Ext 6-8 Sampler

14 ProblemSolvingSteps&Strategies Research indicates that students taughtwithmanipulatives arebetter able toapply their conceptual understanding inproblem solving situations and scorehigher on achievement tests. Extensions includes explicit instruction on steps inproblem solvingand usingdifferent strategies to solve the sameproblem. Lesson6, 6ETeacherGuide 17 Objective45: Touse the five-stepproblem-solvingmodel to solveproblems involving addition, subtraction, multiplication, anddivision. ELL Materials: ProblemSolvingSteps andStrategies (Master 13) Problem-SolvingSteps Aproblem-solving situation existswhen the student is confrontedwith anunfamiliarproblem forwhichno immediatepath to the answer is apparent. Thus, formany students, solvingwordproblems isproblem solving. Goodproblem solvers are risk-takers. It is important studentsunderstand that taking risks isnecessary for learning to takeplace. Let students know that you expect errors and these errors areoftennecessary stepping stones to solutions. For this activity itwill behelpful tohave a copyof theProblemSolvingSteps andStrategies (Master 13).Have students build a class chart as theywork through the fiveproblem-solving steps together. Write the followingproblemon theboard: A soccer leaguehas 23 teams. Each team averages 20players. Howmanyplayers are in the soccer league? Today,wearegoing to review thegeneral problem-solving steps.What is the first thingwemustdo to solve thisproblem? (Read it.) Is it enough to just read theproblem? (No, youmust alsounderstand it.)To check forunderstanding, have avolunteer read theproblemout loud and show sheunderstands theproblemby restating theproblem inher ownwords. What is thenext step in solving theproblem? (Find the question andneeded facts.)Have avolunteerunderline the question and circle the facts (23 teams; 20 students per team). What is thenext thingwemustdo to solve this problem? (Decideon aprocess to solve theproblem.) What are some ideasor strategieswe canuse tohelp decidehow to solve thisproblem? Discuss the various strategies together, such as act it out, use amodel, drawapicture, simplify thenumbers, etc. Be sure tohave studentsmodel the strategies as they are discussed. Studentsmight draw abar showing23groups of 20: 23 groups of 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 20 Whatprocess shouldweuse to solve theproblem? (multiplication) Howdoyouknow tousemultiplication? (We areputting together groups of equal size.) What is thenext step? (Estimate.)Ask avolunteer to estimate for step4. (20 20=400) After estimating theanswer,what shouldwedo? (Solve theproblem.)Have avolunteer solve theproblem. (23 20=460) Howdoweknow if theanswer is reasonable? (Compare the answer to the estimate.) Howdo wedecide if theanswer is correct? (Check theproblemby putting the answer back into theproblem.) Together, read the example at the topof thepage. As a class,walk through the steps in this problem as in the introductory activity.Draw students’ attention to the problem-solving steps at the topof thepage.Have students complete thepageon their own. Encourage students to draw apicture for eachproblem. Skill Builders 45-5, 45-6 17 ©Math TeachersPress, Inc.,Reproduction by anymeans is strictly prohibited. Steps for ProblemSolving San Francisco’sGoldenGateBridge is 4,200 feet long.NewYork’sGeorgeWashington Bridge is 3,500 feet long.Which bridge is longer?Howmuch longer? Steps 4& 5 GoldenGateBridge is4,200 feet long andGeorgeWashington Bridge is3,500 feet long 4,200 –3,500 1. TheCarters travelled 220miles to Grandma’s house. They drove 55 miles per hour.Howmany hours did it take for them to get there? Est._______ Actual _______ 3. The odometer inCory’s car reads 46,325miles. The odometer read 21,850when he bought the car.How manymiles has he driven his car? Est._______ Actual _______ 5. Kim’s sister earned $1,142 babysitting last year and $756 this year.How much hasKim’s sister earned? Est._______ Actual _______ 2. Carla’s friend earns $68 per hour as a computer consultant.Howmuch would she earn on a 20-hour project? Est._______ Actual _______ 4. TheBashmans pay $528 in rent each month.Howmuch rent do they pay in 12months? Est._______ Actual _______ 6. Dwayne’s family used 12 gallons of gas to drive 276miles.Howmany miles did they drive per gallon of gas? Est._______ Actual _______ The ________________________ Bridge is ____ feet longer. Read.Underline the question.Circle the needed facts.Complete the problem solving steps.Label the answer. 1.Read. 2.Find facts. 3.Decide. 4.Estimate. 5.Solve. Steps 1& 2 “Howmuch longer”means to compare by subtraction. Step 3 GoldenGate 700 4 24,000 1,800 1,400 5,000 30 4 24,475 1,898 1,360 6,336 23 TeacherManual CONCEPTUALBASED INSTRUCTION 5 Step 17 ©Math Teachers Pr ss, Inc., Reproduction by nymeans is strictly prohibited. Steps for ProblemSolving San Francisco’sGoldenGate Bridge is 4,200 feet long. NewYork’sGeorgeWashington Bridge is 3,500 feet long. Which bridge is longer?Howmuch longer? Steps 4& 5 GoldenGate Bridge is 4,200 feet long andGeorgeWashington Bridge is3,500 feet long 4,200 –3,500 1. TheCarters travelled 220miles to Grandma’s house. They drove 55 miles per hour. Howmany hours did it take for them to get there? Est._______ Actual _______ 3. The odometer inCory’s car reads 46,325miles. The odometer read 21,850when he bought the car. How manymiles has he driven his car? Est._______ Actual _______ 5. Kim’s sister earned $1,142 babysit ing last year and $756 this year. How much has Kim’s sister earned? Est._______ Actual _______ 2. Carla’s friend earns $68 pe hour as a computer consultant. Howmuch would she earn on a 20-hour project? Est._______ Actual _______ 4. The Bashmans pay $528 in rent each month. Howmuch rent do they pay in 12months? Est._______ Actual _______ 6. Dwayne’s family used 12 gallons of gas to drive 276miles. Howmany miles did they drive per gallon of gas? Est._______ Actual _______ The ________________________ Bridge is ____ feet longer. Read. Underline the question. Circle the needed facts. Complete the problem solving steps. Label the answer. 1. Read. 2. Find facts. 3. Decide. 4. Estimate. 5. Solve. Steps 1& 2 “Howmuch longer”means to compare by subtraction. Step 3 StudentBook