6th Grade Math Textbook, Fundamentals

473 Pages·2011·44.33 MB·English

Alfred S. Posamentier
Catherine D. LeTourneau
Edward William Quinn
Program Consultants
Joanne Mellia Paul M. Beaudin Alice Russo Dunning
Hommocks Middle School Professor of Education Adjunct, School of Education
Larchmont, NY Iona College Long Island University
New Rochelle, NY Purchase, NY
Carlota E. Morales Regina Panasuk
Principal Professor of Mathematics Education
Sts. Peter and Paul School University of Massachusetts
Miami, FL Lowell, MA

Sadlier-Oxford
A Division of William H. Sadlier, Inc.
www.sadlier-oxford.com
Reviewers
The publisher wishes to thank the following teachers and administrators, who read
portions of the series prior to publication, for their valuable contributions.
Sean Corcoran Susan Blumberg John Negherbon Jr. Mary Anne Corcoran
Grades 7 & 8 Mathematics Teacher Grades 7, 8, & Algebra I Grade 8
Teacher Coordinator Teacher Teacher
Philadelphia, PA Grades 1–8 Vero Beach, FL Philadelphia, PA
Merrick, NY
Marcia Escandar Francis P. Franklin Katherine Herbst Emily Sheridan
Middle School Grade 8 Grades 7–12 Grade 8
Math Teacher Math/Algebra Teacher Supervisor of Mathematics Teacher
Miami, FL Newport, OR Ridgefield Park, NJ Hicksville, NY
Amy Talley Marie Bicsak Margaret Clinton Dr. Jeanne Rast
Middle School Grades 7–9 Teacher Grades K–8
Math Teacher Instructor/Consultant Philadelphia, PA Teacher
San Antonio, TX Harrison Twp., MI Hapeville, GA
Maureen Barnhart Valery Melnick Sylvia Anna Nomikos Maureen Thorley
Grade 8 Grade 7 Math Teacher/Coordinator Grades 6–8
Teacher Math Teacher Brooklyn, NY Mathematics Specialist
Portland, OR Havertown, PA Bethlehem, PA
Peggy Barrie Sr. Agnes White Thomas R. Filippi Bernadette Dougherty
Grades 7 & 8 Principal Dean of Academics Principal
Math/Algebra Teacher Rockaway Park, NY Aventura, FL Wayne, PA
Belmar, NJ
Gary Rubinstein Elizabeth Warren Br. Ralph Darmento, Richard L. Cotten
Grades 9–12 Grades 7 & 8 FSC Grades 9–12
Teacher Math/Algebra Teacher Deputy Superintendent Mathematics Teacher
New York, NY Eagle Creek, OR Newark, NJ Oviedo, FL
Joanne DeMizio Judith A. Devine Stephanie D. Garland
Associate Superintendent Educational Consultant Educational Consultant
Curriculum & Staff Development Springfield, PA St. Louis, MO
New York, NY
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ISBN: 978-0-8215-8207-7
3456789/14 13 12 11 10 09
AMathematicsAdvisoryBoardconsistingofhighlydistinguishedmatheducatorsfrom
acrossthecountrywasestablishedtoreviewthecurriculumandpedagogyof
ProgressinMathematics,GradesK–8.Therecommendationstheyprovidedwere
invaluabletothedevelopmentoftheprogram.
DavidKlahr SandraStotsky R.JamesMilgram*
ProfessorofPsychology ProfessorofEducationReform ProfessorofMathematics
CarnegieMellonUniversity 21stCenturyChairinTeacherQuality StanfordUniversity
Pittsburgh,PA UniversityofArkansas PaloAlto,CA
Fayetteville,AR *Dr.Milgram’sworkwiththeMathematics
Chair,Mathematics AdvisoryBoardencompassesGradesK–5
andAlgebraI
AdvisoryBoard
ReginaPanasuk VernWilliams
PaulM.Beaudin ProfessorofMathematicsEducation MathematicsDepartment CarlotaE.Morales
ProfessorofEducation UniversityofMassachusetts LongfellowMiddleSchool Principal
IonaCollege Lowell,MA FairfaxCounty,VA Sts.PeterandPaulSchool
NewRochelle,NY Miami,FL
KirkP.Gaddy DouglasJ.Keeler
Principal Superintendent(Ret.)
St.KatharineSchool ClaremontUnified
Baltimore,MD MembersoftheSadlier-OxfordMathematicsAdvisoryBoard SchoolDistrict
(NotpicturedaboveisSr.MarieCooper,IHM) Claremont,CA
MargaretE.Curran RosaliePedalinoPorter Sr.MarianneViani Sr.MarieCooper,IHM
Principal ConsultantBilingual/ESL Assoc.Supt.ofCurriculum Professor:Departmentof
AnnunciationCatholicAcademy Programs ArchdioceseofSanFrancisco Mathematics,Physics,and
AltamonteSprings,FL Amherst,MA SanFrancisco,CA ComputerScience
ImmaculataUniversity
Immaculata,PA
iiiiii
..xii–xviii
Chapter Chapter
Integers Expressions and Equations
Chapter Opener . . . . . . . . . . . . . . . . . . . . . . . . .1 Chapter Opener . . . . . . . . . . . . . . . . . . . . . . . . 29
1-1 Integers and Absolute Value . . . . .2 2-1 Mathematical Expressions . . . . . 30
1-2 Compare and Order Integers. . . . .4 2-2 Simplify and Evaluate
1-3 Add Integers . . . . . . . . . . . . . . . . .6 Algebraic Expressions . . . . . . . . . . . . . . 32
1-4 Subtract Integers. . . . . . . . . . . . . .8 2-3 Equations . . . . . . . . . . . . . . . . . . 34
Check Your Progress I (Lessons 1–3)
1-5 Multiply Integers. . . . . . . . . . . . . . 10
1-6 Divide Integers. . . . . . . . . . . . . . .12 2-4 Solve Addition Equations. . . . . . . 36
Check Your Progress I (Lessons 1–6) 2-5 Solve Subtraction Equations. . . . 38
1-7 Properties . . . . . . . . . . . . . . . . . .14 2-6 Solve Multiplication Equations. . . 40
1-8 Closure Property . . . . . . . . . . . . . . . . . .16 2-7 Solve Division Equations. . . . . . . 42
Check Your Progress II (Lessons 4–7)
1-9 Powers and Laws of Exponents . . . . . . . 18
Check Your Progress II (Lessons 7–9) 2-8 Solve Two-Step Equations. . . . . . 44
1-10 Order of Operations. . . . . . . . . . . 20 2-9 Formulas. . . . . . . . . . . . . . . . . . . 46
Check Your Progress III (Lessons 8–9)
1-11 The Coordinate Plane . . . . . . . . . . . . . . 22
2-10 Problem-Solving Strategy:
Check Your Progress III (Lessons 10–11)
OOrrggaanniizzee DDaattaa .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 4488
1-12 Problem-Solving Strategy:
Enrichment:
Guess and Test . . . . . . . . . . . . . . . . . . .24
Be a Math Magician. . . . . . . . . . . . . . . . 50
Enrichment:
Sequence Sums. . . . . . . . . . . . . . . . . . . 26 Test Prep . . . . . . . . . . . . . . . . . . . . . . . . 52
Test Prep . . . . . . . . . . . . . . . . . . . . . . . .27
iv
Chapter Chapter
Inequalities Rational Numbers:
Decimals
Chapter Opener . . . . . . . . . . . . . . . . . . . . . . . . 53
3-1 Inequalities . . . . . . . . . . . . . . . . . 54 Chapter Opener . . . . . . . . . . . . . . . . . . . . . . . . 71
3-2 Graph Inequalities on a 4-1 Rational Numbers . . . . . . . . . . . . 72
Number Line. . . . . . . . . . . . . . . . . . . . . . 56 4-2 Equivalent Rational Numbers . . . 74
Check Your Progress I (Lessons 1–2)
4-3 Compare and Order Decimals. . . 76
3-3 Model Properties of Inequality. . . 58 4-4 Estimate Decimal Sums
3-4 Solve Inequalities and Differences . . . . . . . . . . . . . . . . . . . 78
Using Addition and Subtraction . . . . . . . 60 4-5 Add and Subtract Decimals. . . . . 80
Check Your Progress II (Lessons 3–4)
Check Your Progress I (Lessons 1–5)
3-5 Solve Inequalities 4-6 Multiply Decimals . . . . . . . . . . . . 82
Using Multiplication . . . . . . . . . . . . . . . . 62
4-7 Estimate Decimal Products
3-6 Solve Inequalities and Quotients. . . . . . . . . . . . . . . . . . . . . 84
Using Division . . . . . . . . . . . . . . . . . . . . 64
4-8 Divide Decimals. . . . . . . . . . . . . . 86
Check Your Progress III (Lessons 5–6)
4-9 Negative Exponents . . . . . . . . . . 88
3-7 Problem-Solving Strategy:
Find a Pattern. . . . . . . . . . . . . . . . . . . . . 66 4-10 Scientific Notation . . . . . . . . . . . . 90
Enrichment: 4-11 Operations with Scientific
Define, Substitute, and Compute . . . . . . 68 Notation . . . . . . . . . . . . . . . . . . . . . . . . . 92
Test Prep . . . . . . . . . . . . . . . . . . . . . . . . 69 Check Your Progress II (Lessons 6–11)
4-12 Addition and Subtraction
Equations with Decimals . . . . . . . . . . . . 94
4-13 Multiplication and Division
Equations with Decimals . . . . . . . . . . . . 96
4-14 Solve Two-Step Equations
with Decimals. . . . . . . . . . . . . . . . . . . . . 98
4-15 Rename Metric Units
of Measure. . . . . . . . . . . . . . . . . . . . . . 100
Check Your Progress III(Lessons 12–15)
4-16 Problem Solving:
Review of Strategies. . . . . . . . . . . . . . . 102
Enrichment:
Binary Numbers . . . . . . . . . . . . . . . . . . 104
Test Prep . . . . . . . . . . . . . . . . . . . . . . . 105
v
Chapter Chapter
Rational Numbers: Ratio and Proportion
Fractions
Chapter Opener . . . . . . . . . . . . . . . . . . . . . . . 147
Chapter Opener . . . . . . . . . . . . . . . . . . . . . . . 107 6-1 Ratio . . . . . . . . . . . . . . . . . . . . . 148
5-1 Prime Factorization. . . . . . . . . . . . . . . . 108 6-2 Unit Rate and Unit Cost. . . . . . . 150
5-2 Greatest Common Factor . . . . . . . . . . . 110 6-3 Write and Solve Proportions . . . 152
5-3 Least Common Multiple . . . . . . . . . . . . 112 Check Your Progress I (Lessons 1–3)
5-4 Fraction Sense: Close to (cid:2)1, (cid:2)1 6-4 Direct Proportion . . . . . . . . . . . . 154
2
0, 12, or 1 . . . . . . . . . . . . . . . . . . . . . . . . 114 6-5 Proportion by Parts . . . . . . . . . . 156
5-5 Compare and Order 6-6 Scale Drawings and Models . . . 158
Rational Numbers. . . . . . . . . . . . . . . . . 116
6-7 Similarity . . . . . . . . . . . . . . . . . . 160
Check Your Progress I(Lessons 1–5)
6-8 Indirect Measurement . . . . . . . . 162
5-6 Add and Subtract Fractions . . . . 118
Check Your Progress II (Lessons 4–8)
5-7 Add and Subtract
Mixed Numbers . . . . . . . . . . . . . . . . . . 120 6-9 Inverse Proportion. . . . . . . . . . . 164
5-8 Multiply Fractions. . . . . . . . . . . . 122 6-10 Dimensional Analysis. . . . . . . . . . . . . . 166
5-9 Multiply Mixed Numbers . . . . . . 124 Check Your Progress III (Lessons 9–10)
5-10 Divide Fractions. . . . . . . . . . . . . 126 6-11 Problem-Solving Strategy:
Solve a Simpler Problem . . . . . . . . . . . 168
5-11 Divide Mixed Numbers. . . . . . . . 128
Enrichment:
Check Your Progress II (Lessons 6–11)
Bicycle-Gear Math . . . . . . . . . . . . . . . . 170
5-12 Properties of Rational Test Prep . . . . . . . . . . . . . . . . . . . . . . . 171
Numbers. . . . . . . . . . . . . . . . . . . . . . . . 130
5-13 Order of Operations
with Rational Numbers. . . . . . . . . . . . . 132
5-14 Addition and Subtraction
Equations with Fractions . . . . . . . . . . . 134
5-15 Multiplication and Division
Equations with Fractions . . . . . . . . . . . 136
5-16 Solve Two-Step Equations
with Fractions. . . . . . . . . . . . . . . . . . . . 138
5-17 Rename Customary Units
of Measure. . . . . . . . . . . . . . . . . . . . . . 140
Check Your Progress III (Lessons 12–17)
5-18 Problem-Solving Strategy:
Make a Drawing. . . . . . . . . . . . . . . . . . 142
Enrichment:
Different Ways to Find the GCF . . . . . . 144
Test Prep . . . . . . . . . . . . . . . . . . . . . . . 145
vi
Chapter Chapter
Percent and Consumer Data Analysis and
Applications Statistics
Chapter Opener . . . . . . . . . . . . . . . . . . . . . . . 173 Chapter Opener . . . . . . . . . . . . . . . . . . . . . . .207
7-1 Percents. . . . . . . . . . . . . . . . . . .174 8-1 Samples and Surveys . . . . . . . . . . . . .208
7-2 Fractions, Decimals, Percents . . . . . . .176 8-2 Measures of Central Tendency
7-3 Percents Greater Than 100%/Less and Range . . . . . . . . . . . . . . . . . . . . . .210
Than 1%. . . . . . . . . . . . . . . . . . . . . . . . 178 8-3 Interpret Data. . . . . . . . . . . . . . . . . . . . 212
7-4 Find a Percentage of a Number. . . . . . 180 8-4 Choose an Appropriate Graph . . . . . . . 214
7-5 Find a Percent . . . . . . . . . . . . . . . . . . . 182 Check Your Progress I (Lessons 1–4)
7-6 Find the Original Number or 8-5 Multiple Bar Graphs . . . . . . . . . . . . . . . 216
the Base. . . . . . . . . . . . . . . . . . . . . . . . 184 8-6 Histograms. . . . . . . . . . . . . . . . . . . . . . 218
Check Your Progress I (Lessons 1–6)
8-7 Stem-and-Leaf Plots . . . . . . . . . . . . . .220
7-7 Estimate with Percents . . . . . . . 186 8-8 Box-and-Whisker Plots. . . . . . . . . . . . .222
7-8 Percent Increase . . . . . . . . . . . . 188 Check Your Progress II (Lessons 5–8)
7-9 Percent Decrease . . . . . . . . . . . 190 8-9 Venn Diagrams. . . . . . . . . . . . . . . . . . .224
7-10 Sales Tax and Tips. . . . . . . . . . . . . . . . 192 8-10 Multiple Line Graphs . . . . . . . . . . . . . .226
7-11 Discount and Markup. . . . . . . . . . . . . . 194 8-11 Scatter Plots. . . . . . . . . . . . . . . . . . . . .228
Check Your Progress II (Lessons 7–11)
8-12 Misleading Statistics and Graphs. . . . .230
7-12 Commission . . . . . . . . . . . . . . . . . . . . . 196 Check Your Progress III (Lessons 9–12)
7-13 Simple Interest. . . . . . . . . . . . . . . . . . . 198 8-13 Technology:
7-14 Compound Interest. . . . . . . . . . . . . . . .200 Create Graphs . . . . . . . . . . . . . . . . . . .232
Check Your Progress III (Lessons 12–14) 8-14 Problem Solving:
7-15 Problem-Solving Strategy: Review of Strategies. . . . . . . . . . . . . . .234
Reason Logically . . . . . . . . . . . . . . . . . 202 Enrichment:
Financial Spreadsheets . . . . . . . . . . . .236
Enrichment:
Successive Discounts and Increases. . 204 Test Prep . . . . . . . . . . . . . . . . . . . . . . .238
Test Prep . . . . . . . . . . . . . . . . . . . . . . . 205
vii
Chapter Chapter
Two-Dimensional Two-Dimensional
Geometry Geometry and
Measurement Applications
Chapter Opener . . . . . . . . . . . . . . . . . . . . . . . 239
9-1 Points, Lines, and Planes. . . . . . . . . . . 240 Chapter Opener . . . . . . . . . . . . . . . . . . . . . . . 271
9-2 Classify and Measure Angles. . . . . . . . 242 10-1 Precision and Accuracy
9-3 Angle Pairs . . . . . . . . . . . . . . . . 244 in Measurement. . . . . . . . . . . . . . . . . . 272
9-4 Parallel Lines and 10-2 Perimeter. . . . . . . . . . . . . . . . . . 274
Transversals. . . . . . . . . . . . . . . . . . . . . 246 10-3 Squares and Square Roots. . . . 276
9-5 Congruent Angles and 10-4 Irrational Numbers. . . . . . . . . . . 278
Line Segments. . . . . . . . . . . . . . . . . . . 248 10-5 Pythagorean Theorem. . . . . . . . 280
9-6 Line Constructions. . . . . . . . . . . . . . . . 250
Check Your Progress I (Lessons 1–5)
Check Your Progress I (Lessons 1–6)
10-6 Area of Parallelograms . . . . . . . 282
9-7 Polygons . . . . . . . . . . . . . . . . . . 252 10-7 Area of Triangles
9-8 Triangles . . . . . . . . . . . . . . . . . . 254 and Trapezoids. . . . . . . . . . . . . . . . . . . 284
9-9 Congruent Triangles . . . . . . . . . 256 10-8 Circumference and Area
9-10 Triangle Constructions . . . . . . . . . . . . . 258 of a Circle. . . . . . . . . . . . . . . . . . . . . . . 286
Check Your Progress II(Lessons 6–8)
Check Your Progress II (Lessons 7–10)
9-11 Quadrilaterals. . . . . . . . . . . . . . . . . . . . 260 10-9 Area of Complex Figures. . . . . . 288
9-12 Circles . . . . . . . . . . . . . . . . . . . . . . . . . 262 10-10 Symmetry. . . . . . . . . . . . . . . . . . . . . . . 290
9-13 Make a Circle Graph . . . . . . . . . . . . . . 264 10-11 Tessellations. . . . . . . . . . . . . . . . . . . . . 292
Check Your Progress III (Lessons 9–11)
Check Your Progress III (Lessons 11–13)
10-12 Technology:
9-14 Problem-Solving Strategy:
Adopt a Different Point of View. . . . . . . 266 Relate Perimeter and Area. . . . . . . . . . 294
10-13 Problem-Solving Strategy:
Enrichment:
Quadrilaterals from Quadrilaterals. . . . 268 Account for All Possibilities. . . . . . . . . . 296
Enrichment:
Test Prep . . . . . . . . . . . . . . . . . . . . . . . 270
Area of Irregular Polygons . . . . . . . . . . 298
Test Prep . . . . . . . . . . . . . . . . . . . . . . . 300
viii
Chapter Chapter
Three-Dimensional Probability
Geometry
Chapter Opener . . . . . . . . . . . . . . . . . . . . . . . 329
Chapter Opener . . . . . . . . . . . . . . . . . . . . . . . 301 12-1 Sample Space . . . . . . . . . . . . . . . . . . . 330
11-1 Three-Dimensional Figures . . . . . . . . . 302 12-2 Fundamental Counting Principle
11-2 Draw Three-Dimensional Figures. . . . . 304 and Factorials. . . . . . . . . . . . . . . . . . . . 332
Check Your Progress I (Lessons 1–2)
11-3 Surface Area of Prisms . . . . . . . 306
12-3 Theoretical Probability. . . . . . . . 334
Check Your Progress I (Lessons 1–3)
11-4 Surface Area of Pyramids . . . . . 308 12-4 Experimental Probability . . . . . . 336
11-5 Surface Area of Cylinders 12-5 Odds and Fairness . . . . . . . . . . 338
and Cones . . . . . . . . . . . . . . . . . . . . . . 310 12-6 Compound Events. . . . . . . . . . . 340
11-6 Estimate Surface Area. . . . . . . . 312 Check Your Progress II (Lessons 3–6)
Check Your Progress II (Lessons 4–6) 12-7 Permutations. . . . . . . . . . . . . . . 342
11-7 Volume of Prisms. . . . . . . . . . . . 314 12-8 Combinations . . . . . . . . . . . . . . 344
11-8 Volume of Pyramids. . . . . . . . . . 316 Check Your Progress III (Lessons 7–8)
11-9 Volume of Cylinders 12-9 Problem Solving:
and Cones . . . . . . . . . . . . . . . . . . . . . . 318 Review of Strategies. . . . . . . . . . . . . . . 346
11-10 Surface Area and Enrichment:
Volume of Complex Pascal’s Triangle. . . . . . . . . . . . . . . . . . 348
Three-Dimensional Figures. . . . . . . . . . 320 Test Prep . . . . . . . . . . . . . . . . . . . . . . . 349
11-11 Changing Dimensions
of Three-Dimensional Figures . . . . . . . 322
Check Your Progress III (Lessons 7–11)
11-12 Problem-Solving Strategy:
Work Backward . . . . . . . . . . . . . . . . . . 324
Enrichment:
Three-Dimensional Figures and
the Ratio of Similarity. . . . . . . . . . . . . . 326
Test Prep . . . . . . . . . . . . . . . . . . . . . . . 328
ix