Authors Altieri • Balka • Day • Gonsalves • Grace • Krulik Malloy • Molix-Bailey • Moseley • Mowry • Myren Price • Reynosa • Santa Cruz • Silbey • Vielhaber About the Cover Located in the Piney Woods region of Texas, Tyler is known as the Rose Capital of America It is also home to a popular 85-foot, 6-lane, wooden slot car track The track is designed for 1:32 and 1:24 scale cars You will learn more about ratios in Chapter About the Graphics Colored Truchet bands Created with Mathematica A random 2D Truchet image is constructed The connected arcs of the image are identified and randomly colored in a band-like manner For more information, and for programs to construct such graphics, see: www.wolfram.com/r/textbook Copyright © 2007 by The McGraw-Hill Companies, Inc All rights reserved Except as permitted under the United States Copyright Act, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without prior permission of the publisher Send all inquiries to: Glencoe/McGraw-Hill 8787 Orion Place Columbus, OH 43240-4027 ISBN-13: 978-0-02-105657-6 ISBN-10: 0-02-105657-9 Printed in the United States of America 10 055/027 15 14 13 12 11 10 09 08 07 06 Start Smart Chapter Place Value and Number Sense Chapter Addition Chapter Subtraction Chapter Multiplication Concepts and Facts Chapter More Multiplication Facts Chapter Division Concepts and Facts Chapter More Division Facts Chapter Measurement: Customary System Chapter Measurement: Metric System Chapter 10 Measurement and Geometry Chapter 11 Statistics: Data, Graphs, and Probability Chapter 12 Fractions Chapter 13 Fractions and Decimals Chapter 14 Multiply by One-Digit Numbers Chapter 15 Divide by One-Digit Numbers Standards Review Looking Ahead to Grade iii Authors Mary Behr Altieri Putnam/Northern Westchester BOCES Yorktown Heights, New York Philip D Gonsalves Mathematics Coordinator Alameda County Office of Education and California State University East Bay Hayward, California Ellen C Grace Consultant Albuquerque, New Mexico Rhonda J Molix-Bailey Mathematics Consultant Mathematics by Design Desoto, Texas iv Doug Martin Photography Don S Balka Professor Emeritus Saint Mary’s College Notre Dame, Indiana Roger Day, Ph.D Mathematics Department Chair Pontiac Township High School Pontiac, Illinois Stephen Krulik Mathematics Consultant Cherry Hill, New Jersey Lois Gordon Moseley Staff Developer NUMBERS: Mathematics Professional Development Houston, Texas Carol E Malloy Assistant Professor of Mathematics Education University of North Carolina at Chapel Hill Chapel Hill, North Carolina Brian Mowry Independent Math Educational Consultant/Part time Pre-K Instructional Specialist Austin Independent School District Austin, Texas Meet the Authors at ca.gr3math.com Christina L Myren Consultant Teacher Conejo Valley Unified School District Thousand Oaks, California Jack Price Professor Emeritus California State Polytechnic University Pomona, California Mary Esther Reynosa Instructional Specialist for Elementary Mathematics Northside Independent School District San Antonio, Texas Rafaela M Santa Cruz SDSU/CGU Doctoral Program in Education San Diego State University San Diego, California Robyn Silbey Math Content Coach Montgomery County Public Schools Gaithersburg, Maryland Kathleen Vielhaber Mathematics Consultant St Louis, Missouri Contributing Authors Viken Hovsepian Professor of Mathematics Rio Hondo College Whittier, California Donna J Long Mathematics, Consultant Indianapolis, Indiana Dinah Zike Educational Consultant Dinah-Might Activities, Inc San Antonio, Texas v Doug Martin Photography California Mathematics Advisory Board Glencoe wishes to thank the following professionals for their invaluable feedback during the development of the program They reviewed the table of contents, the prototype of the Teacher Wraparound Edition, and the California Standards Review chapter Cheryl L Avalos Mathematics Consultant Retired Teacher Hacienda Heights, California William M Bokesch Rancho Bernardo High School San Diego, California Patty Brown Teacher John Muir Elementary Fresno, California David J Chamberlain Secondary Mathematics Resource Teacher Capistrano Unified School District San Juan Capistrano, California Eppie Chung K-6 Teacher Modesto City Schools Modesto, California Lisa Marie Cirrincione Middle School Teacher Lincoln Middle School Oceanside, California Carol Cronk Mathematics Program Specialist San Bernardino City Unified School District San Bernardino, California Ilene Foster Teacher Specialist– Mathematics Pomona Unified School District Pomona, California Grant A Fraser, Ph D Professor of Mathematics California State University, Los Angeles Los Angeles, California vi File Photo Suzanne Bocskai Freire Teacher Kingswood Elementary Citrus Heights, California Beth Holguin Teacher Graystone Elementary San Jose, California Donna M Kopenski, Ed D Mathematics Coordinator K-5 City Heights Educational Collaborative San Diego, California Kelly Mack 6th Grade Teacher Captain Jason Dahl Elementary San Jose, California Juvenal Martinez Dual Immersion/ESL Instructor Aeolian Elementary Whittier, California John McGuire Associate Principal Pacific Union School Arcata, California Dr Donald R Price Teacher, Adjunct Professor Rowland Unified School District Rowland Heights, California Kasey St James Mathematics Teacher Sunny Hills High School Fullerton, California Arthur K Wayman, Ph D Professor of Mathematics Emeritus California State University, Long Beach Long Beach, California Beverly Wells First Grade Teacher Mineral King Elementary School Visalia, California Frances Basich Whitney Project Director, Mathematics K-12 Santa Cruz County Office of Education Capitola, California vii File Photo Consultants Macmillan/McGraw-Hill wishes to thank the following professionals for their feedback They were instrumental in providing valuable input toward the development of this program in these specific areas Mathematical Content Family Involvement Viken Hovsepian Professor of Mathematics Rio Hondo College Whittier, California Grant A Fraser, Ph.D Professor of Mathematics California State University, Los Angeles Los Angeles, California Arthur K Wayman, Ph.D Professor of Mathematics Emeritus California State University, Long Beach Long Beach, California Paul Giganti, Jr Mathematics Education Consultant Albany, California Assessment Jane D Gawronski Director of Assessment and Outreach San Diego State University San Diego, California Cognitive Guided Instruction Susan B Empson Associate Professor of Mathematics and Science Education University of Texas at Austin Austin, Texas English Learners Cheryl Avalos Mathematics Consultant Los Angeles County Office of Education, Retired Hacienda Heights, California Kathryn Heinze Graduate School of Education Hamline University St Paul, Minnesota viii Literature David M Schwartz Children’s Author, Speaker, Storyteller Oakland, Califorinia Vertical Alignment Berchie Holliday National Educational Consultant Silver Spring, Maryland Deborah A Hutchens, Ed.D Principal Norfolk Highlands Elementary Chesapeake, Virginia California Reviewers Each California Reviewer reviewed at least two chapters of the Student Edition, giving feedback and suggestions for improving the effectiveness of the mathematics instruction Sherry G Anderson Teacher/G.A.T.E Coordinator Will Rogers Elementary Lynwood, California Kristi Iverson First Grade Teacher Village Oaks Elementary Stockton, California Deborah Shapiro 5th Grade Teacher Nancy Cory Lancaster, California Ysaaca Axelrod Kindergarten Teacher El Monte Elementary Concord, California Sheri Leiken Teacher Weathersfield Elementary Thousand Oaks, California Cathy Bullock Teacher Capri Elementary Encinitas, California Sarab H Lopes Teacher Anza Elementary El Cajon, California Maureen Smith Curriculum Specialist Fremont Unified School Dist (retired 6/2006) Fremont, California Michelle Callender Teacher Morgan/Kincaid Preparatory School of Integrated Studies Victorville, California Karen E Lund 5th Grade Teacher Meadow Park Elementary Irvine, California M Olivia Campos 4th Grade Teacher Morrison Elementary Norwalk, California Malaura Page Easton, M.S Kindergarten Teacher La Pluma School La Mirada, California Priscilla S Edwards 5th Grade Classroom Teacher David Reese Elementary Sacramento, California Lisa B Friedberg 4th Grade Teacher Alderwood Basics Plus School Irvine, California Wendy Smith Hernandez Kindergarten Teacher Herndon-Barstow Elementary Fresno, California Beth Holguin Teacher Graystone School San Jose, CA Efrain Melendez Teacher Livermore Valley USD Livermore, California Jean A Nelson Teacher Fremont Elementary School Alhambra, California Tara Pahia Elementary Teacher Bear Gulch Elementary Rancho Cucamonga, California Dr Donald R Price Teacher, Adjunct Professor Rowland Unified School District Rowland Heights, California Kitty Ritz, M.A Teacher Monte Vista Elementary Rohnert Park, California Corinne E Schwartz First Grade Teacher Lincrest Elementary School Yuba City, CA Joseph M Snodgrass 3rd Grade Teacher Park Elementary School Alhambra, California Marie W Stevens Elementary Mathematics Coordinator LAUSD Los Angeles, California Jane Traut Classroom Teacher Lang Ranch Elementary School Thousand Oaks, California Rachel C Trowbridge Teacher Evergreen Elementary San Jose, California Cynthia H Vandemoortel Educator Alderwood Basics Plus School Irvine, California Norine Yale Teacher Justin Elementary Simi Valley, California Dr Darlene York Education Consultant Associate Professor/Antioch University Seattle, Washington ix Problem Solving: The Great Giants Number Sense: Now That’s Hot! Algebra and Functions: At the Aquarium Measurement: Measure Away Geometry: Food and Geometry 10 Statistics, Data Analysis, and Probability: How Fast Can You Go? 12 3, 5, 7, 9, 11, 13 x Arthur Morris/CORBIS Associative Property of Addition/centimeter propiedad asociativa de la asición/centímetro quart (qt) (p 354) A customary unit for measuring capacity quart = cups cuarto (ct) Unidad inglesa de capacidad cuarto = tazas Ver Tabla de medidas quotient (p 256) division problem 15 ÷ = cociente Respuesta a un problema de división Ejemplo: 15 ÷ = 5 es el cociente The answer to a is the quotient Glossary/Glosario R rectangle (p 438) A quadrilateral with four right angles; opposite sides are equal length and parallel rectángulo Cuadrilátero cuatro ángulos rectos; los lados opuestos son iguales y paralelos rectangular solid (p 444) A 3-dimensional figure with six faces that are rectangles prisma rectangular Figura tridimensional seis caras rectangulares regroup (p 74) To use place value to exchange equal amounts when renaming a number reagrupar Usar el valor de posición para intercambiar cantidades iguales cuando se convierte un número related fact(s) (p xxx) Basic facts using the same numbers Sometimes called a fact family 4+1=5 × = 30 1+4=5 × = 30 5-4=1 20 ÷ = 5-1=4 20 ÷ = operación (u operaciones relacionada(s) Operaciones básicas que usan los mismos números A veces llamadas familia de operaciones 4+1=5 5-4=1 1+4=5 5-1=4 × = 30 × = 30 R64 Glossary/Glosario 20 ÷ = 20 ÷ = Associative Property of Addition/centimeter propiedad asociativa de la asición/centímetro rhombus (p xxx) A parallelogram with four sides of the same length rombo Paralelogramo cuatro lados del mismo largo right angle (p xxx) An angle of a square corner (90˚) ángulo recto Ángulo que se forma en una esquina cuadrada (90°) right triangle (p 435) one right angle triángulo rectángulo Triángulo un ángulo recto A triangle with redondear Cambiar el valor de un número por uno el que es más fácil trabajar Ejemplo: 27 redondeado a la décima más cercana es 30 S scale (p 472) Equally spaced marks along an axis of a graph escala Conjunto de números igualmente separados en un lado de una gráfica scalene triangle (p 434) with no congruent sides triángulo escaleno Triángulo sin lados congruentes A triangle ft ft simplest form (p xxx) A fraction in which the numerator and the denominator have no common factor greater than _ is the simplest form because and ft ft ft ft forma reducida Fracción en que el numerador y el denominador no tienen un factor común mayor que Ejemplo: _ es la forma reducida de _ 10 have no common factors other than Glossary/Glosario R65 Glossary/Glosario round (p 44) To change the value of a number to one that is easier to work with To find the nearest value of a number based on a given place value 27 rounded to the nearest 10 is 30 Glossary/Glosario Associative Property of Addition/centimeter propiedad asociativa de la asición/centímetro skip count (p xxx) To count forward or backward by a given number or in intervals of a number 3, 6, 9, 12 … conteo salteado Contar hacia adelante o hacia atrás por un número dado o en intervalos de un número Ejemplo: 3, 6, 9, 12, … solid figure (p 444) A solid figure having the three dimensions: length, width, and height figura sólida Figura sólida tridimensional: largo, ancho y alto sphere (p 444) A 3-dimensional figure that has the shape of a round ball esfera Figura tridimensional forma de pelota redonda square (p.438) A rectangle with four congruent sides cuadrado Rectángulo cuatro lados congruentes standard form/standard notation (p 25) The usual way of writing a number that shows only its digits, no words Example: 537 89 1642 forma estándar/notación estándar La manera habitual de escribir un número que sólo muestra sus dígitos, sin palabras Ejemplo: 537 89 1642 standard units (p xxx) Measuring units from the customary or metric system See Table of Measures unidades estándar Unidades de medida del sistema inglés o del métrico Ver Tabla de medidas subtraction (subtract) (p xxx) An operation that tells the difference, when some or all are taken away 9-4=5 resta (sustracción) Operación que indica la diferencia cuando se elimina algo o todo Ejemplo: - = sum (p xxx) The answer to an addition problem + = 13 suma Respuesta a un problema de adición + = 13 R66 Glossary/Glosario Associative Property of Addition/centimeter survey (p 473) data propiedad asociativa de la asición/centímetro A method of collecting encuesta datos Un método para reunir T table (p xxx) A way to organize and display data with rows and columns [Caption:] table tabla Manera de organizar y representar datos filas y columnas [Caption:] tabla tally chart (p 471) A way to keep track of data using tally marks to record the results tabla de conteo Una manera de llevar la cuenta de los datos usando marcas de conteo para anotar los resultados What is Your Favorite Color? Color What is Your Favorite Color? Tally Color Blue Blue Green Green Tally marcas(s) de conteo Marca hecha para llevar la cuenta y presentar datos reunidos una encuesta tenth (p 553) or _ décima ó _ One of ten equal parts 10 Una de diez partes iguales 10 thousand(s) (p xxx) A place value of a number In 1,253, the is in the thousands place millares Valor de posición de un número Ejemplo: 1,233, el está en el lugar de las unidades de millar 3-dimensional figure (p 444) A solid figure that has length, width, and height figura tridimensional Figura sólida que tiene largo, ancho y alto triangle (p 419) A polygon with three sides and three angles triángulo Polígono tres lados y tres ángulos Glossary/Glosario R67 Glossary/Glosario tally mark(s) (p 471) A mark made to keep track and display data recorded from a survey Associative Property of Addition/centimeter propiedad asociativa de la asición/centímetro figura bidimensional El contorno de una figura, como un triángulo, un cuadrado o un rectángulo, que sólo tiene largo, ancho y área También se llama figura plana 2-dimensional figure (p 419) The outline of a shape, such as a triangle, square, or rectangle, which has only length, width, and area Also called a plane figure U unit cost (p 314) piece or item The price of a single costo unitario El precio de una sola pieza o artículo Glossary/Glosario unlikely (p xxx) An event that will probably not happen It is unlikely you will choose a yellow tile improbable Evento que probablemente no sucederá V vertex (p 444) a a point of a 2- or 3-dimensional figure where two or more edges of the figure meet The plural is vertices b the common endpoint of sides of an angle vértice a un punto, de una figura bidimensional o tridimensional, donde concurren dos o más aristas de la figura b el extremo común de los lados de un ángulo volume (p 454) The number of cubic units needed to fill a 3-dimensional figure or solid figure volumen Número de unidades cúbicas necesarias para llenar una figura tridimensional o sólida W weight (p 362) A measurement that tells how heavy an object is peso Medida que indica la pesadez de un cuerpo whole number (p xxx) 0, 1, 2, 3, … número entero 0, 1, 2, 3, … The numbers Los números Y yard (yd) (p 346) A customary unit for measuring length yard = feet or 36 inches R68 Glossary/Glosario yarda (yd) Medida inglesa de longitud yarda = pies Associative Property of Addition/centimeter propiedad asociativa de la asición/centímetro Z Zero Property of Multiplication (p 186) The property that states any number multiplied by zero is zero 0×5=0 5×0=0 propiedad del producto nulo de la multiplicación Propiedad que establece que cualquier número multiplicado por cero es igual a cero [Ejemplo: ] × = 5×0=0 Glossary/Glosario Glossary/Glosario R69 Index A Act It Out, 185, 227, 275, 319, 564–565, 573, 576, 599, 649, 716 Index Activities Add Fractions, 526–527 Area, 426–427 Capacity, 352–353 Divide Using a Multiplication Table, 293–294 Division, 634–635 Equivalent Fractions, 514–515 Fractions and Decimals, 551–552 Fractions, Decimals, and Money, 566–567 Length to the Nearest Inch, 341–342 Make a Bar Graph, 471–472 Millimeter and Centimeter, 383–384 Multiplication Table, 201–202 Multiplication with Regrouping, 600–601 Place Value, 22–23 Probability, 492–493 Relate Multiplication to Division, 256–257 Subtract Fractions, 534–535 Subtract Three-Digit Numbers with Regrouping, 122–123 Understand Division, 251–252 Volume, 452–453 Addition, 62–81, 84–100, 686–688, 724, 725 Associative Property of Addition, 65–67, 96, 97 Commutative Property of Addition, 65–67, 96, 97 Estimation, 70–73, 90, 94, 96, 97, 686, 687 Fractions, 526–531, 543, 714 Identity Property of Addition, 65–67, 96, 97 Money, 78–81, 89, 90, 94, 99, 686–688 Multi-digit, 74–76, 86–95, 98–100 Regrouping, 74–76, 86–95, 98–100 R70 Index Repeated addition, 155–159, 167, 191, 206–209, 214–216 Algebra, 6, 7, 36, 67, 73, 76, 90, 132, 138–141, 148, 162, 166, 187, 205, 206, 208, 215–217, 220, 224, 228–231, 234–237, 239, 244, 245, 254, 261, 267, 287, 292, 297, 300, 306, 307, 312, 316, 319, 320–327, 329, 331, 333, 334, 497, 517, 525, 530, 538, 556, 596, 608, 638, 653, 664–675, 684, 686, 691, 697, 699, 700, 702, 703 Equations, 320–323, 328, 333, 702 Expressions, 138–141, 148, 320–328, 333, 334, 691, 703 Function rules, 6, 7, 208, 234–238, 244, 664–671 Function tables, 208, 234–237, 244, 316, 664–666, 668–671, 697, 699 Functions, 6, 7, 208, 234–237, 244 Missing factors, 216, 224, 229, 241 Ordered pairs, 672–675 Writing equations, 320–323, 333 Writing expressions, 320–327, 333, 334 Angles, 419–421, 434–436, 461, 709 Greater than a right angle, 435, 436, 461, 709 Less than a right angle, 435, 436, 461, 709 Right angles, 435, 436, 438–441, 461, 709 Area, 426–431, 460, 709 Estimating, 426, 427 Square units, 426–431, 460 Arrays, 160–167, 174, 191, 201–205, 207, 218, 219, 222, 238–239, 257, 260, 282, 295, 304, 692, 698 Assessment Chapter Test, 59, 101, 149, 195, 245, 287, 335, 377, 413, 465, 503, 545, 579, 621, 659 Formative, 31, 77, 117, 167, 217, 267, 307, 359, 395, 437, 482, 482, 525, 561, 593, 639 Mid-Chapter Check, 31, 77, 117, 167, 217, 267, 307, 359, 395, 437, 482, 525, 561, 593, 639 Spiral Review, 27, 37, 51, 73, 81, 95, 113, 127, 137, 141 163, 181, 188, 209, 221, 231, 237, 261, 271, 278, 301, 317, 323, 327, 349, 365, 371, 388, 401, 407, 425, 431, 441, 446, 457, 479, 487, 497, 518, 531, 539, 556, 571, 597, 605, 613, 633, 653 Standards Practice, 27, 31, 37, 41, 51, 59, 60–61, 73, 77, 81, 95, 101, 102–103, 113, 117, 127, 137, 141, 149, 150–151, 163, 167, 181, 188, 195, 196–197, 209, 217, 221, 231, 237, 245, 246–247, 261, 267, 271, 278, 287, 288–289, 301, 307, 317, 323, 327, 335, 336–337, 349, 357, 359, 365, 371, 377, 378–379, 388, 395, 401, 407, 413, 414–415, 425, 431, 437, 441, 446, 457, 465, 466–467, 479, 482, 487, 497, 503, 504–505, 518, 525, 531, 539, 545, 546–547, 556, 561, 571, 579, 580–581, 593, 597, 605, 613, 621, 622–623, 633, 639, 653, 659–661 Study Guide and Review, 52–58, 96–100, 142–148, 190–194, 238–244, 282–286, 328–334, 372–376, 408–412, 458–464, 498–502, 540–543, 574–578, 616–620, 654–658 Summative Assessment, 59, 60–61, 101, 102–103, 149, 150–151, 195, 196–197, 245, 246–247, 287, 288–289, 335, 336–337, 377, 378–379, 413, 414–415, 465, 466–467, 503, 504–505, 545, 546–547, 579, 580–581, 621, 622–623, 659, 660–661 Associative Property of Addition, 65–67, 96, 97 Associative Property of Multiplication, 228–231, 238, 243 Bar graphs, 12, 13, 471–475, 482, 483, 493, 495, 496, 499 C Capacity, 338–340, 352–358, 375, 392–395, 404–407, 410, 704, 706 Cups, 352–358, 375, 704 Estimating, 358, 393, 394 Gallons, 352–358, 375, 704 Liters, 392–394, 404–407, 410, 706 Milliliters, 392–394, 404–407, 410, 706 Pints, 352–358, 375, 704 Quarts, 352–358, 375, 704 Centimeters, 8, 9, 383–389, 404–407, 409, 705 Challenge H.O.T Problems, 27, 51, 81, 90, 95, 109, 132, 141, 159, 170, 188, 237, 266, 357, 365, 371, 431, 436, 441, 497, 644, 671, 679 Chapter Test, 59, 101, 149, 195, 245, 287, 335, 377, 413, 465, 503, 545, 579, 621, 659 Choose an Operation, 84, 85, 99, 262, 263, 284, 361, 397, 443 Commutative Property of Addition, 65–67, 96, 97 Commutative Property of Multiplication, 161–163, 201, 202, 214, 215, 223, 692 Complex solid figures, 448, 449, 463, 710 Cones, 10, 11, 444–446, 448 Congruent figures, 676, 677 Converting measures, 348, 349, 354–357, 363–365, 368–371, 373, 375, 376, 388, 404–407, 412, 703, 705–707 Cross-Curricular Connections, The Buzz on Insects, 532–533 Communities Within Communities, 272–273 Continents, 562–563 Eggs!, 488–489 Gardens under Glass, 450–451 Lengths, Heights, and Weights, Oh My!, 366–367 Lots of Arms and Legs, 182–183 The Mighty Mississippi, 42–43 Not Just a Blanket, 232–233 Roller Coaster Physics, 646–647 The Sounds of the Symphony, 118–119 Stamp Collecting, 614–615 Stars and Stripes, 308–309 A Visit to the Supermarket, 402–403 A Walk in the Park, 82–83 Cubes, 10, 11, 444–446 Cubic units, 452–457, 464 Cups, 352–358, 375, 704 Customary system, 8, 9, 40, 341–349, 352–358, 362–365, 372–376, 703–705 Cups, 352–358, 375, 704 Gallons, 352–358, 375, 704 Half inch, 343–345 Inches, 8, 9, 341–349, 373 Ounces, 362–365, 376, 705 Pints, 352–358, 375, 704 Pounds, 362–365, 376, 705 Quarts, 352–358, 375, 704 Yards, 346–349, 373, 703 Cylinders, 10, 11, 444–449 D Data, 468–483, 492–502, 711 Analysis, 12, 13 Bar graphs, 12, 13, 471–475, 482, 483, 493, 495, 496, 499, 711 Collecting, 12, 13 Displays, 471–483, 492–497 Graphing, 471–481, 483, 493, 495–497, 499 Line plot, 468, 476–479, 482, 493, 495, 496, 498, 711, 712 Pictographs, 12, 13 Predictions, 494–497, 502 Recording, 492, 493 Surveys, 473–475 Tally chart, 12, 13, 471–475, 494–497 Data File, 30, 76, 112, 126, 176, 236, 266, 312, 364, 406, 445, 486, 530, 555, 596, 604 Decimals, 548–563, 566–571, 574–578 Decimal points (.), 78 Fraction equivalence, 548–563, 566–571, 574 Hundredths, 558–560, 574, 575 Money, 566–571, 574, 577 Place value, 553–556, 558–561, 574, 575 Tenths, 553–556, 574, 575 Denominator, 509–511 Digits, 14–16, 22–31, 683 Divide a number by itself, 280, 281 Division, 248–273, 276–279, 282–334, 624–639, 642–645, 650–661, 697–701, 720–722, 730, 731 As repeated subtraction, 253–257, 268–271, 276–278, 282, 283 By 0, 280, 281 By 2, 264–266, 284 By 3, 295–297, 329 By 4, 298–301, 329 By 5, 268–271, 285 By 6, 304–306, 331 By 7, 304–306, 331 By 8, 310–312, 331 By 9, 310–312, 331 Index R71 Index B Comparing Fractions, 522–524, 543, 714 Measures, 353 Numbers, 4, 5, 34–37, 56, 684 By 10, 276–278, 286 By 1-digit numbers, 624–626 By multiples of 10, 627–629, 655 By multiples of 100, 627–629, 655 By multiples of 1,000, 627–629, 655 Divide a number by itself, 280, 281 Dividend, 257 Division-multiplication relationship, 253–267, 272, 273, 276–278, 282–289, 296, 298–301, 305, 310–312, 328, 698 Divisor, 257 Estimating, 630–633, 645, 654, 655 Facts, 248–273, 276–279, 282–334, 697–701, 730 Functions, 668–671 Money, 650–653, 658, 722 Patterns, 627–629, 720 Properties, 280, 281, 286 Quotient, 257 Regrouping, 634–648 Repeated subtraction, 253–257, 268–271, 276–278, 282, 283, 296, 299, 305, 311, 328, 697 Three-digit quotients, 642–644, 657 Two-digit quotients, 636–638, 656 Unit cost, 314–317, 328, 332, 651–653, 702, 722 Doubling (multiplication facts), 169, 178–181, 207, 219, 239 Draw a Picture, 185, 227, 275, 319, 512–513, 521, 541, 573, 599, 649 E Index Equal to (=), 4, 5, 34–37, 56, 522–524, 684, 714 Equations, 320–323, 328, 333, 702 Writing equations, 320–323, 333 Equilateral triangles, 434–436, 461 Equivalent fractions, 514–519, 542, 713 R72 Index Estimation, 71–73, 590–593, 618, 630–633, 645, 654, 655 Addition, 70–73, 90, 94, 96, 97, 686, 687 Area, 426, 427 Capacity, 358, 393, 394 Division, 630–633, 645, 654, 655, 720 Front-end estimation, 71–73, 592 Length, 341–343, 383, 384 Mass, 399–401 Multiplication, 590–592, 618, 718 Subtraction, 110–113, 143, 686, 689 Volume, 455–457, 464 Weight, 363 Estimation or Exact Answer, 68, 69, 85, 97, 129, 686 Expanded form, 4, 5, 24–31, 37, 54, 683, 684 Expressions, 138–141, 148, 320–328, 333, 334, 691, 703 Writing expressions, 320–327, 333, 334 Extra or Missing Information, 172, 173, 193, 693 F Fact family, 259–261, 282, 698 Factors, 158, 159, 171, 201, 202 Facts Addition, 724, 725 Division, 248–273, 276–279, 282–334, 697–701, 730 Doubling (multiplication), 169, 178–181, 207, 219, 239 Fact family, 259–261, 282 Fast Facts, 177, 210, 225 Multiplication, 152–171, 174–181, 186–189, 191–194, 198–247, 692–697 Subtraction, 726, 727 Find the Error H.O.T Problems, 24, 27, 41, 73, 95, 113, 127, 163, 170, 266, 27, 41, 301, 323, 371, 407, 421, 457, 487, 531, 538, 629, 644, 667, 675 Foldables, 15, 52, 63, 105, 142, 153, 190, 199, 238, 249, 282, 291, 328, 339, 372, 381, 408, 417, 458, 469, 498, 507, 540, 549, 574, 583, 616, 625, 654 Foot (feet), 346–349, 373, 703 Formative Assessment, 31, 77, 117, 167, 217, 267, 307, 359, 395, 437, 482, 482, 525, 593, 639 Four-Step Plan, 2, 3, 20, 21, 32, 33, 53, 66, 85, 129, 185, 227, 275, 319, 361, 397, 443, 491, 521, 573, 599, 649, 683 Fractions, 506–563, 566–571, 574–578, 713, 714 Addition, 526–531, 543, 714 Comparing, 522–524, 543, 714 Denominator, 509–511 Fraction-decimal equivalence, 548–563, 566–571, 574, 715 Money, 716 Numerator, 509–511 Parts of a whole, 509–511 Subtracting, 534–539, 544 Front-end estimation, 71–73, 592 Function rules, 6, 7, 208, 234–238, 244, 664–671 Function tables, 208, 234–237, 244, 316, 664–666, 668–671, 697, 699 Functions, 6, 7, 208, 234–237, 244, 668–671 Division, 668–671 Multiplication, 668–671 Subtraction, 664–667 G Gallons, 352–358, 375, 704 Game Time, Capacity Guess, 358 Catch Me If You Can, 483 Do Not Zero Out, 133 Factor Power, 171 Fraction Concentration, 519 Fractoes and Decimoes, 557 High and Low, 609 Hit the Target, 389 How Low Can You Go?, 91 Number Cubes, 279 Quotient Roll, 313 Round Numbers, 47 That’s Close!, 645 Three in a Row, 211 What’s the Shape?, 447 Grams, 398–401, 404–407, 411, 707 Graphing, 471–481, 483, 493, 495–497, 499 Bar, 12, 13, 471–475, 482, 483, 493, 495, 496, 499 Coordinate grids, 672–675 Line plot, 468, 476–479, 482, 493, 495, 496, 498, 711, 712 Ordered pairs, 672–675 Pictographs, 12, 13 Scale, 471, 472 Greater than (>), 4, 5, 34–37, 56, 522–524, 684, 714 Greater than a right angle, 435, 436, 461, 709 Guess and Check, 390, 391, 397, 410, 443, 491, 521, 573, 706 518, 524, 538, 556, 560, 571, 587, 597, 605, 608, 633, 638, 653, 667, 671, 675, 677, 679 Reasoning, 436, 446, 511 Which One Doesn’t Belong? 37, 51, 81, 137, 141, 176, 181, 216, 231, 237, 261, 271, 297, 306, 317, 327, 349, 401, 518, 560, 571, 605, 613, 633, 677, 216, 231, 237 Hundreds chart, 17–19, 24–30, 35, 38, 56, 57 I Identity Property of Addition, 65–67, 96, 97 Identity Property of Multiplication, 186–188, 202 Inches, 8, 9, 341–349, 373, 703 Isosceles triangles, 434–436, 461 H Hexagons, 419–421, 676–677 Horizontal bar graph, 474, 475, 482, 499, 711 H.O.T Problems, Challenge, 27, 51, 81, 90, 95, 109, 132, 141, 159, 170, 188, 237, 266, 357, 365, 371, 431, 436, 441, 497, 644, 671, 679 Find the Error, 24, 27, 41, 73, 95, 113, 127, 163, 170, 266, 27, 41, 301, 323, 371, 407, 421, 457, 487, 531, 538, 629, 644, 667, 675 Number Sense, 19, 41, 51, 109, 127, , 216, 221, 224, 261, 277, 297, 365, 431, 457, 524, 556, 605, 613, 653, 671 Open Ended, 19, 30, 37, 46, 67, 73, 76, 90, 116, 132, 159, 166, 170, 188, 205, 209, 221, 231, 255, 271, 277, 281, 297, 306, 312, 317, 323, 327, 345, 349, 357, 365, 394, 401, 421, 425, 431, 441, 446, 449, 457, 475, 478, 487, 511, K Key Concepts, 49, 65, 204, 228, 280, 299, 362, 405, 422, 434, 444, 484, 529, 537, 568 Kilograms, 398–401, 404–407, 411, 707 Kilometers, 385–388, 404–407, 409, 705 L Length, 338–349, 373, 383–388, 404–407, 409, 703 Centimeters, 8, 9, 383–389, 404–407, 409, 705 Estimating, 341–343, 383, 384 Foot (feet), 346–349, 373, 703 Half inch, 343–345 Inches, 8, 9, 341–349, 373, 703 Kilometers, 385–388, 404–407, 409, 705 Meters, 385–388, 404–407, 409, 705 Miles, 346–349, 373, 703 Index R73 Index Geometry, 10, 11, 416–441, 444–446, 676–679, 707 Angles, 419–421, 434–436 Closed figures, 419–421 Complex solid figures, 448, 449, 463, 710 Cones, 10, 11, 444–449 Congruent figures, 676, 677 Cubes, 10, 11, 444–446 Cylinders, 10, 11, 444–449 Edges, 710 Equilateral triangles, 434–436, 461 Faces, 710 Hexagons, 419–421, 676, 677 Isosceles triangles, 434–436, 461 Octagons, 419–421 Open figures, 419–421 Parallel lines, 438–441, 461 Parallelograms, 438–441, 461 Pentagons, 419–421, 676, 677 Plane figures, 416–421, 708, 709 Polygons, 419–421, 447, 459, 707 Pyramids, 10, 11, 444–446 Quadrilaterals, 419–421, 438–441, 461, 709 Rectangles, 10, 11, 438–441 Rectangular prisms, 10, 11, 444–446 Rhombus, 438–441, 461 Right angles, 435, 436, 438–441, 461, 709 Scalene triangles, 434–436 Sides, 10, 11, 419–421, 434–436, 438–441 Solid figures, 416–418, 444–446, 448, 449, 463, 710 Spheres, 10, 11, 444–446, 448, 449 Squares, 10, 11, 438–441 Symmetry, 678, 679 Three-dimensional figures, 10, 11, 416–418 Trapezoids, 438–441, 461 Triangles, 10, 11, 419–421, 434–436, 461, 708 Two-dimensional figures, 10, 11, 416–421 Vertex, 710 Millimeters, 383–388, 404–407, 409, 705 Yards, 346–349, 373, 703 Less than (), 4, 5, 34–37, 56, 522–524, 684, 714 Less than (