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LESSON8.5Fractions on a Number LineFOCUSCOHERENCERIGORLESSON AT A GLANCEF C R Focus:Common Core State Standards3.NF.A.2a Represent a fraction 1/b on a number line diagram bydefining the interval from 0 to 1 as the whole and partitioning it intob equal parts. Recognize that each part has size 1/b and that the endpoint of the partbased at 0 locates the number 1/b on the number line.3.NF.A.2b Represent a fraction a/b on a number line diagram by marking off alengths 1/b from 0. Recognize the resulting interval has size a/b and that its endpointlocates the number a/b on the number line.Also 3.NF.A.2MATHEMATICAL PRACTICESMP1 Make sense of problems and persevere in solving them. MP4 Model with mathematics.MP7 Look for and make use of structure.F C R Coherence:Learning ObjectiveRepresent and locate fractions on anumber line.Language ObjectiveStudents use the sequence words first, next,then, and finally to explain how you canrepresent and locate fractions on a number line.MaterialsMathBoard, Fraction Strips (see eTeacherResources), color pencilsStandards Across the GradesBeforeGrade 3 After2.MD.B.6 3.NF.A.2a 4.NF.B.33.NF.A.2bF C R Rigor:Level 1: Understand Concepts.Share and Show (Checked Items)Level 2: Procedural Skills and Fluency.On Your OwnLevel 3: Applications.Think Smarter and Go DeeperF C R For more about how GO Math! fosters Coherencewithin the Content Standards and Mathematical Progressionsfor this chapter, see page 441J.About the MathProfessional DevelopmentTeaching for DepthIn this lesson, students will be introduced to using anumber line to represent fractions.A number line is a measurement model. Fractions on anumber line represent the distance from 0 to the locationmarked on the number line. So, if the distance from 0 to1 is partitioned into 4 equal increments, the third markrepresents 3 4 because it is 3 4 of the distance from 0 to 1.It may help if students visualize the distance between0 and 1 as the whole and see the length between the tickmarks as fractional parts.Professional Development Videos467AChapter 8'' (( ()* The point represents the fraction 3 4 .

1 ENGAGEDaily RoutinesCommon CoreProblem of the Day 8.5Dan ordered a pizza. It was divided into8 equal slices. His brother ate 1 slice. Howmuch of the pizza did his brother eat?One eighth;18–––––––VocabularyEssential QuestionHow can you represent and locate fractions on anumber line?Making ConnectionsInvite students to talk about farms. Pose the following questions.Have you ever been to a farm where they grow a crop? What typesof food did they grow on the farm? Where do farmers sell theircrops?Learning Activity Interactive Student Edition Multimedia eGlossaryFluency Builderwith the Interactive Student EditionConnect the story to the problem.Common Core FluencyStandard 3.OA.C.7Division Facts Write the following divisionproblems on the board. Have studentspractice their division facts by solving eachproblem. Then have students check eachanswer by writing a related multiplicationfact.27 3 9; 3 9 2735 7 5; 7 5 3540 4 10; 4 10 4018 3 6; 3 6 1816 2 8; 2 8 1624 6 4; 4 6 2456 8 7; 8 7 5618 9 2; 9 2 18 What information are you given in this story? The potatoes are 1 4of the way to the vegetable stand. The onions are 3 4 of the way to thevegetable stand. When might you use a fraction to describe a distance? on a familytripLiteracy and MathematicsYou may choose one or both of the following activities. Ask students to describe how displaying the fractions on a numberline helps them determine the distances between the stops. Have students use rulers to draw number lines that represent daytrips they would like to take. Have them mark and label six placesof interest they’d like to visit or see at equal distances apart ontheir number lines. Invite students to share their number lines withthe class. Then have the students write a short story about whatthey would do on one of those day trips.How can you representand locate fractions ona number line?Lesson 8.5467B

LESSON8.53.NF.A.2a Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioningit into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number1/b on the number line. 3.NF.A.2b Represent a fraction a /b on a number line diagram by marking off a lengths 1/b from 0.Recognize the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.2 EXPLOREUnlock the ProblemLesson 8.5NameHandsOnFractions on a Number LineMP1 Make sense of problems andpersevere in solving them. Make sure thatstudents understand that the number linerepresents the complete trip in the problem. What does way mean? the total distance to Billy’sBilly’s family is traveling from his house to hisgrandma’s house. They stop at gas stations whenthey are 1 4 and 3 4 of the way there. How can yourepresent those distances on a number line? What does of the mean? part of the total1 of the way. What part One gas station is4of this fraction tells the number of equalparts? the denominator, 4 What does the numerator tell you? TheActivityBilly’s House0ActivityStudents rephrase modeled steps to showunderstanding of how fractions can equal onewhole. Have students fold a strip of paper intofourths. Have them color one fourth after the1.teacher models and explains why it is412344444STEP 2 At the end of each strip, draw a mark on the line. Houghton Mifflin Harcourt Publishing CompanySTEP 3 Count the fourths from zero to 1 to label the distances from zero.STEP 4 Think: 1 4 is 1 out of 4 equal lengths.Draw a point at 1 4 to represent the distance from 0 to 1 4 .Label the point G1.STEP 5 Think: 3 4 is 3 out of 4 equal lengths.Draw a point at 3 4 to represent the distance from 0 to 3 4 .Label the point G2.Chapter 8Reteach 8.52Lesson 8.5ReteachNameLesson 8.5EnrichNameFractions on a Number LineFraction FindWrite a fraction that names the shaded part ofeach whole. Then locate the fraction on thenumber line below. Write the letter of the modelthat represents the fraction.Use the fraction strips to help name the points on the number line.1.Draw a point to show3Step 1 The denominator is 3, so use fraction strips for thirds. Placethe fraction strips above the number line. Use the fractionstrips to divide the number line into three equal lengths.A.B.Step 2 Label each mark on the number line.1 of the totalThink: The distance between each mark islengths. 3distance, so count the number of 131Step 3 Draw a point on the number line to show .301.381131313031323331 of 3equal lengths2 of 3equal lengths3 of 3equal lengths141414234444Write the fraction that names the point.01606point A16A16Chapter Resources Houghton Mifflin Harcourt Publishing Company1626163.8-13point B51656468E.F.4416B3611141D.82.Complete the number line. Draw a point to show4068C.0 of 3equal lengths0467DifferentiatedInstructionEnrich 8.5312.467 Chapter 814Place four 1 4 -fraction strips end-to-end above the line to help. Continue to color each fourth until all parts4 equals one whole.are colored. Explain4 Ask students to rephrase in their own wordsto a partner why 4 4 equals one whole.14STEP 1 Divide the line into four equal lengths, or fourths.4 , or at2.between 0 and44RephraseGrandma’s House1G21404denominator of the fractions, which means there will be4 equal lengths in the whole.ELLG114MP4 Model with mathematics.Direct students’ attention to the number line. Why is the number line being divided into4 equal lengths? Possible answer: because 4 is theStrategy:Locate fractions on a number line.Materials fraction stripsnumber of equal lengths that have been traveled so far.Have students describe how they would makea number line for this situation if one werenot provided for them.MP2 Reason abstractly andquantitatively.1 Billy’s family stops for lunch when they are2of the way to his grandma’s house. Howwould you show this on the number line?How many fourths is this? Place a point halfwayA point on a number lineshows the endpoint of alength, or distance, fromzero. A number or fractioncan name the distance.You can use a number line to show fractions. Thelength from one whole number to the next wholenumber represents one whole. The line can bedivided into any number of equal parts, or lengths.distance3 equal lengths, or three fourths.HandsOnUnlockUnlock thethe ProblemProblemgrandma’s house How do you know where to draw a point3? The numerator is 3, so I counted from zerofor4Number and Operations—Fractions—3.NF.A.2a, 3.NF.A.2bAlso 3.NF.A.2MATHEMATICAL PRACTICESMP1, MP4, MP7Essential Question How can you represent and locate fractions on anumber line?MATHEMATICAL PRACTICES2888106608Reteach1CChapter Resources Houghton Mifflin Harcourt Publishing CompanyEA488-14DB78FEnrich

DO NOT EDIT--Changes must be made through “File info”CorrectionKey BDO NOT EDIT--Changes must be made through “File info”CorrectionKey BExampleHandsOnExampleGuide students to complete the numberline. Make sure that they understand thatthe denominators of the fractions match thenumber of equal lengths between two wholenumbers on the number line. What fraction names the point?  56 Whatdoes the numerator show? the number of equalComplete the number line to name the point.Materials color pencilsWrite the fraction that names the point on the number line.Think: This number line is divided into six equal lengths, or sixths.106.The length of one equal part is1616061616116161234566666lengths that are shaded663 EXPLAINShade the fraction strips to show the location of the point.5 out of6 equal lengths shaded.There areThe shaded length shows 5 6 .Share and Show5names the point.So,6BOARD131313012333331180818181828382. point A18A1848185818B18C88683. point BUse Math Talk to focus onstudents’ understanding of howthe number line connects to fractions.Possible explanation: 1 3 ofthe whole distance, or thelength, from zero to 1Write the fraction that names the point.0BOARDMathTalkMATHEMATICAL PRACTICES 4Use Models What doesthe length betweeneach mark on thisnumber line represent?784. point C Houghton Mifflin Harcourt Publishing Company0Mathalk1 T Houghton Mifflin Harcourt Publishing Company1. Complete the number line. Draw a point to show 23 .MATHThe first problem connects to the learningmodel. Have students use the MathBoard toexplain their thinking.MATHShareShare andand ShowShowHandsOnUse the checked exercises for Quick Check.Students should show their answers for theQuick Check on the MathBoard.3Rt ICheckaQuickstudent missesthe checkedRt IQuick Check2132If1exercisesIf468Then3 MNLESE342149 C08L05.indd 46815/10/14 11:18 PMVisual / arnersPartnersMaterials Fraction Strips (see eTeacher Resources) Write the following problem on the board.Mr. Smith is driving to work. He stops for breakfast1 of the way to work.How can you show thiswhen he is 2distance on the number line? Have one student choose the fraction strips that willrepresent the problem. Then the partner draws a numberline and uses the fraction strips to show the distance onthe number line.Differentiate Instruction with Reteach 8.5 Personal Math Trainer3.NF.A.2a, 3.NF.A.2b RtI Tier 1 Activity (online)COMMON ERRORSError Students do not label a point on theCOMMONnumberline correctly. ERRORSExample For Exercise 1, a studentmay label the point at   1 instead of  2 .3Springboard to Learning Have students3use a shading method to correct the error.0 to  13 , and then  13 to  23 Students shade from 32to understand that  3 represents the distancefrom 0 to that point.Lesson 8.5468