LESSON 12 Add Fractions

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LessonOverviewLESSON 12Add FractionsLesson ObjectivesContent Objectives Given two fractions with unlikedenominators, write equivalent fractionswith a common denominator. Use visual models to represent addingfractions with unlike denominators. Use equivalent fractions to add fractionsand mixed numbers with unlikedenominators.Language Objectives Define common denominator and use theterm in a discussion with a partner.Prerequisite Skills Find multiples of whole numbers. Understand the meaning of addingfractions. Add fractions and mixed numbers withlike denominators. Find fractions equivalent to a givenfraction. Regroup fractions greater than 1 asmixed numbers.Standards for MathematicalPractice (SMP) Draw fraction models or number lines toshow a sum of fractions with unlikedenominators.SMPs 1, 2, 3, 4, 5, and 6 are integratedin every lesson through the Try-DiscussConnect routine.* Rewrite sums of fractions with unlikedenominators as sums with likedenominators using equivalent fractions.In addition, this lesson particularlyemphasizes the following SMPs:2 Reason abstractly and quantitatively.Lesson VocabularyThere is no new vocabulary. Review thefollowing key terms. common denominator a number that isa common multiple of the denominatorsof two or more fractions. denominator the number below theline in a fraction that tells the number ofequal parts in the whole. equivalent fractions two or moredifferent fractions that name the samepart of a whole or the same point on anumber line. mixed number a number with a wholenumber part and a fractional part. multiple the product of a given numberand any other whole number. numerator the number above the linein a fraction that tells the number ofequal parts that are being described.5 Use appropriate tools strategically.7 Look for and make use of structure.* See page 1i to see how every lesson includesthese SMPs.Learning ProgressionIn Grade 4 students added fractions(including mixed numbers) with likedenominators. They understood theconcept of fraction addition as similar toaddition with whole numbers. Studentsalso learned to find equivalent fractions bymultiplying the numerator anddenominator of a fraction by the samenumber.225aLesson 12 Add FractionsIn this lesson students extend theconcept of fraction addition to addingfractions (including mixed numbers) withunlike denominators. They replacefractions with equivalent fractions to showequivalent sums of fractions and mixednumbers with like denominators. Thenthey add the fractions using the methodsthey used in Grade 4.In the next lesson students will subtractfractions and mixed numbers with unlikedenominators. Students will do furtherwork with estimating sums and differencesof decimals in word problem contexts in alater lesson. Curriculum Associates, LLCCopying is not permitted.

Lesson Pacing GuideTeacher ToolboxSmall Group DifferentiationWhole Class InstructionSESSION 1Explore45–60 minSESSION 2Develop45–60 minSESSION 3Develop45–60 minSESSION 4Refine45–60 minAdding Fractions Start 5 min Try It 10 min Discuss It 10 min Connect It 15 min Close: Exit Ticket 5 minAdditional PracticeLesson pages 229–230Adding Fractions with UnlikeDenominators Start 5 min Try It 10 min Discuss It 10 min Picture It & Model It 5 min Connect It 10 min Close: Exit Ticket 5 minAdditional PracticeLesson pages 235–236Adding with Mixed Numbers Start 5 min Try It 10 min Discuss It 10 min Picture It & Model It 5 min Connect It 10 min Close: Exit Ticket 5 minAdditional PracticeLesson pages 241–242Adding Fractions Start 5 min Example & Problems 1–3 15 min Practice & Small GroupDifferentiation 20 min Close: Exit Ticket 5 minLesson Quizor DigitalComprehension CheckReady Prerequisite LessonsFluencyAdding Fractions withUnlike DenominatorsFluencyAdding with MixedNumbersLesson(Required)Per pair: 1 set of fraction tiles, 2 sets of fraction circlesActivity Sheet:1-Centimeter Grid PaperActivitiesPer pair: 1 set of fraction circles, 1 set of fraction tilesActivity Sheet:Number LinesMath Toolkitfraction tiles, fraction circles, fraction bars, grid paper, number linesDigital MathToolsFraction Models, Number LineCopying is not permitted.Grade 4 Lesson 17 Understand Equivalent Fractions Lesson 20 Add and Subtract Fractions Lesson 21  Add and Subtract MixedNumbersRETEACHTools for InstructionGrade 4 Lesson 17 Equivalent Fractions Lesson 20 Add and Subtract Fractions Lesson 21 Add and Subtract Mixed NumbersGrade 5 Lesson 12  Add Fractions with UnlikeDenominatorsREINFORCEMath Center ActivityLesson Materials Curriculum Associates, LLCPREPAREGrade 5 Lesson 12 Fraction Addition: True or False!EXTENDEnrichment ActivityGrade 5 Lesson 12 Addition GridsLesson 12 Add Fractions225b

LESSON 12Connect to Family, Community, and Language DevelopmentThe following activities and instructional supports provide opportunities to foster school,family, and community involvement and partnerships.Connect to FamilyUse the Family Letter—which provides background information, math vocabulary, and an activity—to keep families apprised of what their child is learning and to encourage family involvement.Available in SpanishTeacher ToolboxAdd FractionsACTIVITY12Dear Family,This week your child is learning to add fractionswith unlike denominators.Work together with your child to solve real-world problems about adding fractions. Suppose you want to make some healthy snacks and you have 7 cup of cream8··cheese and 3 cup raisins.4·· Look at the two recipes below. Add fractions to decide if there is enough creamcheese and raisins to make both recipes.Here is how a model can show fraction addition, such as 1 3 1 1 .5··ADDING f On Do this activity with your child to add fractions.3··1315131The denominators, 5 and 3, tell howmany equal parts are in the whole.5 and 3 are unlike denominators.Recipe for Creamed CrackersRecipe for Celery LogsIngredients:12 crackers(any variety)Ingredients:6 two-inch piecesof celery12 cup cream cheese··The parts of the whole are different sizes, thirds and fifths. You cannot adddifferent-size parts. You need to divide the model to show equal-sizeparts, fifteenths.1··4 cup raisinsDirections:Spread creamcheese evenly oncrackers.Sprinkle with raisins.1··3 cup cream cheese1··8 cup raisinsDirections:Spread creamcheese evenly oncelery.Sprinkle with raisins.1391 53 5 151 5 5 1 15The denominator, 15, tells that thereare 15 equal parts in the whole. So, 15and 15 are like denominators.Then add. 1 3 1 1 5 1 9 1 5 5 1 145··3··15··15··15··Some other ways your child can think about adding fractions are to use a numberline model or to use multiplication to replace the given fractions with equivalentfractions that have the same denominator.Invite your child to share what he or she knows about adding fractions by doing thefollowing activity together.225 Curriculum Associates, LLC Copying is not permitted.Lesson 12 Add Fractions225226226Answer: There is enough cream cheese and enough raisins to make both recipes.Lesson 12 Add Fractions Curriculum Associates, LLC Copying is not permitted.GoalMath Talk at HomeThe goal of the Family Letter is to enlist the family in helpingstudents learn how to add fractions with unlike denominators.Encourage students to discuss situations in which they have to addfractions at home. This could be when using recipes to preparefood dishes or when mixing soil and fertilizer in a garden. Students are encouraged to discuss adding fractions usingdifferent strategies, such as using an area model, a number line,or multiplication to find equivalent fractions with likedenominators. How do you add fractions in recipes?ActivityStudents and family members review two recipes with fractionswith unlike denominators to determine if there are enoughingredients to make both dishes. Look at the Adding Fractionsactivity and adjust if needed to connect with students.225–226Conversation Starters Below are additional conversation startersstudents can write in their Family Letter or math journal to engagefamily members:Lesson 12 Add Fractions Have you had to adjust a recipe for more people? How do youcalculate the amounts? Do all the cooking tools use only fractions? Why? Curriculum Associates, LLCCopying is not permitted.

Connect to Community and Cultural ResponsivenessUse these activities to connect with and leverage the diverse backgrounds and experiences of all students.Sessions 1 and 2 Use anytime during these sessions.Sessions 3 and 4 Use anytime during these sessions. Adding fractions is very common when using recipes. Ask students tobring recipes that use fractions from their homes. Have students workin small groups and search online or in cookbooks for recipes that usefractions to specify the amounts of some ingredients. Encouragestudents to make different scenarios in which they must double ortriple the amounts called for in a recipe to feed a larger number ofpeople, such as their fellow students in class. Have students form small groups and assign one of the followingcountries to each group: India, China, France, Italy, or Russia. Havestudents research a traditional dessert from each of the countries andmake a chart that lists the ingredients for each recipe. Ask students tocompare the ingredients for the different recipes. If there is a commoningredient in all the recipes, have students find which recipe uses themost of that ingredient and which recipe uses the least.Connect to Language DevelopmentFor ELLs, use the Differentiated Instruction chart to plan and prepare for specific activities in every session.ELLEnglish Language Learners:Differentiated InstructionPrepare for Session 1Use with Try It.Levels 1–3Reading/Speaking Before reading theTry It problem, have students underline theterms like denominators and unlikedenominators in the directions. Read theTry It problem and ask students to identifythe unlike denominators. Prompt students torestate the problem to a partner, using thepicture of the stick of butter to support theirretellings. Allow time for students to solvethe problem independently, then call onvolunteers to share their solution strategies.Validate understanding and revoice theiranswers as needed to model fluent speaking. Curriculum Associates, LLCCopying is not permitted.Levels 2–4Reading/Speaking Read the Try Itproblem with students. Organize them intosmall groups to share ideas about how to addfractions with unlike denominators. Haveeach group member choose a tool from theMath Toolkit to model the problem andexplain why they think it is the best tool forthe problem. After each group member hasshared, give students the opportunity tochange their mind if they discovered a bettertool during the discussion. Allow time forstudents to engage in productive struggle tosolve the problem independently, then havethem compare answers with the group.Levels 3–5Reading/Speaking Have students readthe Try It problem. Allow time for students toapply what they know about adding likedenominators and choose a strategy foradding unlike denominators. Have themform pairs to compare answers and solutionsstrategies. If possible, have students find apartner who solved the problem using adifferent method. Have partners whosolved the problem differently compareand contrast their solution strategies.Ask partners who used the same strategy tothink of a different way to solve or model theproblem together.Lesson 12 Add Fractions226a

LESSON 12ExploreSESSION 1LESSON 12Explore Adding FractionsPurposeIn this session students draw ontheir understanding of adding fractions with likedenominators. They explore various solutionmethods based on replacing one fraction in asum with an equivalent fraction to producefractions with like denominators. They willlook ahead to think about sums in whichboth addends need to be replaced withequivalent fractions.You know how to add fractions with like denominators. Now youwill learn how to add fractions with unlike denominators. Use whatyou know to try to solve the problem below.Emiliano needs 1 stick of butter to make2··corn bread. He also needs 1 stick of4··Learning Target Add and subtract fractions withunlike denominators (includingmixed numbers) by replacing givenfractions with equivalent fractions insuch a way as to produce anequivalent sum or difference offractions with like denominators.SMP 1, 2, 3, 4, 5, 6, 7butter to make apple muffins. Whatfraction of a stick of butter does heneed in all?StartTRY ITConnect to Prior KnowledgePossible student work:Materials For each pair: 1 set of fraction tiles1524··211534 ··4 ··4··2··Math Toolkitfraction tilesfraction circlesfraction barsfraction modelsgrid papernumber linesEmiliano needs 3 stick of butter.4··Sample BHow Have students use sets of fraction tiles orfraction circles to build 5 possible equivalentfractions for   1   .12142··Possible SolutionsUse fraction tiles to make fivefractions equivalent to 1.152··152··152·· Sample AWhy Support students’ facility with findingequivalent fractions for  1  , foreshadowing the work2··they will do with equivalent fractions to solve theTry It problem.StartSESSION 1152··152··2··   2 ;  3 ;  4 ;   5 ;   6 4 ··6 ··8 ··10 ··12··DISCUSS IT1 and 1 together are the same length as 3 .44····Emiliano needs 3 stick of butter.4··Ask your partner: Why didyou choose that strategy?2··Tell your partner:I knew . . . so I . . .227 Curriculum Associates, LLC Copying is not permitted.TRY ITGrade 5 Lesson 12 Session 1 Explore Adding Fractions Curriculum Associates, LLCCopying is permitted.Make Sense of the ProblemTo support students in making sense of theproblem, have them identify the amount of butterEmiliano needs for corn bread and for apple muffins.DISCUSS ITSupport Partner DiscussionEncourage students to share what did not work forthem as well as what did as they talk to each other.Look for, and prompt as necessary for,understanding of: only same-size parts can be added an equivalent amount for  1 can be shown using2··fourthsLesson 12 Add Fractions227Common Misconception Look for students who count parts without concern thateach whole is divided into same-size parts. As students present solutions, have themspecify why they used 4 as the denominator.Select and Sequence Student SolutionsOne possible order for whole class discussion: physical parts showing halves and fourths drawings to represent the problem number lines marked in fourths equations showing   1 replaced with the equivalent fraction  2 2··4··Support Whole Class DiscussionPrompt students to note the relationship between the numbers in each model andthe numbers in the problem.Ask How do [student name]’s and [student name]’s models show the number offourths that is the same amount as  1 and the amount of butter needed in all?2··Listen for   2 is the same amount of the whole as  1   . The parts  2 and  1 combined are4244········  3 of a stick of butter.4··227Lesson 12 Add Fractions Curriculum Associates, LLCCopying is not permitted.

LESSON 12CONNECT IT1 LOOK BACKSESSION 1EXPLORECo ItLOOK BACK1Explain how you found how much butter Emiliano needs.Look for understanding that an equivalent amountin fourths had to be shown for  1 in order to find how2··much butter is needed in all.Possible answer: I found a common denominator for1 and 1 , fourths. Then I added to get 3 of a stick of butter.44····2··2 LOOK AHEADBefore adding fractions, the fractions must have the same-size parts of a whole.You can use what you know about multiples and equivalent fractions to find acommon denominator for fractions that have unlike denominators.Hands-On ActivityUse fraction circles to add fractions.a. Use the fractions 1 and 1 . Write the next four multiples of each denominator.If . . . students are unsure about the concept of2··3··finding an equivalent fraction to add fractions,Then circle the multiple that 2 and 3 have in common.Then . . . use this activity to have them modelMultiples of 2:2,4,6,8,10an equivalent fraction when one denominator isa multiple of the other denominator.Multiples of 3:3,6,9,12,15b. Complete the models and equations to show equivalent fractions for 1 and 12··3··using the common multiple as the common denominator. Possible models shown.Materials For each pair: 1 set of fraction circles Have students model  1 and  1   .2··4·· Point out that the sizes of the pieces are notthe same. Ask: Can you name this sum? [no]5 Have students find the number of fourths ittakes to cover the half and replace the halfwith those pieces. [2 fourths] Ask: Can youname this sum? 3   3   4 12553c. Use the equivalent fractions to add. Repeat activity for other sums, such as  2 1  1 3 ··6··and  1 1  3   . 3   5    ;  5    4 4 ··8 ··6 ··8··Students should be able to explain the termscommon denominator, multiple, and equivalentfractions and use this language to discuss theprocess of writing two fractions with denominatorsthat show same-sized parts of the whole.Ask The first pair of fraction models in problem 2bshows that when you change the number of parts inthe whole from 2 to 6, you change the number ofparts in  12 from 1 to 3. What operation changes 2··into 6 and 1 into 3? What equation can you write toshow changing   1 into  3   ?2··6··Listen for You can change 2 into 6 and 1 into 3 bymultiplying by 3. So you can change  12 into  36 ····by multiplying the numerator and denominatorby 3:  1 5  3 3 1 5  3    .2··332·····6·· Curriculum Associates, LLCCopying is not permitted.261115 3 1 2 5 53 ····666··········2··What equivalent fractions could you write to add 1 and 2 ? Explain.23····Possible answer: The number 6 is a common multiple of 2 and 3. So, you can usethe equivalent fractions 3 and 4 to add 1 and 2 .6··Point out that when the fractions in a sum haveunlike denominators and one denominator is not amultiple of the other denominator, each addendmust be replaced with an equivalent fraction.53 REFLECT4··2 LOOK AHEAD1366··2··3··228228Lesson 12 Add Fractions Curriculum Associates, LLC Copying is not permitted.Close: Exit Ticket3 REFLECTLook for understanding that to be added, fractions must have same-size parts of awhole. Student responses should include the common multiple of 2 and 3 to be usedas the common denominator, as well as the equivalent fractions for  1 and  2   .2··3··Common Misconception If students correctly name a multiple to use as thecommon denominator in each equivalent fraction but neglect to make acorresponding change in the numerators, then provide students with fraction tiles.Have students find the number of  16 s that equal  12 and the number of  61 s that equal  32 ········and write the corresponding fractions. Discuss what students notice about thenumerators and denominators.Real-World ConnectionEncourage students to think about everyday places or situations where peoplemight need to add fractions with unlike denominators. Have volunteers share ideas.Examples include combining measurements given in fractions of a pound, fractionsof an hour, or fractions of a mile.Lesson 12 Add Fractions228

LESSON 12SESSION 1Additional PracticeName:11Have students repeat common denominatorafter you. Have students form pairs and discusswhen they have used the term common before.Clarify the meaning as needed and providean example sentence, such as: People fromSpanish-speaking countries speak a commonlanguage: Spanish.Think about what you know about equivalent fractions. Fill in each box. Use words,numbers, and pictures. Show as many ideas as you can.Possible answers:Examples5Point out that in mathematics, a commondenominator is a denominator that is the same fortwo or more fractions.ExamplesWhen two or morefractions have the samedenominator, they havea common denominator.5ExamplesHave students work in pairs to complete the graphicorganizer. Provide examples as needed to stimulatestudent thinking.15 312···15 26 ···12··4··2commondenomina

Grade 4 Lesson 17 Equivalent Fractions Lesson 20 Add and Subtract Fractions Lesson 21 Add and Subtract Mixed Numbers Grade 5 Lesson 12 Add Fractions with Unlike Denominators REINFORCE Math Center Activity Grade 5 Lesson 12 Fraction Addition: True or False! EXTEND Enrichment Activity Grade 5 Lesson 12 Addition Grids

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