Volume 2 J/i^ my name about tt|e SfiT aWfi v--.* - Ife'-'- 1 Lfll m 1
THIS BOOK IS THE PROPERTY OF: STATE PROVINCE_ _ COUNTY_ PARISH _ SCHOOL DISTRICT OTHER_ ISSUED TO Book No._ Enter information in spaces to the left as instructed YEAR USED CONDITION ISSUED RETURNED PUPILS to whom this textbook is issued must not write on any page or mark any part of it in any way, consumable textbooks excepted. 1. Teachers should see that the pupil’s name is clearly written in ink in the spaces above in every book issued. 2. The following terms should be used in recording the condition of the book; New; Good; Fair; Poor; Bad.
Mc6raw-HUl My favorite TV program or video game is My favorite class is 5 of Course! Welcome to My Math — your very own math book! You can write in it — in fact, you are encouraged to write, draw, circle, explain, and color as you explore the exciting world of mathematics. Let's get started. Grab a pencil and finish each sentence. My favorite hobby or sport is My name is My favorite color is Education Bothell, WA • Chicago, IL • Columbus, OH • New York, NY
connectED.mcgraw-hiU.com Education Copyright © 2013 The McGraw-Hill Companies, Inc. All rights reserved. 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 the prior written consent of The McGraw-Hill Companies, Inc., including, but not limited to, network storage or transmission, or broadcast for distance learning. STEM McGraw-Hill is committed to providing instructional materials in Science, Technology, Engineering, and Mathematics (STEM) that give all students a solid foundation, one that prepares them for college and careers in the 21st century. Send all inquiries to: McGraw-Hill Education STEM Learning Solutions Center 8787 Orion Place Columbus, OH 43240 ISBN: 978-0-02-116191-1 (Vo/ume 2) MHID: 0-02-116191-7 Printed in the United States of America. 22 23 24 LWI 21 20 19 18 Common Core State Standards© Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. Our mission is to provide educational resources that enable students to become the problem solvers of the 21st century and inspire them to explore careers within Science, Technology, Engineering, and Mathematics (STEM) related fields. The McGraw-HillCompanies
Copyright©Tlie McGraw-Hill Companies, Inc. Abby CrLiJ-cl^lty The Market Math Winning this contest made me feel like i had butterflies in my stomach! I didn't think I would win out of the 72 finalists. Volume i M«// Using Math to Build Math means everything to me. It is my favorite subject in school. I got the idea because I like to build and I thought a K'Nex vehicle would make a cool math book cover. Volume 2 Beach Math-1 Math Angel Math in Nature Math in My Neighborhood Math With My Fingers KtUty T%cr>rtf>^(rk\ Doggy Shapes The Book of Math-«ws Kaya Ujcr^% Math is in My Neighborhood ycryxafcri^ 3arktl We Use Math Skills Everyday elht Hail Patterns Qwirkle tiles reproduced with the permission of MindWare*. Find out more about the winners and other finalists at www.MHEoniine.com We wish to congratulate all of the entries in the 2011 McGraw-HillMyMath "What Math Means To Me" cover art contest. With over 2,400 entries and more than 20,000 community votes cast, the names mentioned above represent the two winners and ten finalists for this grade. Hi
it's all at connectED.mcgraw-hill.com Go to the Student Center for your eBook, Resources, Homework, and Messages. McGraM-H8l My Math: Student Center X I i SeSii-t) ^ Favorites ^ | j McGraw-Hill My Math: Sludem Center p -rl Taois Hollo, Student 1 Home 1 ConnoctED I Help I Logout McGraw-Hilt 0 Home 0 Homework Resources -L. [ Chapter S: Multiply with Two-Digit Numbers Lesson 1: Multiply by Tens Multiply with Two-Oigit Numbers ^ Multiply by Tens Due: Morvlay. October 7.2011 Assignment Title f You have unread teacher commente. More Messages Monday. October 7. 2011 Don’t forget to study for the test on Friday. More' {hMewadftiedoAmogthnktrftf/agg /otosTodt; IrySyMaBon/Tht fmageBonVOettyimages The McGrawHtllCompaniei 79rmtiy$*\ TtdnuntSupport \ limkmmSfrtmMtfairmetits Th« Mc0rww4«l Cttmpom* Iftt -4. IV Copyright ©The McGraw-Hill Companies, Inc. (inset)Meinrad Riedo/imagebroker RF/age fotostock, Sylvia Bors/The Ijiilaa BanWGetty Images
Copyright ©The McGraw-Hill Companies, Inc. I 'i I r Get your resources online to help you in class and at home. Vocab Find activities for building vocabulary. Watch Watch animations of key concepts. Tools Explore concepts with virtual manipulatives. Check / Self-assess your progress. eHelp Get targeted homework help. Games Reinforce with games and apps. Tutor See a teacher illustrate examples and problems. Scan this QR code with your smart phone* or visit ^ mheonline.com/stem_apps. *May require quick response code reader app. Education Tpi^Trac Interactive ^ learning wltK^ mobile apps | Science I technology 1 engmeenna) math lashoarda What 8 New iThat MonXtr SquMZ* Equtvaitnt FracUoM" KtiitipScatton 14 Facta Coitvu**r Math AKoy Addition Top-tl ! V
Chapter 1 Chapter 2 Chapter 3 Place Value Addition Subtraction Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Understand Multiplication Understand Division Multiplication and Division Patterns Multiplication and Division Apply Multiplication and Division Properties and Equations Chapter 10 Fractions Chapter 11 Measurement Chapter 12 Represent and Interpret Data Chapter 13 Perimeter and Area Chapter 14 Geometry Mathematical PRACTICE Woven Throughout Online Content at^connectED.mcgraw'hill.com Contents in Brief Organized by Domain Common Core State Standards rations and Algebraic Thinking Geometry Standardsior 1 rfJji] Copyright ©The McGraw-Hill Companies. Inc,
Copyright ©The McGraw-Hill Companies, Inc. (t)Dorling Kindersley/Getty Images, (b)Geri Lavrov/Photographer’s Choice/Getty Images Gbai Place Value ESSENTIAL QUESTION How can numbers be expressed, ordered, and compared? Getting Started Am My My My Vocabulary Math Foldable I Ready? Words .3 Cards .4 .5 7 Lessons and Homework Lesson 1 Place Value Through Thousands .9 Lesson 2 Compare Numbers .15 Lesson 3 Order Numbers .21 Check Lesson My 4 Progress Round to the .27 Nearest Ten.29 Lesson 5 Round to the Nearest Hundred.35 Lesson 6 Problem-Solving Investigation: Use the Four-Step Plan .41 Wrap Up My Chapter Review .47 Reflect .50
'^liifVTSTi'|-| ilPRPfn Oiapter ESSENTIAL QUESTION How can place value help me add larger numbers? Getting Started Am My My Vocabulary Math I Ready? Words .53 Cards .54 .55 My Foldable 59 Lessons and Homework Lesson 1 Addition Properties .61 Lesson 2 Patterns in the Addition Table .67 Lesson 3 Addition Patterns .73 Lesson 4 Add Mentally .79 Check My Progress .85 Lesson 5 Estimate Sums .87 Lesson 6 Hands On: Use Models to Add .93 Lesson 7 Add Three-Digit Numbers .99 Check My Progress .105 Lesson 8 Add Four-Digit Numbers .107 Lesson 9 Problem-Solving Investigation: Reasonable Answers .113 Wrap Up Fluency Practice .... My Chapter Review f Reflect . . 124 connectED.mcgraw-hill.com Vlll
Chapter ESSENTIAL QUESTION How are the operations of subtraction and addition related? h: Getting Started Am I Ready? .127 ^ My Math Words .128|. 'I My Vocabulary Cards .129 My Foldable BffiEUS .131 Lessons and Homework Lesson 1 Subtract Mentally .133 Lesson 2 Estimate Differences .139 Lesson 3 Problem-Solving Investigation; Estimate or Exact Answer .145 Check My Progress .151 Lesson 4 Hands On: Subtract with Regrouping .153 Lesson 5 Subtract Three-Digit Numbers .159 Lesson 6 Subtract Four-Digit Numbers .165 Lesson? Subtract Across Zeros .171 r s 03 Wrap Up Fluency Practice . My Chapter Review . Reflect .. 177 Look for this! g elicit online and you can get more help while doing your homework. connectED.mcgraw-hill.com A.;-; ■■■■: te; msm,. ,
m. F-f.-'iW ESSENTIAL QUESTION What does multiplication mean? ^'Ji^ Yummy! Getting Started Am My Math I Ready? Words .. .186 My Vocabulary Cards .137 Lessons My Foldable and Homework . Lesson 1 Hands On: Model Multiplication .193 Lesson 2 Multiplication as Repeated Addition .199 Lesson 3 Hands On: Multiply with Arrays .205 Lesson 4 Arrays and Multiplication .211 Check My Progress .217 Lesson 5 Problem-Solving Investigation: Make a Table .219 Lesson 6 Use Multiplication to Find Combinations .225 Wrap Up My Chapter Review .231 eflect .234 connectED.mcgraw-hill.com Copyrigtrt©The McGraw-Hill Companies, Inc. (I)JGI/Jamie Grill/Blend Images/Getty Images, (r)Jonelle Weaver/Phofodisc/Getty Images
Copyright ©Tlie McGraw-Hill Companies, Inc. (t)Digital Archive Japan/Alamy, {b)Mike Kemp/Rubberball/Getty Images pOLDABLES ESSENTIAL QUESTION What does division mean? Getting Started Am I Ready? . My Math Words . My Vocabulary Cards ... My Foldable Lessons and Homework Lesson 1 Hands On: Model Division . Lesson 2 Division as Equal Sharing . Lesson 3 Relate Division and Subtraction Check Lesson My 4 Progress Hands On: . Relate Division and Multiplication . Lesson 5 inverse Operations . Lesson 6 Problem-Solving investigation: Use Models 277 f-LA Wrap Up My Reflect Chapter .286 Review . connectED.mcgraw-hill.com Look for this! ClicK online and you con find tools that will help you explore concepts ‘.r.v
Chapter ‘ 'M BIT^ST OFF Getting Started Am I Ready? .289 My Math Words .290 My Vocabulary Cards .291 My Foldable 293 Lessons and Homework Lesson 1 Patterns in the Multiplication Table .295 Multiply by 2 .301 Divide by 2 .307 Multiply by 5 .313 Divide by 5 .319 Check My Progress .325 Lesson 6 Problem-Solving Investigation: Look for a Pattern .327 Lesson 2 Lesson 3 Lesson 4 Lesson 5 ESSENTIAL QUESTION What is the importance of patterns in learning multiplication and division? Jmi r i Lesson 7 Multiply by 10 Lesson 8 Multiples of 10 Lesson 9 Divide by 10 . Wrap Up Fluency Practice .A My Chapter Review .. .M Reflect ..V 333 'M 339 345 351 353 356 connectED.mcgraw-hilLcom CopyrigW ©^'McGraw-tJliyjiij^nies, Inc. (t)Steve Cole/Photodisc/Getty Images, (bjDidier Robcis/Getty Images
Copyright ©The McGraw-Hill Companies, Inc, Brand New Images/The Image Bank/Getty Images Chapter ESSENTIAL QUESTION What strategies can be used to learn multiplication and division facts? Getting Started Am My My My Vocabulary Math Foldable 1 Ready? Words UsMISw . Cards . . . Lessons and Homework Lesson Lesson 2 1 Multiply Divide by by 3 3 . . Lesson 3 Hands On: Double a Known Fact Lesson Lesson 4 5 Multiply Divide by by 4 4 . . Check Lesson My 6 Progress Problem-Solving . Investigation: Extra or Missing information .. Lesson 7 Multiply by 0 and 1 . Lesson 8 Divide with 0 and 1 . Wrap Up Fluency Practice .. My Chapter Review Reflect ... Look for this! Click online and you can watch a teacher solving problems. ^ connectED.mcgraw-hill.com iterations and Algebraic Tbinbing Multiplication and Division pOLDABLES
rChapter .. ;7 .-'-s:?'-,€rjr4- , -.4 ’ *, -r- • ’‘*'^^ \ ^7 Op^sstsns A;^€i^'Sir V ESSENTIAL QUESTION How can multiplication and division facts with smaller numbers be applied to larger numbers? Getting Started Am I Ready? .423 My Math Words .424 My Vocabulary Cards .425 My Foldable .427 Lessons and Homework Lesson 1 Multiply by 6 .429 Lesson 2 Multiply by 7 .435 Lesson 3 Divide by 6 and 7 .441 Check My Progress .447 Lesson 4 Multiply by 8 .449 Lesson 5 Multiply by 9 .456 Lesson 6 Divide by 8 and 9 .461 Check My Progress.467 Lesson 7 Problem-Solving Investigation: Make an Organized List .469 Lesson 8 Multiply by 11 and 12 .475 Lesson 9 Divide by 11 and 12 .481 Wrap Up , r \ Fluency Practice . My Chapter Review . Reflect .. connectED.mcgraw-hilLcom CopyiigM ©TTie McGraw-Hill Companies, Inc. (l)Siede Preis/Getty Images, (r)PholoSpin/Alamy
^IChsptGr t-'i Operations and AlgebraicThlnkji^ ...■■■iM ., . 1— Ti^t. ESSENTIAL QUESTION How are properties and equations used to group numbers? c-w. i^Ji connectED.mcgraw-hill.com ss.;^ P Look for this! Click online and you can find activities to help build your vocabulary. Getting Started Am I Ready? .495 My Math Words .496 My Vocabulary Cards .497 My Foldable 499 Lessons and Homework Lesson 1 Hands On: Take Apart to Multiply .501 Lesson 2 The Distributive Property .507 Lesson 3 Hands On: Multiply Three Factors .513 Lesson 4 The Associative Property .519 Check My Progress . 525 Lesson 5 Write Expressions .527 Lesson 6 Evaluate Expressions .533 Lesson 7 Write Equations .539 Lesson 8 SolveTwo-Step Word Problems .545 Lesson 9 Problem-Solving Investigation: Use Logical Reasoning .551 Wrap Up My Chapter Review .557 Reflect .560
I ve got the answer! iMm Chapter Ill' ESSENTIAL QUESTION How can fractions be used to represent numbers and their parts? S'1? -iC ... m- m - Getting Started Am I Ready? .563 My Math Words .564 My Vocabulary Cards .565 My Foldable 557 Lessons and Homework Lesson 1 Unit Fractions .569 Lesson 2 Part of a Whole .575 Lesson 3 Part of a Set .581 Lesson 4 Problem-Solving Investigation: Draw a Diagram .587 Check My Progress.593 Lesson 5 Hands On: Fractions on a Number Line _595 Lesson 6 Equivalent Fractions . 601 Lesson 7 Fractions as One Whole 607 Lesson8 Compare Fractions . Wrap Up My Chapter Review .-IHIf.619 Reflect ..iMM_622 ;.;v . : It•i*';' connectED.mcgraw-hill.com XVI rV; -- Wi
Copyright ©The McGraw-Hili Companies, Inc. (t)Mark Steinmetz/The McGraw-Hill Companies, (b)Dave King/Dorling Kindersley/Getty Images ESSENTIAL QUESTION Why do we measure? UJJJiJJJ. Getting Started Am I Ready? .625 My Math Words .626 My Vocabulary Cards .627 My Foldable 631 Lessons and Homework Lesson 1 Hands On: Estimate and Measure Capacity .633 Lesson 2 Solve Capacity Problems.639 Lesson 3 Hands On: Estimate and Measure Mass ...645 Lesson 4 Solve Mass Problems .651 Check My Progress .657 Lesson 5 Tell Time to the Minute .659 Lesson 6 Time Intervals .665 Lesson 7 Problem-Solving Investigation: Work Backward .671 Wrap Up My Chapter Review . Reflect L ' ,-‘- • .V. •- - . I':?4 connectED.mcgraw-hill.com XVII
f Chapter ESSENTIAL QUESTION How do we obtain useful information from a set of data? ---— __m Getting Started Am I Ready? .683 My Math Words .684 My Vocabulary Cards .685 My Foldable 689 Lessons and Homework Lesson 1 Collect and Record Data .691 Lesson 2 Draw Scaled Picture Graphs .697 Lesson 3 Draw Scaled Bar Graphs .703 Lesson 4 Relate Bar Graphs to Scaled Picture Graphs .709 Lesson 5 Draw and Analyze Line Plots .715 Check My Progress.721 Lesson 6 Hands On: Measure to Halves and Fourths of an Inch .723 Lesson 7 Collect and Display Measurement Data ...729 Lesson 8 Problem-Solving Investigation: Solve a Simpler Problem .735 Wrap Up My Chapter Review .741 Reflect .744 -c.'.yconnectED.mcgraw-hill.com
Copyright ©The McGraw-Hill Companies, Inc. (t)Stockl)yte/PictureQuest, (b)Asia Images Group/Getty Images J'A’J!: ... ..... Perimeter and Area ESSENTIAL QUESTION How are perimeter and area related and how are they different? -aferr-'-' Getting Started Am I Ready? .747 My Math Words .748 My Vocabulary Cards .749 My Foldable 751 Lessons and Homework Lesson 1 Hands On: Find Perimeter .753 Lesson 2 Perimeter .759 Lesson 3 Hands On: Understand Area .765 Lesson 4 Measure Area .771 Check My Progress .777 Lesson 5 Hands On:Tile Rectangles to Find Area ...779 Lesson 6 Area of Rectangles .785 Lesson 7 HandsOn: Area and the Distributive Property .791 Lesson 8 Area of Composite Figures .797 Check My Progress .803 Lesson 9 Area and Perimeter .805 Lesson 10 Problem-Solving Investigation: Draw a Diagram 811 Wrap Up My Chapter Review Reflect . connectED.mcgraw-hill.com XIX
Chapter mm ESSENTIAL QUESTION How can geometric shapes help me solve real-world problems? Getting Started Am I Ready? .823 My Math Words .824 My Vocabulary Cards .825 My Foldable 032 Lessons and Homework Lesson 1 Hands On: Angles .833 Lesson 2 Polygons .839 Lesson 3 Hands On: Triangles .845 Lesson 4 Quadrilaterals .851 Check My Progress .857 Lesson 5 Shared Attributes of Quadrilaterals .859 Lesson 6 Problem-Solving Investigation: Guess, Check, and Revise .865 Lesson 7 Partition Shapes .871 Wrap Up M^* mm connectED.mcgraw-hill.com XX Copyright ©The McGraw-Hill Companies, Inc, Clarissa Leahy/Cultura/Getty Images
Copyright ©The McGraw-Hill Companies, Inc. John Qiustina/Photodisc/Getty Images, (inset)Comslock/Getty Images Chapter ESSENTIAL « QUESTION ^ How can fractions be used to represent numbers and their parts?
V'. . /iMi t'lri^J,- • . . '^ y- 'Ti^ a';-. .^v^''^.w>:>^.'' '* -j 'rr'!''3.NF.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. 3.NF.3a Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. 3.NF.3b Recognize and generate simple equivalent fractions, e.g., why the fractions are equivalent, e.g., by using a visual fraction model. 3.NF.3C Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. 3.NF.3d Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. 3.NF.1 Understand a fraction -j- as the quantity b formed by 1 part when a whole is partitioned into b equal parts; understand a fraction as the quantity formed by a parts of size p 3.NF.2 Understand a fraction as a number on the number line; represent fractions on a number line diagram. 3.NF.2a Represent a fraction on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size ^ and that the endpoint of the part based at 0 locates the number on the number line. b 3.NF.2b Represent a fraction on a number line diagram by marking off a lengths ~ from 0. Recognize that the resulting interval has size ^ and that its endpoint locates the number ^ on the number line. Geometry This chapter also addresses this standard: 3.C.2 Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. Standardsiori^ Mathematical PRACTICE 1. Make sense of problems and persevere in solving them. '.dltm Reason abstractly and quantitatively. ^ Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. ’ = focused on in this chapter 562 Chapter 10 Fractions Copyright ©The McGraw-Hill Companies, Inc.
Copyright ®The Mc6taw-Hill Companies, Inc. Write the number of parts. Tell whether each figure shows parts that are equal or not equal. to take the Readiness Quiz / Write the name of the equal parts. Write halves, thirds, or fourths. 6. Circle the point which represents each given number. 7. 380 8. 169 300 320 340 1^7 173 175 177 9. Jill draws a figure and divides it into thirds. Draw what her figure could look like. m. How Did I Do? Online Content Shade the boxesto show the problems you answered correctly. 1 2 3 4 5 6 7 8 9 at^conYfectED.mcgraw-hUl.com 563
Name 1 fourths halves thirds Review Vocabulary Making Connections Circle the review vocabulary word which represents each example. Fourths Halves Thirds ( 1 1 Fourths Halves Thirds \ Fourths Halves Thirds 1 L 1 Fourths Halves Thirds What does whole mean? What does part of a whole mean? ••• 564 Chapter 10 Fractions
Mathematical PRACTICE Lesson 10-6 equivalent fractions Lesson 10-2 denominator ift'Jb U, IN w.. i = l M 2 Lesson 10-1 fraction Lesson 10-2 numerator Lesson 10-1 unit fraction .V" \_ 3 X iCD o s a> ' >
Ideas for Use • Write a tally mark on each card every time you read the word in this chapter or use it in your writing. Challenge yourself to use at least 5 tally marks for each card. • Use the blank cards to draw or write phrases or examples that will help you with concepts like comparing fractions. ( Fractions that represent the same part of the ] [ The bottom number in a fraction. It is the | whole. total number of equal parts. The prefix non- means "not." Describe 2 Draw models to show three different non-equivalent fractions. Write an example. fractions that all have a denominator of 4. L j L J f'The top number in a fraction. It is the number^ f'A number that represents an equal part of a ^ of equal parts being represented. whole or an equal part of a set. In the fraction what is the numerator? Draw a rectangle, and divide it into 6 equal What does it show? parts. Color the parts to represent ^ Represents the quantity formed by one part when a whole is partitioned into equal parts. Unit can mean "a single thing." How does this help you understand the definition of unit fraction?
Copyright©The McGraw-Hill Companies, Inc. Foldables Follow the steps on the back to make your Foldable. f St St St St St St St St
study Organizer 4
Copyright © The McGraw-Hill Companies, Inc. Sabine Scheckel/Photodisc/Getty Images What fraction tiles did you place? So each person received or one half, of a whole granola bar. Model the whole granola bar. Place two equal-sized fraction tiles so that the combined length is equal to one whole. Name A fraction is a number that represents an equal part of a whole or equal part of a set. Math in My World Tools Watch Tutor m* Lesson 1 ESSENTIAL QUESTION How can fractions be used to represent numbers and their parts? for you! One for me! Example 1 Danny shared his granola bar with Steph. He broke it into two equal pieces. What fraction of the granola bar did each receive? A unit fraction represents one equal part of the whole. The top number of a unit fraction is 1. Example 2 One whole is divided into four equal parts. What unit fraction represents one equal part of the whole? Write the unit fraction. 1 Online Content at ^^connectED.mcgraw-hill.com Lesson 1 569
- — - , Example 3 Ian made a loaf of bread as his final project in health class. He divided the loaf equally among some students. Each student received of the loaf. Into how many equal O parts did Ian cut the loaf? i Use the fraction tiles to model one whole and one whole divided into equal parts. Draw your models. ! Count the equal parts. There are * Label each equal-sized part o equal parts. one part of eight or one-eighth ' V_ So, Ian cut the loaf into - equal parts, or eighths. Guided Practice Divide the whole into equal parts. Then label each part with its unit fraction. 1. 2 equal parts 2. 4 equal parts 3. 8 equal parts What is a unit fraction? 570 Chapter 10 Fractions Copyright © The McGraw-Hill Companies, Inc. Stockdisc/PunchStock
Copyright ©The McGraw-Hill Companies, Inc. Name independent Practice Divide the whole into equal parts. Then label each part wjth its unit fraction. 4. 3 equal parts 5. 6 equal parts Write how many equal parts. Shade one part. Write its unit fraction. ’ ^ equal parts unit fraction: 7. equal parts 8. equal parts unit fraction: equal parts unit fraction: Circle the correct unit fraction for the shaded section of each model. Lesson 1 Unit Fractions 571
Problem Solving 16. Max folded a piece of paper in half. Then he folded it in half one more time. How many equal-sized parts did he have when he opened the paper? What unit fraction represents each part? Msithpinsitirsil 17. PRACTICE^ Use Math Tools Jenny is holding a fraction tile labeled y. How many y-fraction tiles are needed to equal the fraction tile labeled 1? 18. Mr. dinger divided the gymnasium floor into 8 equal sections. Draw lines to divide the whole into equal parts. Then label each part with its unit fraction. M3th6ni3tic3l 19. PRACTICE Reason How are all unit fractions alike? How are they different? 20. ^^Building on the Essential Question What happens to the size of each equal part when you divide a whole into more and more equal parts? 572 Chapter 10 Fractions Copyright © The McGraw-Hill Companies, Inc.
Copyright © The McGraw-Hill Companies, Inc. Name Homework Helper Need help? ^connectED.mcgraw-hill.com Franny wants to braid string to make a bracelet. She has one long piece of string. Franny needs to divide the string into 3 equal pieces for braiding. Model the whole string divided into 3 pieces. Write the unit fraction for 1 piece of the string. Use the one whole fraction tile to represent the whole piece of string. Use “fraction tiles to model 3 equal parts. 1 1 1 3 3 3 V. The string was divided into 3 equal pieces. The unit fraction that represents 1 of those pieces is y. Practice Divide the whole into equal parts. Then label each part with its unit fraction. 1. four equal parts 2. two equal parts 3. six equal parts 4. three equal parts Lesson 1 My Homework 573
Write how many equal parts. Shade one part. Write its unit fraction. equal parts Problem Solving Mathematical 9. PRACTICE Justify Conclusions Louis has a rectangular piece of construction paper. Can he divide the shape into 4 equal parts? Explain. Vocabulary Check Choose the correct word(s) to complete each sentence. fraction unit fraction 10. A is exactly one equal part of a whole. 11. A represents an equal part of a whole. Test Practice 12. Which unit fraction represents the shaded part of the whole? @1 © 1 © - ^ 6 ® - ^ 8 574 Need more practice? Download Extra Practice at ^connectED.mcgraw-hill.com Copyright ©The McGraw-Hill Companies, Inc.
Lesson 2 ESSENTIAL QUESTION How can fractions be used to represent numbers and their parts? Name The bulletin board represents one whole. The whole is divided into 4 equal parts, or fourths. Use fraction tiles to model the equal parts of the bulletin board. Trace the tiles. Color one part green. Use a model. Math in My World Example 1 The background paper of Mrs. Dempsey's bulletin board is divided equally into four stripes. What fraction of the bulletin board is green? Write: ^ Read: one-fourth i j" i 4 4 DQ(g9[piM IrGW Sometimes is also read one-quarter. I 1 part that is green- 1 <-numerator total number of parts- 4 -denominator The numerator tells the number of equal parts being represented. The denominator tells the total number of equal parts. So, or one- , of the bulletin board is Online Content at <7connectED.mcgraw-hill.com Lesson 2 575
Not all fractions are unit fractions. Tutor Example 2 |Q) What fraction of the flag is red? 2 <-redparts 3 -total number of equal parts Write: Read: -thirds 2 So, or two- of the flag is Explain why — is not a unit fraction. Guided Practice Complete the chart. Write a fraction for each part. Fraction Model Part that is Yellow Part that is not Yellow 576 Chapter 10 Fractions Copyright ©The McGraw-Hill Companies, Inc. (t)Thomas Northcut/Photodisc/Getty Images, (b)Tom Fowlks/Photodisc/Getty Images
Copyright ©The McGraw-Hill Companies. Inc. Name Independent Practice n Complete the chart. Write a fraction for each part. i Fraction Model Part that is Blue Part that is not Blue , 4. Shade each figure to represent the fraction. 8. 2 4 9. 2 8 Match each fraction to its word name. 11. 12. n. 8 6 3 • five-sixths • three-fourths • three-eighths Lesson 2 Part of a Whole 577
Problem Solving Mathematical PRACTICE Use Math Tools The primary colors are red, blue, and yellow. The secondary colors are green, orange, and violet. Use the color wheel to answer Exercises 14-17. 14. What fraction of the primary and secondary colors is red? 15. What fraction is blue or orange? 16. What fraction is not violet? 17. What fraction of colors Is not a primary color? iU 5G®'Tj* Mathematical 18. PRACTICE Model Math Draw and shade a model to represent the fraction 19. ^^Building on the Essential Question Explain how to write a fraction to describe part of a whole. 578 Chapter 10 Fractions Copyright ©The McGraw-Hill Companies, Inc.
Copyright ©The Name f Homework Helper Need help? gj connectED.mcgraw-hill.com Dennis and 2 friends are sharing a submarine sandwich equally. All but one part has hot peppers. What fraction of the sandwich has hot peppers? What fraction of the sandwich does not have hot peppers? Model the problem. The entire sandwich is the whole. It is divided into 3 equal parts. Two of the 3 parts have hot peppers. I parts with hot peppers I total number of equal parts ^ 2 ^ 3 1 3 part without hot peppers total number of equal parts So, y of the sandwich has hot peppers, and y of the sandwich does not. j iPractice Complete the chart. Write a fraction for each part. Fraction Model Part that is Green Part that is not Green 1. ^ > Lesson 2 My Homework 579
shade each figure to represent the fraction. fraction. Write the fraction below. Explain why it is a unit fraction. Problem Solving 8. A loaf of bread is cut into 8 equal slices. What fraction of the bread is left after 6 slices have been used for sandwiches? 9. Kristen made a pinwheel with 6 points. She colored 1 point red, 2 points blue, and 3 points purple. What fraction of the points are neither red nor purple? / \ Vocabulary Check Draw a line to match the vocabulary term with its meaning. 10. denominator • the number of parts being represented 11. numerator • the total number of equal parts Test Practice 12. Which fraction of the figure is yellow? 0 — ^ 6 ©1 ^ 6 580 Need more practice? Download Extra Practice at ^connectED.mcgraw-hili.com Copyright ©The McGraw-Hill Companies, Inc.
Copyright © The McGraw-Hill Companies, Inc. Steve Wisbauer/Photodisc/Getty Images Online Content at^connectED.mcgraw-hill.com Lesson 3 581 Name Draw and color the counters on the fraction below to represent the fraction of yellow counters. numerator-2 yellow counters J 2 denominator-6 total counters J ^ Write: ^ o _ Read: two-sixths —( use words' So, the fraction of yellow markers is V___ use numbers Lesson 3 ESSENTIAL QUESTION How can fractions be used to represent numbers and their parts? 1 imfw Fractions can also be used to name part of a set. Tools Watch Math in My World iy" Example 1 Mrs. Maynard gave each group of students 2 yellow and 4 red markers. What fraction of the set of markers is yellow? Use a set of 6 counters to represent the set of 6 markers. Tutor 2 yellow markers 4 red markers
Example 2 Cody told his four dogs to sit. What fraction of the listened to Cody? set of dogs The yellow counters represent the sitting dogs. The red counter represents the standing dog. 3 dogs, out of a total of dogs, are sitting. ^ —( dogs sitting ) Write: j ^ ^ ^ total dogs J Read: three-fourths So, or -fourths, of the dogs obeyed. What fraction of the set of dogs did not listen to Cody? 582 Chapter 10 Fractions dog, out of a total of 4 dogs, is standing. or one- , of the dogs did not listen to Cody. Check^ Guided Practice Complete the chart. Write a fraction for each part. IIUVUIV/II u different than Fraction Model Part that is Part that is Yellow not Yellow Copynght©JM«PGravv-HillCompanies, Inc. (tlHarVsAImages, (tcrfe»>^totoc/G^J{l»3C^(bl)Getty Images, (br)Digital Stock/CORBIS
Copyright © The McGraw-Hill Companies, Inc. (t)The McGraw-Hill Companies, (cl)Ken Cavanagh/The McGraw-Hill Companies, (cr)Photodisc/Getty Images, (bl)The McGraw-Hill Companies, (br)Mark Steinmetz Name Independent Practice Writ^ach fraction. 3. What fraction of the set of daisies is yellow? 4. What fraction of the set of buttons is round? 5. What fraction of the set of chairs is not blue? 6. What fraction of the set of seashells is purple? shade each set to represent the fraction. 1 7. — shaded OO 9. ^ shaded 6 8. 4 shaded 4 oooo 10. shaded o oooooo oooooooo m Write the missing numerator or denominator. 11. What fraction of the set of spools 12. What fraction of the set of cups of thread is red? is yellow? Lesson 3 Part of a Set 583
Problem Solving Use the picture of the fruit to answer Exercises 13-16. 13. There are 8 pieces of fruit in the set. Circle the word used to describe all 8 pieces of fruit. numerator denominator 14. What fraction of the set of fruit is not an apple? 15. Suppose Kyle ate one pear. What fraction of the pears did Kyle eat? Mathematical 16. PRACTICE Reason Describe which pieces of fruit can be represented by the fraction 8 Mathematical 17. PRACTICE Model Math Draw a set of objects that represents a fraction with a numerator of 4. Write the fraction. 18. ^Building on the Essential Question How is finding a fractional part of a set different than finding a fractional part of a whole? 584 Chapter 10 Fractions
Copyright © The McGraw-Hill Companies, Inc. The McGraw-Hill Companies Carolyn has put together gift bags for guests at her party. There are 6 bags in all. What fraction of the set of bags is ^ yellow? What fraction of the set of bags is blue? ( \ The total number of bags is 6. This is the denominator. The : numerator for each fractional part Is the number of yellow bags and the number of blue bags. 4 — yellow bags 2 — blue bags ; 5 — total number of bags 5 — total number of bags , So, ^ of the gift bags are yellow, and ^ of the gift bags are blue. Practice shade each set to represent the fraction. 1. 3 4 0000 000000 000 00 > 5. Write a fraction for each part. part that is red part that is not red Lesson 3 My Homework 585
6. What fraction of the set of balloons 7. What fraction of the set of books is green? is blue? 8. What fraction of the set of bees is flying away? Problem Solving 9. What fraction of the set of signs is square? 10. Ramona writes each letter of her first name on separate index cards. What fraction of the cards has a vowel? Mathematical 11. PRACTICE W Keep Trying Bryan has 3 nickels, 3 dimes, and 2 quarters. What fraction of the coins is either a dime or a quarter? 12. The Morse family went shoe shopping. Harry got a pair of rain boots and a pair of tennis shoes. Kate got a pair of tennis shoes and a pair of sandals. What fraction of the set of new shoes is rain boots? Test Practice 13. What fraction of the birds are on the window sill? 586 Need more practice? Download Extra Practice at ^connectED.mcgraw-hUl.com Copyright © Ttie McGraw-Hill Companies, Inc. The McGraw-Hill Companies
Copyright © The McGraw-Hill Companies, Inc. Joe Polillio/The McGraw-Hill Companies Problem-Solving STRATEGY: Draw a Diagram Lesson 4 ESSENTIAL QUESTION How can fractions be used to represent numbers and their parts? Learn the Strategy Watch Anessa and a classmate have 8 insects in a jar. Four-eighths of the insects are beetles. One is a firefly and the rest are crickets. What fraction of the insects are crickets? r< Understand What facts do you know? There are 8 insects. One is a Four-eighths are . The rest are What do you need to find? the fraction of insects that are Plan I will draw a diagram to solve the problem. Solve • Draw a figure that is divided into 8 equal parts. • Shade 4 the figure for the beetles. Label with B. O • Shade 1 part for the firefly. Label with F. of the insects are crickets. ( So, 4)> Check Does your answer make sense? Explain. ’4.. . rti’- v%. Online Content at ^connectED.mcgraw-hill.com Lesson 4 587
( Practice the Strategy Six students brought their pet to school on Pet Day. Three of the pets were dogs and were cats. The rest of the pets were birds. What fraction of the pets were birds? ^ Understand What facts do you know? What do you need to find? 41 Check I Does your answer make sense? Explain. \ 588 Chapter 10 Fractions Copyright ©The McGraw-Hill Companies, Inc. (l)Radius Images/Getty Images, (r)lngram Publishing/SuperStock