Authors Basich Whitney • Brown • Dawson • Gonsalves • Silbey • Vielhaber Jupiter Images Photo Credits Cover, i Jupiter Images; iv (tl)File Photo, (tc tr)The McGraw-Hill Companies, (cl c)Doug Martin, (cr)Aaron Haupt, (bl bc)File Photo; v (L to R 11 12)The McGraw-Hill Companies, (5 10 13 14)File Photo; vii CORBIS; viii Mitchell Funk/Getty Images; ix S Alden/PhotoLink/Getty Images; x Peter Barritt/Alamy; 2–3 Getty Images; (t)Getty Images, (b)The McGraw-Hill Companies, Inc./Bob Coyle, photographer; 16 Bettmann/CORBIS; 30 Mark Ransom/RansomStudios; 32 Masterfile; 37 Getty Images; 45 CORBIS; 51 Jupiter Images; 54–55 Arnulf Husmo/Getty Images; 55 CORBIS; 56 Keith Ovregaard/Cole Group/Getty Images; 57 (l)Photodisc/Getty Images, (r)CORBIS; 58 Mark Ransom/ RansomStudios; 59 John A Rizzo/Getty Images; 60 (t)Jules Frazier/Getty Images, (b)Mark Ransom/RansomStudios; 67 CORBIS; 76 Gary Cralle/Getty Images; 82 (t)Getty Images, (b)Lawrence Manning/CORBIS; 83 GK & Vikki Hart/Getty Images; 89 (frame)Getty Images, (insert)Mark Ransom/RansomStudios Copyright © 2008 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: 978-0-07-878213-8 MHID: 0-07-878213-9 Printed in the United States of America 10 055/027 16 15 14 13 12 11 10 09 08 07 California Math Triumphs Volume 6A California Math Triumphs Volume Place Value and Basic Number Skills 1A Chapter Counting 1A Chapter Place Value 1A Chapter Addition and Subtraction 1B Chapter Multiplication 1B Chapter Division 1B Chapter Integers Volume Fractions and Decimals 2A Chapter Parts of a Whole 2A Chapter Equivalence of Fractions 2B Chapter Operations with Fractions 2B Chapter Positive and Negative Fractions and Decimals Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc Volume Ratios, Rates, and Percents 3A Chapter Ratios and Rates 3A Chapter Percents, Fractions, and Decimals 3B Chapter Using Percents 3B Chapter Rates and Proportional Reasoning Volume The Core Processes of Mathematics 4A Chapter Operations and Equality 4A Chapter Math Fundamentals 4B Chapter Math Expressions 4B Chapter Linear Equations 4B Chapter Inequalities Volume Functions and Equations 5A Chapter Patterns and Relationships 5A Chapter Graphing 5B Chapter Proportional Relationships 5B Chapter The Relationship Between Graphs and Functions Volume Measurement 6A Chapter How Measurements Are Made 6A Chapter Length and Area in the Real World 6B Chapter Exact Measures in Geometry 6B Chapter Angles and Circles iii Authors and Consultants AUTHORS Frances Basich Whitney Kathleen M Brown Dixie Dawson Project Director, Mathematics K–12 Santa Cruz County Office of Education Capitola, California Math Curriculum Staff Developer Washington Middle School Long Beach, California Math Curriculum Leader Long Beach Unified Long Beach, California Philip Gonsalves Robyn Silbey Kathy Vielhaber Mathematics Coordinator Alameda County Office of Education Hayward, California Math Specialist Montgomery County Public Schools Gaithersburg, Maryland Mathematics Consultant St Louis, Missouri Viken Hovsepian Professor of Mathematics Rio Hondo College Whittier, California Dinah Zike Educational Consultant, Dinah-Might Activities, Inc San Antonio, Texas CONSULTANTS Assessment Donna M Kopenski, Ed.D Math Coordinator K–5 City Heights Educational Collaborative San Diego, California Instructional Planning and Support ELL Support and Vocabulary Beatrice Luchin ReLeah Cossett Lent Mathematics Consultant League City, Texas Author/Educational Consultant Alford, Florida iv (tl)File Photo, (tc tr)The McGraw-Hill Companies, (cl c)Doug Martin, (cr)Aaron Haupt, (bl bc)File Photo Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc CONTRIBUTING AUTHORS California Advisory Board CALIFORNIA ADVISORY BOARD Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc 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 Student Study Guide, the prototype of the Teacher Wraparound Edition, and the professional development plan Linda Anderson Cheryl L Avalos Bonnie Awes Kathleen M Brown 4th/5th Grade Teacher Oliveira Elementary School, Fremont, California Mathematics Consultant Retired Teacher Hacienda Heights, California Teacher, 6th Grade Math Monroe Clark Middle School San Diego, California Math Curriculum Staff Developer Washington Middle School Long Beach, California Carol Cronk Audrey M Day Jill Fetters Grant A Fraser, Ph.D Mathematics Program Specialist San Bernardino City Unified School District San Bernardino, California Classroom Teacher Rosa Parks Elementary School San Diego, California Math Teacher Tevis Jr High School Bakersfield, California Professor of Mathematics California State University, Los Angeles Los Angeles, California Eric Kimmel Donna M Kopenski, Ed.D Michael A Pease Chuck Podhorsky, Ph.D Mathematics Department Chair Frontier High School Bakersfield, California Math Coordinator K–5 City Heights Educational Collaborative San Diego, California Instructional Math Coach Aspire Public Schools Oakland, California Math Director City Heights Educational Collaborative San Diego, California Arthur K Wayman, Ph.D Frances Basich Whitney Mario Borrayo Melissa Bray Professor Emeritus California State University, Long Beach Long Beach, California Project Director, Mathematics K–12 Santa Cruz County Office of Education Capitola, CA Teacher Rosa Parks Elementary San Diego, California K–8 Math Resource Teacher Modesto City Schools Modesto, California v (L to R 11 12)The McGraw-Hill Companies, (5 10 13 14)File Photo California Reviewers CALIFORNIA REVIEWERS Each California Reviewer reviewed at least two chapters of the Student Study Guides, providing feedback and suggestions for improving the effectiveness of the mathematics instruction Melody McGuire Math Teacher California College Preparatory Academy Oakland, California 6th and 7th Grade Math Teacher McKinleyville Middle School McKinleyville, California Eppie Leamy Chung Monica S Patterson Teacher Modesto City Schools Modesto, California Educator Aspire Public Schools Modesto, California Judy Descoteaux Rechelle Pearlman Mathematics Teacher Thornton Junior High School Fremont, California 4th Grade Teacher Wanda Hirsch Elementary School Tracy, California Paul J Fogarty Armida Picon Mathematics Lead Aspire Public Schools Modesto, California 5th Grade Teacher Mineral King School Visalia, California Lisa Majarian Anthony J Solina Classroom Teacher Cottonwood Creek Elementary Visalia, California Lead Educator Aspire Public Schools Stockton, California vi Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc Bobbi Anne Barnowsky Volume 6A Measurement Chapter How Measurements Are Made 1-1 Unit Conversions: Metric Length 3AF1.4, 3MG1.4, 6AF2.1 1-2 Unit Conversions: Customary Length 11 3AF1.4, 3MG1.4, 6AF2.1 Progress Check .18 1-3 Unit Conversions: Metric Capacity and Mass 19 3AF1.4, 3MG1.4, 6AF2.1, 7MG1.1 1-4 Unit Conversions: Customary Capacity and Weight… 25 3AF1.4, 3MG1.4, 6AF2.1 Progress Check .32 1-5 Time and Temperature 33 3AF1.4, 3MG1.4, 6AF2.1, 7MG1.1 1-6 Analyze Units of Measure .39 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc 6AF2.1, 7MG1.1, 7MG1.3 Progress Check .46 Assessment Study Guide .47 Chapters and are contained in Volume 6A Chapters and are contained in Volume 6B Standards Addressed in This Chapter 3AF1.4 Express simple unit conversions in symbolic form (e.g., _ inches = _ feet × 12) 3MG1.4 Carry out simple unit conversions within a system of measurement (e.g., centimeters and meters, hours and minutes) 6AF2.1 Convert one unit of measurement to another (e.g., from feet to miles, from centimeters to inches) 7MG1.1 Compare weights, capacities, geometric measures, times, and temperatures within and between measurement systems (e.g., miles per hour and feet per second, cubic inches to cubic centimeters) 7MG1.3 Use measures expressed as rates (e.g., speed, density) and measures expressed as products (e.g., person-days) to solve problems; check the units of the solutions; and use dimensional analysis to check the reasonableness of the answer Chapter Test .50 Standards Practice 52 Lake Tahoe vii CORBIS Contents Chapter Length and Area in the Real World Standards Addressed in This Chapter 2-1 Length 56 2MG1.3, 4MG2.2, 4MG2.3 2-2 Perimeter 63 3MG1.3 Progress Check .70 2-3 Introduction to Area .71 3MG1.2 2-4 Introduction to Volume 77 3MG1.2 Progress Check .83 Assessment 2MG1.3 Measure the length of an object to the nearest inch and/or centimeter 3MG1.2 Estimate or determine the area and volume of solid figures by covering them with squares or by counting the number of cubes that would fill them 3MG1.3 Find the perimeter of a polygon with integer sides 4MG2.2 Understand that the length of a horizontal line segment equals the difference of the x-coordinates 4MG2.3 Understand that the length of a vertical line segment equals the difference of the y-coordinates Study Guide .84 Chapter Test .88 Standards Practice 90 Mitchell Funk/Getty Images Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc viii Alamo Square, San Francisco Contents Chapter Exact Measures in Geometry 3-1 Area of a Rectangle 3MG1.2, 4MG1.1 3-2 Area of a Parallelogram 11 4MG1.1, 5MG1.1 Progress Check .18 3-3 Area of a Triangle 19 3MG1.2, 5MG1.1 3-4 Surface Area of Rectangular Solids 27 3MG1.2, 4MG1.1, 5MG1.2 Progress Check .36 3-5 Volume of Rectangular Solids .37 3MG1.2, 5MG1.3 Assessment Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc Study Guide .43 Chapter Test .48 Standards Practice 50 Santa Cruz Chapters and are contained in Volume 6A Chapters and are contained in Volume 6B Standards Addressed in This Chapter 3MG1.2 Estimate or determine the area and volume of solid figures by covering them with squares or by counting the number of cubes that would fill them 4MG1.1 Measure the area of rectangular shapes by using appropriate units, such as square centimeter (cm2), square meter (m2), square kilometer (km2), square inch (in.2), square yard (yd.2), or square mile (mi.2) 5MG1.1 Derive and use the formula for the area of a triangle and of a parallelogram by comparing each with the formula for the area of a rectangle (i.e., two of the same triangles make a parallelogram with twice the area; a parallelogram is compared with a rectangle of the same area by pasting and cutting a right triangle on the parallelogram) 5MG1.2 Construct a cube and rectangular box from two-dimensional patterns and use these patterns to complete the surface area for these objects 5MG1.3 Understand the concept of volume and use the appropriate units in common measuring systems (i.e., cubic centimeter [cm3], cubic meter [m3], cubic inch [in.3], cubic yard [yd.3]) to compute the volume of rectangular solids ix S Alden/PhotoLink/Getty Images Contents Chapter Angles and Circles Standards Addressed in This Chapter 4-1 Lines 5MG2.1 54 4-2 Angles 5MG2.1 63 Progress Check 72 4-3 Triangles and Quadrilaterals 5MG2.1 73 4-4 Add Angles 5MG2.1, 5MG2.2, 6MG2.2 81 Progress Check 90 4-5 Congruent Figures 7MG3.4 91 4-6 Pythagorean Theorem 5MG2.1, 7MG3.3 99 Progress Check 108 4-7 Circles 6MG1.2 .109 4-8 Volume of Triangular Prisms and Cylinders 117 6MG1.3 Progress Check 127 Study Guide 128 Chapter Test 134 Standards Practice .136 Mono Lake Tufa State Reserve 5MG2.2 Know that the sum of the angles of any triangle is 180° and the sum of the angles of any quadrilateral is 360° and use this information to solve problems 6MG1.2 Know common estimates 22 of π (3.14, _) and use these values to estimate and calculate the circumference and the area of circles; compare with actual measurements 6MG1.3 Know and use the formulas for the volume of triangular prisms and cylinders (area of base × height); compare these formulas and explain the similarity between them and the formula for the volume of a rectangular solid 6MG2.2 Use the properties of complementary and supplementary angles and the sum of the angles of a triangle to solve problems involving an unknown angle 7MG3.3 Know and understand the Pythagorean theorem and its converse and use it to find the length of the missing side of a right triangle and the lengths of other line segments and, in some situations, empirically verify the Pythagorean theorem by direct measurement 7MG3.4 Demonstrate an understanding of conditions that indicate two geometrical figures are congruent and what congruence means about the relationship between the sides and angles of the two figures x Peter Barritt/Alamy Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc Assessment 5MG2.1 Measure, identify, and draw angles, perpendicular and parallel lines, rectangles, and triangles by using appropriate tools (e.g., straight edge, ruler, compass, protractor, drawing software) Guided Practice How many cubes are in this rectangular prism? How many cubes are in this rectangular prism? Remember, you can find the volume of a solid figure by counting the number of cubic units it contains Step by Step Practice Find the volume of the rectangular prism Step Count the number of cubes along the length The length of the rectangular prism has cubes Step Count the number of cubes along the width cubes Copyright © by The McGraw-Hill Companies, Inc The width of the rectangular prism has × Step The area of the top layer is Step There are + = layers in the prism + = cubes in the prism The volume of the rectangular prism is cubic units Find the volume of each rectangular prism Count the number of cubes along the length, width, and height of the rectangular prism Find the area of the top layer Add that number four times The volume of the rectangular prism is cubic units height width length GO ON Lesson 2-4 Introduction to Volume 79 Count the number of cubes along the length, width, and height of the rectangular prism height Find the area of the top layer Add that number eight times cubic units The volume of the rectangular prism is length width The volume of the rectangular prism is cubic units The volume of the rectangular prism is cubic units Step by Step Problem-Solving Practice Problem-Solving Strategies Draw a diagram Look for a pattern ✓Use a model Solve a simpler problem Work backward Solve GIFTS A present that is shaped like a rectangular prism has a length of feet, a width of feet, and a height of feet What is its volume? Understand Read the problem Write what you know feet, a width of feet feet, and a height of Plan Pick a strategy One strategy is to use a model Solve Use unit blocks to build the rectangular prism Count the number of blocks used Check The length is feet The width is feet There are Copyright © by The McGraw-Hill Companies, Inc A rectangular prism has a length of layers Multiply then add × = + + + + The volume of the rectangular prism is 80 Chapter Length and Area in the Real World + + cubic feet + = MODELS Tina’s model house is 15 inches long, 20 inches wide, and 10 inches tall What is the volume of Tina’s house? Check off each step Understand Plan Solve Check 10 11 PETS Delmar’s doghouse is meters long, meters wide, and meter tall What is the volume of Delmar’s doghouse? Give the length, width, and height of a rectangular prism that has a volume of 36 cubic units Explain Skills, Concepts, and Problem Solving Copyright © by The McGraw-Hill Companies, Inc Find the volume of each rectangular prism 12 13 The volume of the rectangular prism is cubic units 14 The volume of the rectangular prism is cubic units The volume of the rectangular prism is cubic units 15 The volume of the rectangular prism is cubic units GO ON Lesson 2-4 Introduction to Volume 81 Solve 16 PACKAGING What is the volume of the package shown at the right? 17 ART A box of art tools is centimeters long, centimeters wide, and centimeters tall What is the volume of the art box? PACKAGING The package is 10 inches long, inches wide, and inches tall Vocabulary Check Write the vocabulary word that completes each sentence 18 A(n) is a unit for measuring volume 19 is the number of cubic units needed to fill a three-dimensional figure or solid figure 20 Writing in Math Explain how to find the volume of a rectangular prism Spiral Review 15 in 21 15 in 15 in 15 in (Lesson 2-3, p 71) Measure the length of each line segment to the nearest inch (Lesson 2-1, p 56) in 22 The blue line segment is about 23 The red line segment is about Convert inches long inches long (Lesson 1-5, p 33) 24 = s 82 Chapter Length and Area in the Real World (t)Getty Images, (b)Lawrence Manning/CORBIS 25 120 h = d Copyright © by The McGraw-Hill Companies, Inc SPORTS Spud’s Sporting Shop sells softball bases like the one shown What is the area of one of the bases? Chapter Progress Check 2 (Lessons 2-3 and 2-4) Draw a figure that has the given area 42 square units 36 square units Find the area of each figure Copyright © by The McGraw-Hill Companies, Inc The area of the rectangle is square units The area of the figure is square units Find the volume of each rectangular prism The volume of the rectangular prism is cubic units The volume of the rectangular prism is cubic units Solve ROOMS The ceiling tiles in Jackie’s kitchen are in the shape of a square Each tile has sides that measure 54 centimeters What is the area of each tile? PETS What is the volume of Angela’s fish tank? PETS Angela’s fish tank is 12 inches long, 14 inches wide, and 15 inches tall Chapter Progress Check GK & Vikki Hart/Getty Images 83 Chapter Study Guide Vocabulary and Concept Check area, p 71 Write the vocabulary word that completes each sentence centimeter, p 56 A(n) is a customary unit for measuring length and height A(n) The number of square units needed to cover the inside congruent figures, p 77 cube, p 77 cubic unit, p 77 inch, p 56 length, p 56 is used to measure volume of a region or plane figure is the perimeter, p 63 polygon, p 63 A(n) is a metric unit for measuring length and height The unit used for measuring area is called a(n) rectangle, p 63 rectangular prism, p 77 ruler, p 56 square, p 63 square unit, p 71 The distance around a shape or region is its triangle, p 63 volume, p 77 x-coordinate, p 56 y-coordinate, p 56 The of a three-dimensional figure or solid is the number of cubic units needed to fill it in 84 Chapter Length and Area in the Real World 10 Copyright © by The McGraw-Hill Companies, Inc Label each diagram below Write the correct vocabulary term in each blank Lesson Review 2-1 Length Example (pp 56–62) Measure the length of the item to the nearest inch 11 The key is Find the length of the crayon to the nearest inch long Use an inch ruler Line up the “zero mark” of the ruler with the left end of the crayon in in 3 Read the number on the ruler that lines up with the right end of the crayon The crayon is about inches long Measure the length of the item 12 The earthworm is cm Copyright © by The McGraw-Hill Companies, Inc long 2-2 13 Perimeter Find the perimeter of the rectangle in inches Example (pp 63–69) in in Find the perimeter of the polygon in inches in in in in in in 14 Find the perimeter of the polygon in centimeters cm cm cm Add the lengths of the sides + + + = 18 The perimeter of the polygon is 18 inches cm cm Chapter Study Guide 85 2-3 Introduction to Area (pp 71–76) Find the area of each figure 15 Example Estimate the area of the figure What is the area of the square? The area of the square is square units 16 Estimate the area of the figure Count the number of whole squares the figure covers The figure covers whole squares Count the number of half squares the figure covers The figure covers half squares + + + + + 1=3 2 2 2 Add the number of whole squares + = 11 The area of the figure is 11 square units Estimate the area of the figure 86 Chapter Study Guide Copyright © by The McGraw-Hill Companies, Inc 17 2-4 18 Introduction to Volume Find the volume of the rectangular prism (pp 77–83) Example Find the volume of the rectangular prism Count the number of layers of cubes in the prism There are layers of cubes in the rectangular prism Count the number of cubes in the top layer There are cubes in the top layer 19 Find the volume of the rectangular prism Each layer has the same number of cubes There are + + + + cubes The volume of the rectangular prism is 30 cubic units height Example Copyright © by The McGraw-Hill Companies, Inc length width Find the volume of the rectangular prism Count the number of cubes along the length The length of the rectangular prism has cubes 20 Find the volume of the rectangular prism height width Count the number of cubes along the width.The width of the rectangular prism has cubes length Count the number of cubes along the height The height of the rectangular prism has cubes Find the area of the top layer height 3×2=6 Add that number times width length + + + = 24 The volume of the rectangular prism is 24 cubic units Chapter Study Guide 87 Chapter Test What is the height of the toy soldier at the right to the nearest centimeter? Draw a line segment cm that has a length of centimeters 3 Chapter 10 cm 1 What is the perimeter of the polygon? What is the perimeter of the rectangle? cm in cm cm in in cm in Find the length of each segment O y 6 8x Find the area of the figure O y Copyright © by The McGraw-Hill Companies, Inc 1 8x Estimate the area of the figure GO ON 88 Chapter Test Find the volume of the rectangular prism 10 Find the volume of the rectangular prism Solve 11 LANDSCAPING Mrs Fisher asked her daughter to place a rock border around her flower bed There were four different edges surrounding the flower bed, with lengths of feet, feet, feet, and feet What was the perimeter of Mrs Fisher’s flower bed? 12 PICTURES The photograph that Mora’s mom ordered to hang on the wall is shown at the right What is the area of the photograph? 11 in Copyright © by The McGraw-Hill Companies, Inc 14 in Correct the mistakes 13 14 Here is how Elvio answered a question on yesterday’s quiz: What is the area of the rectangular base of a tool box that has a length of 15 inches and a width of inches? Tell what mistake he made 15 + + 15 + = 48 inches Show how you would answer the problem on Elvio’s quiz Chapter Test (frame)Getty Images, (insert)Mark Ransom/RansomStudios 89 Chapter Standards Practice Choose the best answer and fill in the corresponding circle on the sheet at right Find the length of the line to the nearest centimeter A cm C cm B cm D 10 cm O What is the perimeter of the equilateral triangle? 14 in What is the length of the line segment shown on the grid? F 14 inches H 42 inches G 28 inches J 196 inches y (2, 5) What is the area of the shaded figure? (2, 1) 8x F units H units G units J units A square units C 15 square units B 10 square units D 20 square units What is the perimeter of the rectangle? ft What is the volume of the solid figure? ft A 13 feet C 36 feet B 26 feet D 42 feet F cubic units H 16 cubic units G 12 cubic units J 18 cubic units GO ON 90 Chapter Standards Practice Copyright © by The McGraw-Hill Companies, Inc Copyright © by The McGraw-Hill Companies, Inc 10 What is the volume of the solid figure? ANSWER SHEET Directions: Fill in the circle of each correct answer A B C D A 12 cubic units C 30 cubic units F G H J B 18 cubic units D 36 cubic units A B C D F G H J A B C D F G H J A B C D F G H J A B C D 10 F G H J 8,039 millimeters = meters F 803.9 H 8.039 G 80.39 J 0.008039 Which is a reasonable temperature for a cool fall day? A 12°C C 40°C B 30°C D 60°C Success Strategy During a timed test, not spend too much time on any one question Try your best, but then move on Answer the easiest questions first, and then go back to the ones you skipped Markell spent 40 minutes on his math homework, 35 minutes on reading homework, and 38 minutes on writing homework How long did he spend completing his homework? F hour 13 minutes G hour 53 minutes H hours minutes J hours minutes Chapter Standards Practice 91 Index A Algebra and Functions, 4, 11, 19, 25, 33, 39 F Fahrenheit, 33–39 Answer sheet, 53, 91 area, 71–76 irregular shapes, 71, 72, 74, 75, 83 quadrilateral, 71, 72, 73, 74, 75, 83 rectangle, 71, 72, 73, 74, 75, 83 G gram, 19–24 P perimeter, 63–69 polygon, 63, 64, 65, 67, 68 quadrilateral, 63, 67, 68, 70 rectangle, 63, 65, 66, 67, 68 triangle, 67, 68, 70 polygon, 63 I Problem-Solving See Step-byStep Problem Solving Progress Check, 18, 32, 46, 70, 83 inch, 56–62 Assessment, 50–51, 88–89 K B benchmark, 4, 11, 25 Key Concept, 4, 11, 19, 25, 33, 39, 56, 63, 71, 77 C California Mathematics Content Standards, 4, 11, 19, 25, 33, 39, 56, 63, 71, 77 capacity, 19–24, 25–31 Celsius, 33–39 centimeter, 56–62 lines horizontal, 56, 57, 58, 59, 61, 62, 70, 82 vertical, 56, 57, 59, 61, 62, 70 liter, 19–24 M congruent figures, 77 Correct the Mistakes, 51, 89 customary system, 11–17, 25–31, 33–39, 56–62 D degree temperature, 33–39 92 Index R length, 56–62 Chapter Test, 50–51, 88–89 convert, 4–10, 11–17, 25–31, 33–38 quadrilateral area, 71–76 perimeter, 63–69 mass, 19–24 Mathematical Reasoning See Step-by-Step Problem Solving Measurement and Geometry, 4, 11, 19, 25, 33, 39, 56, 63, 71, 77 meter, 4–10 metric system of measurement, 4–10, 19–24, 33–39, 56–62 Real-World Applications advertising, 17, 45 airplanes, animals, 42 art, 30, 76, 82 babies, 32 baseball, 60 books, 76 building, 66 chemistry, 51 construction, 32, 46 cooking, 24, 30, 51 decorating, 16 design, 68 entertainment, 42 food service, 36 gardens, 76 geometry, 74 gifts, 80 groceries, 46 health, 23 history, 16, 36 homes, 14 Copyright © by The McGraw-Hill Companies, Inc Chapter Preview, 3, 55 L Q hobbies, 67, 89 irrigation, 43 land, 18 landscaping, 89 measurement, 29 models, 60, 81 nature, 45, 62 number sense, 18 nutrition, 22, 23, 31 packaging, 38, 82 patios, 67 pets, 10, 30, 81, 83 photography, 45 pictures, 89 races, 16 recipes, 43 rooms, 68, 75, 83 school, 14, 16, 62, 70 science, 36 sewing, shoes, shopping, 60, 75 sports, 8, 14, 51, 82 temperature, 37, 69 travel, 9, 10, 24, 37, 45, 51, 62 work, 43 zoo animals, 29 Copyright © by The McGraw-Hill Companies, Inc rectangle area, 71–76 perimeter, 63–69 rectangular prism volume, 77–82 Reflect, 9, 15, 23, 30, 37, 44, 61, 67, 75, 81 ruler, 11, 56–62, 69, 82 S Spiral Review, 17, 24, 31, 38, 45, 62, 69, 76, 82 square unit, 71–76 Standards Practice (range), 52–53, 90–91 Step-by-Step Practice, 7, 13, 21, 28, 35, 42, 58, 65, 73, 79 Step-by-Step Problem Solving Practice, 8, 14, 22–23, 29, 36, 43, 60, 66–67, 74–75, 80–81 Act it out, 60 Draw a diagram, 66, 74 Look for a pattern, 8, 14, 29 Solve a simpler problem, 22, 43 Use a model, 80 Work backward, 36 Study Guide (range), 47–49, 84–87 Success Strategy, 53, 91 U unit rate, 39–45 V Vocabulary, 4, 11, 19, 25, 33, 39, 56, 63, 71, 77 Vocabulary Check, 10, 16, 24, 31, 38, 45, 62, 69, 76, 82 Vocabulary and Concept Check, 47, 84 volume, 77–82 prism, 77–82, 83 W weight, 25–31 Who is Correct?, 6, 12, 21, 27, 34, 41, 58, 64, 73, 78 Writing in Math, 10, 16, 24, 31, 38, 45, 62, 69, 76, 82 T temperature Celsius, 33–39 Fahrenheit, 33–39 X x-coordinate, 56–62 three-dimensional figure, 77–82 time, 33–39 triangle perimeter, 63 Y y-coordinate, 56–62 Index 93 ... United States of America 10 055/027 16 15 14 13 12 11 10 09 08 07 California Math Triumphs Volume 6A California Math Triumphs Volume Place Value and Basic Number Skills 1A Chapter Counting 1A... Elementary School, Fremont, California Mathematics Consultant Retired Teacher Hacienda Heights, California Teacher, 6th Grade Math Monroe Clark Middle School San Diego, California Math Curriculum Staff... Elementary School San Diego, California Math Teacher Tevis Jr High School Bakersfield, California Professor of Mathematics California State University, Los Angeles Los Angeles, California Eric Kimmel