs472 LESSON91 Simplifying Improper Fractions476 LESSON92 Dividing by Two-Digit Numbers481M65 Table of Contents Page viii Friday, March 28, 2003 12.

6 50 PMContentsixLESSON93 Comparative Bar Graphs486 LESSON94 Using Estimation When Dividing by490 Two-Digit NumbersLESSON95 Reciprocals494 LESSON96 Using Reciprocals to Divide Fractions499 LESSON97 Ratios504 LESSON98 Negative Numbers508 LESSON99 Adding and subtracting Whole512 Numbers and Decimal NumbersLESSON100 Simplifying Decimal Numbers517 INVESTIGATION10 Graphing Points on a Coordinate Plane521 LESSON101 Rounding mixed Numbers to the 524 Nearest Whole NumberLESSON102 subtracting Decimal Numbers Using Zeros528 LESSON103 Volume532 LESSON104 Rounding Decimal Numbers to the537 Nearest Whole NumberLESSON105 Symmetry542 LESSON106 Reading and Ordering Decimal Numbers548 Through Ten-ThousandthsLESSON107 Using Percent to Name Part of a Group554 LESSON108 Schedules559 LESSON109 Multiplying Decimal Numbers564 LESSON110 Multiplying Decimal Numbers: 569 Using Zeros as PlaceholdersINVESTIGATION11 Scale Drawings573 LESSON111 Multiplying Decimal Numbers576by 10, by 100, and by 1000 LESSON112 Finding the Least Common580 Multiple of Two NumbersLESSON113 Writing mixed Numbers as Improper Fractions584 LESSON114 Problems with No Solutions or Many Solutions589 LESSON115 Area, Part 2594xSaxon Math 6 / 5 LESSON116 Finding Common Denominators to Add,598 Subtract, and Compare FractionsLESSON117 Dividing a Decimal number by a Whole Number603 LESSON118 Using Zero as a Placeholder Dividing Decimal608 Numbers by 10, by 100, and by 1000 LESSON119 Dividing by a Decimal Number613 LESSON120 Multiplying mixed Numbers617 INVESTIGATION12 Tessellations621 TOPICAR oman Numerals Through 39629 TOPICBR oman Numerals Through Thousands631 TOPICCBase 5632 Supplemental Practice Problems for635 Selected LessonsGlossary665 Index697M65 Table of Contents Page x Friday, March 28, 2003 12.

7 50 PM xi LETTER FROM AUTHOR STEPHEN HAKE Dear Student ,We study mathematics because of its importance to our lives. Ourschool schedule, our trip to the store, the preparation of our meals,and many of the games we play involve mathematics. You willfind that the word problems in this book are often drawn fromeveryday you grow into adulthood, mathematics will become even moreimportant. In fact, your future in the adult world may depend onthe mathematics you have learned. This book was written to helpyou learn mathematics and to learn it well. For this to happen, youmust use the book properly. As you work through the pages, youwill 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. Eachlesson has four parts. The first part is a Warm-Up that includespractice of basic facts and mental math.

8 These exercises improveyour speed, accuracy, and ability to do math in your head. TheWarm-Up also includes a problem-solving exercise to familiarizeyou with strategies for solving complicated problems. The secondpart of the lesson is the New Concept. This section introduces anew mathematical concept and presents examples that use theconcept. In the next section, the Lesson Practice, you have achance to solve problems involving the new concept. Theproblems are lettered a, b, c, and so on. The final part of the lessonis the mixed Practice. This problem set reviews previously taughtconcepts and prepares you for concepts that will be taught in laterlessons. Solving these problems helps you remember skills andconcepts for a long are variations of the daily lesson. The investigationsin this book often involve activities that fill an entire class contain their own set of questions instead of aproblem set.

9 Remember, solve every problem in every practice set, everyproblem set, and every investigation. Do not skip honest effort, you will experience success and truelearning that will stay with you and serve you well in the future. Stephen HakeTemple City, California M65 Preface Page xi Friday, March 28, 2003 12:49 PM xii ACKNOWLEDGMENTS I wish to acknowledge the following contributors to the revision of SaxonMath 5/4 8/7: Barbara Place, who conceived the Gerald Beer, who provided lesson content and problems on topics ofpattern recognition, functions, scale drawings and models, probability, dataanalysis, and problem McQuade Davis, for her ideas on teaching story-problem Rice, for his conceptual work on story-problem lessons and for hiseditorial work on the Assessments and Classroom Masters. Dan Shippey, who designed the Mercury Freedom 7 scale model for SaxonMath 7/6, Investigation Burleson, who scheduled the project and coordinated efforts among themany Maxwell, who coordinated the production of the Blank, for her extensive and thorough analysis of state standards andnumerous helpful suggestions for addressing those Crisler, for her contributions to the Teacher s Larson, for her generous help and insightful suggestions for theTeacher s Braun, whose invaluable contributions as senior editor span the contentsof the SAXON , whose unwavering focus on Student success continues to inspireand Hake, for her support, encouragement, and patience.

10 Stephen HakeTemple City, California M65 Preface Page xii Friday, March 28, 2003 12:49 PM1 LESSON1 Sequences DigitsWARM-UPNEW CONCEPTSS equencesCounting is a math skill that we learn early in life. Countingby ones, we say the numbers 1, 2, 3, 4, 5, 6, ..These numbers are called counting numbers. We can alsocount by a number other than one. Below we show the firstfive numbers for counting by twos and the first five numbersfor counting by , 4, 6, 8, 10, ..5, 10, 15, 20, 25, ..An ordered list of numbers forms a sequence. Each memberof the sequence is a term. The three dots mean that thesequence continues even though the numbers are not can study a sequence to discover its counting pattern, orrule. The rule can be used to find more terms in the sequence. Example 1 What are the next three terms in this counting sequence?3, 6, 9, 12, _____, _____, _____, ..Facts Practice:100 Addition Facts (Test A) Mental Math:Problem Solving:3+340 + 50 20+20+20 by tens from 10 to 100.