EXT 3-6 Sampler

53 ProblemSolving:Drawing&Writing Lesson25, 5ETeacherGuide 72 72 ©Math TeachersPress, Inc.,Reproduction by anymeans is strictly prohibited. ProblemSolving: Drawing aPicture,WritingaNumber Sentence Heather estimates that she spends � 1 3 � of each day sleeping. About howmany hours does she sleep? (1day = 24 hours) 24 n= of 24 � = = 8 hours z Z z Z z Draw apicture. Write anumber sentence. Solve. 1. Molly is sendingout 28 valentines. Shewrotenames on � 1 2 � of them onMonday night. Howmany valentines have names on them? 4. Earl spent 30 hours ona science project. One-fifth of his timewas spent on a hands-onexperiment. Howmany hours didhe spend on the experiment? 2. There are28 students in themath class. Three fourths of them have finished themath test. Howmany have finished themath test? 3. Themath class is 45minutes long eachday. The class is � 1 3 � over. Howmanyminutes of themath class havepassed?Howmanyminutes are left? 28 � 2 1 � n= � 2 1 � x28 n= � 2 2 8 � = 14 14 valentines Drawapicture tohelp understand theproblem. Writeanumbersentence toshow how tosolve theproblem. Write24asa fraction.Find the productof thenumeratorsand theproduct of thedenominators. Part B 28 3 4 n= � 3 4 � x 28 n=21 students finished the math test 45min 1 3 n= � 3 1 � x 45= 15minover 45 – 15=30min left 30hr 1 5 n= � 5 1 � x 30=6hrs spent on the experiment Objective19: Touse adrawing strategy to solve wordproblems that involvemultiplying a fraction and awholenumber. Drawing aPicture To find a fractional part of anumber, studentsmust understand thewhole-part relationshipbetween the fraction and thenumber that represents thewhole set. Simpleproblemswhere students are asked todraw a pictureof theproblemwill improveunderstandingof the whole-part relationship. Thepicturesdrawnmaymatch the situationof theproblemor be agenericmodel using the concept of areaor length. Writeon theboard: Jane’smotherhas abakery. She cuts someof her cakes intohalves for customerswhodonotwant tobuy awhole cake.OnSaturday she sold six ½ chocolate cakes.Howmanywhole chocolate cakes did she sell? Ask students todiscussdifferent strategies theymight use to solve theproblem.One solutionwouldbe todraw apicture: Writeon theboard: There are ten children in the skating class. 1⁄5 of the childrenhave learned tomake a figure eight. Howmany canmake a figure eight?Draw a picture andwrite anumber sentence to show the solution. To showwhole-part relationships for this problem, an areamodel or linearmodelmaybeused. Write anddrawon theboard: n =number of children that canmake a figure eight 1 2 1 2 1 2 1 2 1 2 1 2 1 2 6 = 3whole cakes 1 2 1 2 1 2 1 2 1 2 1 2 1 5 n = of 10 1 5 10 1 n = = 2 Area: 1 5 n = of 10 1 5 10 1 n = = 2 Linear: Read the example at the topof thepage.Note that this problemuses the linearmodel.Another solutionwould be to circle1hour out of every3hours to find that 8hours wouldbe circledout of 24hours. Journal Prompt There are28 students in themath class. One-fourthof them saymath is their favorite class. Howmany feelmath is their favorite class?Drawpictures andusewords and symbols todescribe your solution. Skill Builders 19-3 Conceptual Understanding - hour hour hour hour hour hour hour hour hour hour hour hour hour hour hour hour hour hour hour hour hour hour hour hour 1 out of every 3= 8 out of 24 5.NF.4, 5.NF.4a, 5.NF.4b, 5.NF.5, 5.NF.5a, 5.NF.6 Studentsmove froman abstractwordproblem to drawingapictureat the representational stage— excellent preparation for Smarter Balancedand PARCCAssessments. Grade5 PartB