Problem Solving Two-Step Problems
LESSON7.10Problem Solving Two-Step ProblemsFOCUSCOHERENCERIGORLESSON AT A GLANCEF C R Focus:Common Core State Standards3.OA.D.8 Solve two-step word problems using the four operations.Represent these problems using equations with a letter standing for theunknown quantity. Assess the reasonableness of answers using mental computationand estimation strategies including rounding.MATHEMATICAL PRACTICESMP4 Model with mathematics. MP5 Use appropriate tools strategically.MP6 Attend to precision.F C R Coherence:Standards Across the GradesBeforeGrade 3 After2.OA.C.4 3.OA.D.8 4.OA.A.3F 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 DeeperLearning ObjectiveSolve two-step problems by using the strategyact it out.Language ObjectiveStudent teams role play to show the class howyou can use the strategy act it out to solve twostep problems.MaterialsMathBoardF C R For more about how GO Math! fosters Coherencewithin the Content Standards and Mathematical Progressionsfor this chapter, see page 363J.About the MathProfessional DevelopmentWhy Teach ThisInteractive Student EditionUsing a graphic organizer to scaffold a problem helpsstudents analyze the problem to understand what theyneed to find, identify what information they need to use,and develop or select a strategy.Personal Math TrainerIn this lesson, students use the act it out strategy. Studentsuse counters, write equations, and work backward to solvetwo-step problems.Students will represent the situations in the steps of aproblem with equations containing a letter that standsfor the unknown quantity. Writing equations withan unknown quantity can help students to relate thesituations in problems to operations. Carrying out eachoperation and finding the unknown helps students tosolve the two-step problems.Professional Development Videos421AChapter 7Math on the SpotiTools: Counters
Daily RoutinesCommon Core1 ENGAGECommon Corewith the Interactive Student EditionDaily RoutinesProblem of the Day 7.10Essential QuestionThe product of two factors is 27. One factoris 9. What is the other factor? 3How can you use the strategy act it out to solve two-step problems?VocabularyInvite students to tell you what they know about division.Making ConnectionsIf 12 beetles are put into 2 equal groups, how many are in eachgroup? 6 If 6 beetles are separated into 3 equal groups, how manyare in each group? 2 Interactive Student Edition Multimedia eGlossaryLearning ActivityFluency BuilderCommon Core FluencyStandard 3.OA.C.7Materials K.I.M. Chart (see eTeacher Resources)Graphic Organizer Have students work ingroups to brainstorm all the division wordsthey have learned. Then have studentscomplete a K.I.M. chart for the words.Students write the term or key idea inthe left column. Then they write theinformation that goes with the term, thedefinition, in the center column. Thenstudents draw a picture of the idea, amemory clue, in the right column.KKey IdeadivisordividendquotientIInformationMMemory ClueWhat is the problem the students are trying to solve? Connect thestory to the problem. How many rabbit holes did the first set of beetles hide in? 4 How many beetles were seen first? 28 How many beetles were seen after the first set hid in the rabbitholes? 8 What is the question asking for? how many beetles will bein each holeLiteracy and MathematicsChoose one or more of the following activities. Have students visualize the beetles separating and hiding inthe holes. Have students draw a picture of four holes with thebeetles hiding. Have students write a short story about what it would be like tolive for 1 day as a beetle.How can you use thestrategy act it outto solve t wo-stepproblems?Lesson 7.10 421B
LESSON7.102 EXPLORE3.OA.D.8 Solve two-step word problems using the four operations. Represent these problems using equations with aDONOTstandingEDIT--Changesmust be madethroughletterfor the unknownquantity.Assess"Filetheinfo"reasonableness of answers using mental computation and estimationCorrectionKey Bstrategies including rounding.Unlock the ProblemUnlockUnlock thethe ProblemProblemMadilyn bought 2 packs of pens and a notebook for 11. The notebook cost 3. Each pack of pens cost thesame amount. What is the price of 1 pack of pens?answer: the total cost for the pens and notebookis 11. You have to subtract the cost of the notebookto find out how much the pens cost.Read the Problem Why do you divide by 2 in the last step?The cost of 2 packs of pens is 8. To find the cost of1 pack, you divide by 2.Use Math Talk to focus on solvingmultistep problems.MP2 Reason abstractly andquantitatively. How would the problem change if Madilynbought 3 packs of pens and a notebookfor 15? You would still subtract the price of theSolve the ProblemWhat do I need to find?Describe how to act out the problem.I need to find the price ofStart with 11 counters. Take away 3 counters.pens1 pack of.totalcostWhat information doI need to use? 11cost ofnotebookp, cost of2 packs of pens 11 in all.Madilyn spent 3 p 8 p 8 .Now I know that 2 packs of pens cost2 packs ofShe bought Houghton Mifflin Harcourt Publishing Company Image Credits: George Doyle/Getty ImagesMathTalkOperations and Algebraic Thinking—3.OA.D.8MATHEMATICAL PRACTICESMP1, MP3, MP6Essential Question How can you use the strategy act it out to solvetwo-step problems?MP1 Make sense of problems andpersevere in solving them. Have studentsexplain how the description to act out theproblem helps them to solve the problem. Why do you subtract 3 from 11? Possiblethe cost of 1 pack of pens, 4 by 2. That gives me 8.Then add the notebook price 3, to 8 to get 11. So,my answer is correct.Lesson 7.10Problem Solving Two-Step ProblemsMATHEMATICAL PRACTICESDiscuss the letter that stands for the unknownin each equation. Tell students that a letter issimilar to the answer lines or the squares thatthey have seen in equations in the position ofthe answer they need to find. How can you use multiplication andaddition to check your answer? I can multiplyPROBLEM SOLVINGName2 equal groups with theNext, make8 remaining counters.1 notebook.pens and 3 .The notebook costp, cost of2 packs of pensnumberof packsc, cost of1 pack of pens How will I use theinformation? 8 I will use the information to2 c 4 c 4 .So, the price of 1 pack of pens isact out the problem.MathTalkMATHEMATICAL PRACTICES 1Make Sense of ProblemsWhy do you need to usetwo operations to solvethe problem?Possible explanation: I need to subtract the cost ofthe notebook to know what the pens cost. Then Ineed to divide to find the cost of 1 pack of pens.Chapter 7 421notebook from 15, but now you would divide theremaining amount by 3 instead of 2.3 MNLESE342132 C07L10.indd 421ELL Strategy:Model LanguageGo over four strategies—act it out, draw adiagram, make a table, and find a pattern. Write the name of each strategy and put anicon or visual to represent the strategy onan index card. Have students draw a card and act out thestrategy. Allow students to use props asneeded. The other students guess whichstrategy is being performed. Discuss the strategy using sentence frames.You can use the strategy to solveproblems by .09/10/14 8:40 PM3Reteach 7.10Lesson 7.10ReteachLesson 7.10EnrichNameProblem Solving Two-Step ProblemsDivision StepsChloe bought 5 sets of books. Each set had the samenumber of books. She donated 9 books to her school.Now she has 26 books left. How many bookswere in each set that Chloe bought?Solve. Show your steps to find the answer.Read the Problem1.Solve the ProblemWhat do I need to find?t, totalbooks number ofdonatedbooksbooksleftsetwere in each.What information do I need to use?26I need to use the information given:5 sets of books.Chloe bought9t355t3.Then divide to find the number of booksin eachset.MXEFL11AWK3X RW C6 L8 ART 01sets of s, bookst, totalnumber of booksin eachbooksset9 books.She donated26 books left.She hasHow will I use the information?act outI will use the information tothe problem.3557s5s5.Sid has 2 boxes of markers with thesame number of markers in eachbox. He gives 3 markers to his sister.Now Sid has 13 markers. How manymarkers were in each box?13 3 16;16 2 8; 8 markersCasey bought 30 basketball tradingcards. He gave 6 to his sister and thenput the rest in an album. If 6 cards fiton one page of the album, how manypages did Casey use?4.Manny ordered 16 skateboard wheels.If he sold 4 wheels to Brad, how manyskateboards can he put wheels on ifeach board uses 4 wheels?6.30 2 6 5 24;24 4 6 5 4; 4 pages7.MXEFL11AWK3X RW C6 L8 ART 022. Tony had 4 equal sets ofsportscards. He gave his friends 5 cards.Now he has 31 cards. How manycards were in each set?8 pencils2.Barron bought a 25-pound bag ofdog food. He still had 3 pounds froman older bag. If he feeds his dogs 4pounds of food each week, how manyweeks until all the dog food is gone?25 1 3 5 28;28 4 4 5 7; 7 weeksKiera has 27 balls of yarn. Her mothergave her 5 more balls. If she makesscarves that use 4 balls each, howmany scarves can she make?16 2 4 5 12; 12 4 4 5 3; 27 1 5 5 32;3 skateboards32 4 4 5 8; 8 scarves7 books were in each set.So,Solve the problem.Jackie had 6 equal packs ofpencils. Her friend gave her4 more pencils. Now she has52 pencils. How many pencilswere in each pack?Veronica bought a pack of 50 CDs.She gave 8 to her friend, Leslie. Thenshe made 6 equal sets of CDs. Howmany CDs are in each set?50 2 8 5 42;42 4 6 5 7; 7 CDsFirst, begin with the number of booksleft. Add the number of books donated.booksI need to find how many1.421 Chapter 7DO NOT EDIT--Changes must be made through "File info"CorrectionKey A1NameDifferentiatedInstructionEnrich 7.102DO NOT EDIT--Changes must be made through "File info"CorrectionKey A9 cardsThomas starts with 36 photos and throwsaway 6 that are too dark. Then he organizes the rest ofthem on scrapbook pages so that there are 5 photos oneach page. How many pages will he use? Draw to explain.6 pages; Possible drawing is shown.MXEFL11AWK3X EN C6 L8 ART 01Chapter Resources Houghton Mifflin Harcourt Publishing Company3 MNLEAN343009 C07R10.indd 237-23ReteachChapter Resources Houghton Mifflin Harcourt Publishing Company17/02/14 8:13 PM3 MNLEAN343009 C07E10.indd 247-24Enrich17/02/14 8:01 PM
Try Another ProblemHave students answer the questions in thegraphic organizer and solve the problem. Suppose you used counters to solve theproblem. How many counters wouldyou start with and why? Possible answer: 19;Try Another ProblemChad bought 4 packs of T-shirts. He gave 5 T-shirtsto his brother. Now Chad has 19 shirts. How manyT-shirts were in each pack?because that is the number of T-shirts Chad has left What would you do next, and why?Read the ProblemWhat information do I needto use?Chad bought 4 packs of T-shirts andgave 5 T-shirts to his brother. Chadhas 19 shirts left.How will I use the information?I will use the information to act out theproblem.Describe how to act outthe problem.final numberT-shirtst, T-shirts inof T-shirtsgiven away4 packs 19 5 t24 t T-shirts Chad started with Why did you divide by 4? to find how manyT-shirts were in each packDiscuss students’ solutions and analyzewhether they are reasonable. How might you use mental math to findif your answer is reasonable? PossibleNow I know there were 24 T-shirts inthe packs.Next, divide the counters into 4 equalgroups to find the number of T-shirts ineach pack.t, T-shirts innumberp, number in4 packsof packseach pack 24 4 p6 pSo, there were 6 T-shirts in each pack. How can you use multiplication and subtraction to check your answer?NPossible answer: I can start with the number of T-shirts in each pack and workthrough the problem. Multiply 6 shirts by 4 packs: 4 6 24. Then subtract 5 T-shirts:24 5 19. So, my answer is correct.Possible explanation: I could draw a diagram adding5 tiles to 19 tiles. Then I would make an array bydividing the 24 tiles into 4 equal rows.MathTalkMATHEMATICAL PRACTICES 3Apply What is anotherstrategy you could useto solve this problem?422Advanced Learners What does 24 represent? the number ofPossible description is given.Start with 19 counters. Add 5 counters.Logical / MathematicalIndividual / Partnersanswer: use a multiplication fact: 4 6 24, andcount back 5 to 19. Houghton Mifflin Harcourt Publishing Company Image Credits: C Squared Studios/Getty ImagesWhat do I need to find?I need to find the number of T-shirts thatwere in each pack.Possible answer: add 5 counters; Since Chad gaveaway 5 T-shirts, you need to add 5 back to find thenumber of T-shirts he had to start with.Solve the Problem How might you use estimation to find ifyour answer is reasonable? Possible answer:think of a multiplication fact for 4 that has a productof about 19. 4 5 20 and 4 6 24, so theanswer is about 5 or 6. How would your strategy change if Chadbought 3 packs of T-shirts, gave away 5,and had 19 T-shirts leftover? I would still add19 and 5, but would divide 24 by 3 instead of 4.MathTalkUse Math Talk to focus onusing different strategies tosolve problems.You may suggest that studentsplace completed Try AnotherProblem graphic organizers in theirportfolios.COMMON ERRORSMaterials play coinsError When solving some multistep Write the following problem on the board.problems, students may not understand theycan use an inverse operation.Cathy had 6 coins. She used 2 coins to buy an apple for50 . Then her friend gave her 35 . Now she has 75 .How much money did Cathy have to start? What arethe coins Cathy had before buying the apple? Have students solve the problem. Provide students withplay coins if they need to act out the problem. 90 ;possible answers: 2 quarters and 4 dimes, or 3 quarters and 3 nickels Have students write out the steps they used to solvethe problem. Challenge students to write more problems on theirown and exchange papers to solve them.Example In this problem, studentsmight want to subtract 5 T-shirtsinstead of adding them, using thereasoning that they were givenaway.Springboard to Learning Tell students thatwhen working a problem from the end tothe beginning, each operation should be aninverse operation.Lesson 7.10 422
DO NOT EDIT--Changes must be made through "File info"CorrectionKey BName3 EXPLAINShareShare andand ShowShowUnlock the ProblemMATH Circle the question. Underline the important facts. Choose a strategy you know.BOARD1. Mac bought 4 packs of toy cars. Then hisShare and Showfriend gave him 9 cars. Now Mac has21 cars. How many cars were in each pack?MATHBOARDAct out the problem by using counters or the pictureand by writing equations.The first problem connects to the learningmodel.First, subtract the cars Mac’s friend gave him.totalcarsSMARTER 21Rt IIfa student misses the checkedexcercisesThenDifferentiate Instruction with Reteach 7.10 Personal Math Trainer 3.OA.D.8 RtI Tier 1 Activity (online)On Your OwnIf students complete the checked excercisescorrectly, they may continue with the OnYour Own section. Have students reviewtheir answers and decide whether they arereasonable.SMARTERExercise 3 is a multistep problem that usesaddition and subtraction. Have studentsshare their methods for solving the problem.Math on the SpotVideo TutorUse this video to help students model andsolve this type of Think Smarter problem.Math on the Spot videos are in the InteractiveStudent Edition and at www.thinkcentral.com.423 Chapter 721c, cars in4 packs 9 c12 cThen, divide to find the number of cars in each pack.c, cars in4 packsnumberof packs 12p, number ineach pack 4 p3 p3 cars in each pack.So, there were2.SMARTERWhat if Mac bought 8 packs of toy boats, and thenhe gave his friend 3 boats? If Mac has 13 boats now, how manyboats were in each pack?2 boats Houghton Mifflin Harcourt Publishing CompanyQuick Check Houghton Mifflin Harcourt Publishing Company Image Credits: C Squared Studios/Getty ImagesExercise 2 requires students to use logicalreasoning to solve a multistep problem. Havestudents review their answers and decidewhether they are reasonable.MP1 Make sense of problems andpersevere in solving them. To extendstudents’ thinking about the steps of amultistep problem, have students think of thehidden question. For example, in Exercise 2 thehidden question is How many boats did Machave before he gave his friend 3 boats?Use the checked excercises for Quick Check.Students should show their answers for theQuick Check on the MathBoard.3cars givento MacOnOn YourYour OwnOwn3.SMARTERRyan gave 7 of his model cars to a friend. Thenhe bought 6 more cars. Now Ryan has 13 cars. How many carsdid Ryan start with?14 carsChapter 7 Lesson 103 MNLESE342132 C07L10.indd 42342309/10/14 8:45 PM
DO NOT EDIT--Changes must be made through "File info"CorrectionKey BMATHEMATICAL PRACTICES4.ANALYZE LOOK FOR STRUCTURE PRECISIONDEEPERChloe bought 5 sets of books. Each set has thesame number of books. She donated 9 of her books toher school. Now she has 26 books. How many bookswere in each set?4 ELABORATE7 booksMATHEMATICAL PRACTICES5. Hilda cuts a ribbon into 2 equal pieces. Then she cuts4 inches off one piece. That piece is now 5 inches long.What was the length of the original ribbon?DEEPER18 inches6.DEEPERTeanna has 2 boxes of color pencils. One box has20 color pencils and the other box has 16 color pencils. Shegives her brother 3 of the color pencils. She wants to putthe color pencils that she has left into 3 equal groups. Howmany color pencils will Teanna put in each group?WRITEWork with students to determine the hiddenquestion in Exercise 4. In this exercise, thehidden question is: How many books didChloe have before she donated books to herschool?MP6 Attend to precision. Exercise 7requires students to use logical reasoningto determine the order of events and thenexplain their thinking.MathShow Your Work11 color pencils7.MATHEMATICAL6 Rose saw a movie, shopped, and ate at aPRACTICErestaurant. She did not see the movie first. She shoppedright after she ate. In what order did Rose do theseactivities? Explain how you know.SMARTERPersonal Math Trainerate, shopped, saw a movie; possible explanation: sinceRose did not see the movie first, she saw it second or third.Since she shopped right after she ate, she saw the moviethird, which means she ate first and shopped second.Personal Math TrainerEleni bought 3 packs of crayons. Eachpack contains the same number of crayons. She thenfound 3 crayons in her desk. Eleni now has 24 crayons.How many crayons were in each pack she bought?Explain how you solved the problem.SMARTER Houghton Mifflin Harcourt Publishing Company8.Possible explanation: First, I subtracted 24 3 21. Then Idivided 21 by 3 and got 7, so there were 7 crayons in each pack.Be sure to assign this problem to students inthe Personal Math Trainer. It features a videoto help them model and answer the problem.If students make errors, encourage them toact out the problem. Students may act outbuying 3 packs of crayons and then pickingup 3 more crayons. Repeating the steps inreverse order will help them visualize thesolution steps.5 EVALUATE FormativeAssessment424Essential Question3 MNLESE342132 C07L10.indd 42409/10/14 8:52 PMDIFFERENTIATED INSTRUCTIONINDEPENDENT ACTIVITIESLiteratureThe Garden FenceReflect Have student teams role play toanswer the Essential Question.How can you use the strategy act it outto solve two-step problems? Possible answer:I can act out the problem by using counters, writingdescriptions, making drawings, or writing equations.It organizes what I am doing and helps me see the steps.It also makes checking my work easy.Differentiated Centers KitActivitiesDivision DilemmasUsing the Language ObjectiveGamesDivision Cover-UpMath JournalWRITEMathWrite a division word problem and explainhow to solve it by acting it out.GamesStudents completepurple ActivityCard 19 byrelating divisionfacts to knownmultiplication facts.Students readthe book and usedivision facts tofind how muchwood they needto build a fence.Studentspractice divisionfacts to placecounters on thegameboard.Lesson 7.10424
Practice and HomeworkNameProblem Solving Two-Step ProblemsLesson 7.10COMMON CORE STANDARD—3.OA.D.8Solve problems involving the four operations, andidentify and explain patterns in arithmetic.Solve the problem.Practice and Homework1. Jack has 3 boxes of pencils with the sameUse the Practice and Homework pages toprovide students with more practice of theconcepts and skills presented in this lesson.Students master their understanding as theycomplete practice items and then challengetheir critical thinking skills with ProblemSolving. Use the Write Math section todetermine student’s understanding of contentfor this lesson. Encourage students to use theirMath Journals to record their answers.number of pencils in each box. His mother giveshim 4 more pencils. Now Jack has 28 pencils.How many pencils are in each box?Think: I can start with 28 countersand act out the problem.8 pencils2. The art teacher has 48 paintbrushes. She puts8 paintbrushes on each table in her classroom.How many tables are in her classroom?6 tables3. Ricardo has 2 cases of video games with thesame number of games in each case. He gives4 games to his brother. Ricardo has 10 gamesleft. How many video games were in each case?7 video games4. Patty has 20 to spend on gifts for her friends.Her mother gives her 5 more. If each giftcosts 5, how many gifts can she buy?5 gifts Houghton Mifflin Harcourt Publishing Company5. Joe has a collection of 35 DVD movies. Hereceived 8 of them as gifts. Joe bought the restof his movies over 3 years. If he bought thesame number of movies each year, how manymovies did Joe buy last year?9 movies6.Math Write a division word problem andWRITEexplain how to solve it by acting it out.Check students’ work.Chapter 7Extend the MathActivityInequalitiesMaterials index cardsInvestigate In this activity, students compare quantitiesusing inequality signs, , or . Prepare index cards by writing problems that are notequal in value (27 4 3, 12 1 4, 18 2 5, and so on) andone index card for each of the signs , and . Write the signs , and . on the board. Explain eachsign to students; , is less than, . is greater than. Explain that an inequality is made using two amountsthat are not equal. The signs , and . show that thetwo sides are not equal.425 Chapter 7425 Write the following examples on the board.2 3 3 , 10 4 145 4 5 . 12 2 7 Have groups of students take turns writinginequalities. Two students each choose an indexcard. They place the cards on the table. Thenanother student chooses the sign card that makesthe inequality true.27 4 3,18 2 5Summarize Ask students to explain how they decidedwhich sign made the inequality true.
Lesson Check (3.OA.D.8)1. Gavin saved 16 to buy packs of2. Chelsea buys 8 packs of markers.baseball cards. His father gives him 4 more. If each pack of cards costs 5, how many packs can Gavin buy?Each pack contains the same numberof markers. Chelsea gives 10 markersto her brother. Then, she has 54markers left. How many markerswere in each pack?4 packs8 markersContinue concepts and skills practice withLesson Check. Use Spiral Review to engagestudents in previously taught concepts andto promote content retention. Common Corestandards are correlated to each section.Spiral Review (3.OA.A.1, 3.OA.A.3, 3.OA.A.4, 3.OA.D.8)3. Each foot has 5 toes. How many toes4. Each month for 5 months, Sophiemakes 2 quilts. How many morequilts does she need to make beforeshe has made 16 quilts?30 toes5. Meredith practices the piano for6 quilts6. Find the unknown factor.3 hours each week. How many hourswill she practice in 8 weeks?9 3624 hours4264 Houghton Mifflin Harcourt Publishing Companydo 6 feet have?FOR MORE PRACTICEGO TO THEPersonal Math TrainerLesson 7.10 426
Solve two-step problems by using the strategy act it out. Language Objective Student teams role play to show the class how you can use the strategy act it out to solve two-step problems. Materials MathBoard F C R Focus: Common Core State Standards 3.OA.D.8 Solve two-step word problems using the four operat
Combating Problem Solving that Avoids Physics 27 How Context-rich Problems Help Students Engage in Real Problem Solving 28 The Relationship Between Students' Problem Solving Difficulties and the Design of Context-Rich Problems 31 . are solving problems. Part 4. Personalizing a Problem solving Framework and Problems.
grade step 1 step 11 step 2 step 12 step 3 step 13 step 4 step 14 step 5 step 15 step 6 step 16 step 7 step 17 step 8 step 18 step 9 step 19 step 10 step 20 /muimn 17,635 18,737 19,840 20,942 22,014 22,926 23,808 24,689 325,57! 26,453 /2qsohrs steps 11-20 8.48 9.0! 9.54 10.07 10.60 11.02 11.45 11.87 12.29 12.72-
Special Rates 562-600 Station Number 564 Duty Sta Occupation 0083-00 City: FAYETTEVILL State: AR Grade Suppl Rate Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Min OPM Tab Eff Date Duty Sta Occupation 0601-13 City: FAYETTEVILL State: AR Grade Suppl Rate Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Min OPM Tab Eff Date
Grade Minimum Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 Step 7 Mid-Point Step 8 Step 9 Step 10 Step 11 Step 12 Step 13 Step 14 Maximum Step 15 12/31/2022 Accounting Services Coordinator O-19 45.20 55.15 65.10 Hourly 94,016 114,712 135,408 Appx Annual 12/31/2022 Accounting Services Manager O-20 47.45 57.90 68.34 Hourly
THREE PERSPECTIVES Problem solving as a goal: Learn about how to problem solve. Problem solving as a process: Extend and learn math concepts through solving selected problems. Problem solving as a tool for applications and modelling: Apply math to real-world or word problems, and use mathematics to model the situations in these problems.
3.3 Problem solving strategies 26 3.4 Theory-informed field problem solving 28 3.5 The application domain of design-oriented and theory-informed problem solving 30 3.6 The nature of field problem solving projects 31 3.7 The basic set-up of a field problem solving project 37 3.8 Characteristics o
General Problem-Solving Steps Questions in the Quantitative Reasoning measure ask you to model and solve problems using quantitative, or mathematical, methods. Generally, there are three basic steps in solving a mathematics problem: Step 1: Understand the problem Step 2: Carry out a strategy for solving the problem Step 3: Check your answer
Shake the bag so that everything mixes together (at least 1 min.) Store in a dark, dry place for 5 days Primary Growing Process Steps one Step two Step three Step four Step five Final step 11 12 Step two Step three Step five Step four Step one Step three Step 7, 8, & 9 Step four Step ten Step 3 &am
