SAMPLE - dibels.uoregon.edu• Review equivalent fractions and related word problems. • Review simplifying fractions. • Define ratio as a multiplicative relationship. A ratio is

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P r o g r a m S a m p l e r

SAMPLE

This program was developed and supported with funding from the Institute of EducationSciences, U.S. Department of Education, Grant Nos.R305K060002andR305A110358to theUniversityofMinnesota.ThePrincipalInvestigatorsontheprojectincludeAshaK.JitendraandJonR.Star.ThispublicationdoesnotnecessarilyrepresentthepolicyoftheU.S.DepartmentofEducation,nordoesthefederalgovernmentnecessarilyendorsethematerial.

Copyright©2016byAshaK.JitendraandJonR.Star.Allrightsreserved.

Theexamplesinthiscurriculumareusedinafictitiousmanner.Wearenotmakingstatementsaboutanyspecificperson,character,business,place,orevent.

This is a Demo Copy of a copyrighted work. You are granted permission to use this Demo Copy solely for the purpose of determining whether or not you wish to purchase this material. As a result, you may share this Demo Copy only with those necessary to make that decision. You may not otherwise use, share, copy or print this Demo Copy without express written permission.

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©2016AshaK.JitendraandJonR.Star.Allrightsreserved.

SCHEMABASEDINSTRUCTION(SBI)CURRICULUM

SCOPEANDSEQUENCE

LESSON CONTENT SCHEDULE

UNIT1:RATIOSANDPROPORTIONS

1&2 Ratios 3days

3&4SolvingRatioWordProblems:

Part-to-PartandPart-to-WholeComparisons3days

5Rates

(QuizoverLessons1-4)1day

6&7 SolvingProportionProblems 3days

8&9ScaleDrawingProblems

(QuizatendofLesson9overLessons1-7)3days

10 Unit1Review 1day

UNIT2:PERCENTS

11 Fractions,Percents,&Decimals

3days

12 SolvingPercentProblems:Part-to-WholeComparisons

13&14 SolvingPercentProblems:PercentofChange 3days

15SolvingSalesTax&TipsProblems:PercentofChange

(QuizoverLessons11-14)3days

16 SolvingMarkup&DiscountProblems:PercentofChange

17 SolvingMultistepPercentageAdjustmentProblems

3days

18 SolvingSimpleInterestProblems

19Review:IdentifyingandCategorizingProblemtypes

(Ratio,Proportion,andPercent)1day

20 Unit2Review 1day

21 Units1&2Review 1day

Total 29daysNote.Scheduleisbasedon45-60minuteclassperiod.

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GuidetoTeacherMaterials

Foreachlessonintheteacherguide,therearecorrespondingmaterialstosupportinstruction.

TeacherGuide:Thisincludesscriptedmaterialsforteachingeachlesson.Thescriptsarenot intended to be read verbatim, but rather to be reviewed and to guide you indevelopingstudents’proportionalreasoningusingthespecifiedexamplesandproblemsolving activities. Worked answers for the Practice Problems for each lesson areincludedattheendofthecorrespondinglesson.

Lessonsmayalsoincludethefollowing:

• Detailedinstructionsorprocedures(e.g.,Think-Plan-Share)• DISCchecklists• JeopardyPowerPoint(Lesson19)

Therearequizzesandquizanswerkeysinthefollowinglessons:

• Lesson5• Lesson9• Lesson15

CorrespondingMaterials:

• StudentWorkbook:This includesblankcopiesofallproblems included intheTeacherGuide.Thisbookalsoincludesareferenceguideforsolvingeachproblemtype,locatedthroughout the corresponding lessons. ADISC checklist is included at the endof thebookforstudentstorefertowhensolvingproblems.

• Student Homework Book: This includes blank copies of all problems included in theTeacherHomeworkAnswerKey. Thisbookalso includesareferenceguideforsolvingeachproblemtype,locatedattheendofthebook.ADISCchecklist is includedattheendofthebookforstudentstorefertowhensolvingproblems.

• Teacher Homework Answer Key: These are the answers (with explanations) for thestudenthomeworkbook.Thefirstpageofeachlessoninthisbookletisanabbreviatedanswerkeywithonlytheanswers.

SAMPLE

TeacherGuide:Ratios—Lesson1 Page1


Lesson1:RatiosLessonObjectivesStudents define ratio as a multiplicative relationship. They identify the base quantity for comparison of

quantitiesinvolvingpart-to-partandpart-to-whole.

Vocabulary:Comparedquantity,basequantity,frontterm,backterm,ratio,valueoftheratio,part-to-part

ratio,part-to-wholeratio

CCSSM:6.RP.A.1,6.RP.A.3,7.NS.A.2,7.NS.A.2.B,7.RP.A.2,7.RP.A.2.A

Introduction:• Reviewequivalentfractionsandrelatedwordproblems.

• Reviewsimplifyingfractions.

• Define ratio as a multiplicative relationship. A ratio is a comparison of any two quantities or

measures,andexpressesamultiplicativerelationshipbetweentwoquantities.

• Introducepart-to-partandpart-to-wholeratios.

Example1.6:Discussratiosandallowforstudentthinking.• Comparetheheightofthetwotreesbyexaminingcomparedquantityandbasequantity.

Example1.7:Studentsworkontasksindividuallyandthenasaclasstodiscoverthemeaningofratios.

Usingtheteacherandstudentdeskpictures,studentswill:

• Representtherelationshipbetweenthetwoquantitiesasaratio.

• Writethevalueoftheratio.

• Labelthefrontandbackterms.

• Describetherelationshipbetweenthetwoquantities.

Example1.8:Usediagramstorepresenttheratios.

• ComparethenumberofbrowniesLisaandTimbought.

• AskstudentshowmanytimesthenumberofbrowniesLisaboughtistothenumberofbrownies

Timboughtandviceversa.

Example1.9:Usethink-aloudtomodelsolvingtheproblem.

• ComparetherelationshipbetweenRyanandSteve’sheights.

Example1.10:Explainthemeaningofratiosinwords.

• Discusssurveyresultsof7thgraders’favoritedrink(Oranginavs.Sprite).

• Findtheratioandthevalueofeachratio,andsaywhattheratiomeansusingwordsandnumbers.

• Checktomakesurestudentsunderstandthemeaningofratiosandratiovalues.

ChallengeProblems(optional):

Challenge Problem 1.11: Have students write two ratios comparing the time that Lucinda spent on

homeworkonMondaytothetimeshedidhomeworkonWednesday.

Lesson1Overview

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• Remindstudentstoconvertthetwodifferentunitsoftime(minutesandhours)toacommon

unitoftime.

ChallengeProblem1.12:HavestudentssolveforStacy’sweightonthemoon.

• Remindstudentstoconsiderhowthetworatios/ratesaresimilar(astronaut:174lbsonEarth

29lbsonthemoon;

Stacy:102lbsonEarthxlbsonthemoon

)

Lesson1:Ratios

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Teacher: 1.1 Circletheequivalentfractions(thereare3equivalentfractionsineachset):

12

510

715612

392861813

1.2 Indicatewhethereachpairoffractionsisequivalentornot(YesorNo):

!

35,!

1220 (YesorNo)

2540,3045

(YesorNo)

1.3 Completetheequivalentfractionbyfillinginthemissingpart:

12= 3

17=21

4 = 5

25

1.4 Simplifyeachfraction:

1215

= 2244

=614

= 1035

= 927

=

FractionWordProblem:

1.5 Aclassishavingapizzapartyandtheyordered2pizzasfromdifferentrestaurants.Theclass

ate56 ofthepizzafromDon’sPizzeriaand

912 ofthepizzafromPerfectPizza.Didtheyeat

thesameamountofpizzafromeachrestaurant?Explainyourreasoning.

Warm-Up/ReviewofEquivalentFractions

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RatioasaMultiplicativeRelationship

Teacher: Todaywewilllearntocomparequantities.

(DisplayExample1.6)

Example1.6

Therearetwotreesinthispicture.Oneis6feettallandtheotheris2feettall.Therearemany

waysthatyoumightcomparetheheightsofthesetwotrees.Cansomeonetellmeonewaythat

youcancomparethesetwoquantities?

Discussion points:Give students a fewmoments to think about this question by themselves

and/ortochatwithapersonnearby.Walkabouttheroomtoidentifystudentswhodiscussedthe

additiverelationshipbetweenthetwoquantities.Callononeofthesestudentsfirsttopresent

theirresponsefollowedbyresponsesthatfocusedonthemultiplicativerelationship.Notethat

eventhoughbothadditiveandmultiplicativeresponseswillcomeupandbediscussed,optimally

theemphasisshouldbemoreonthemultiplicativeresponses.

TeachingtheLesson

6ft.tree 2ft.tree

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Possiblestudentresponse Teachernotes Teacherresponse

The6-fttreeis4feet

tallerthanthe2-ft

tree.

OR

6ftminus2ftis4

feet.

Thisresponse

focusesonthe

additiverelationshipbetweenthetwo

quantities.

Excellent!Soone/anotherwaywecanrepresenttherelationship

betweenthetwotreesisasfollows(writeonboard):The6-fttreeis4feettallerthanthe2-fttree.Thistellsushowmuchtallerthe

6-ft tree (compared quantity) is than the 2-ft tree (basequantity). This relationshipdescribes thedifference (6 -2=4)betweenthetwoquantities,andthedifferenceisthenumberof

feetyouwouldaddtothe2-fttreetoreachtheheightofthe6-

fttree.

Imeasuredthetrees,

andthe6-fttreeis

threetimestheheight

ofthe2-fttree.

OR

6ftdividedby2ftis3.

Theseresponses

focusonthe

multiplicative

relationship

betweenthetwo

quantities.

Studentsmay

respond3:6or6:3.

Eitherresponseis

correct.

Great! So one/anotherwaywe can represent the relationship

betweenthetwotreesisasfollows(writeonboard):The6-fttree

(compared quantity) is 3 times taller than the 2-ft tree (basequantity). This relationship describes a multiplicative

relationship (3 times) between the two quantities. We can

representtherelationshipbetweenthetwoquantitiesasaratio.

Aratio isacomparisonofany twoquantitiesormeasures.Aratio expresses a multiplicative relationship between twoquantities in a single situation. For example, in the situation

involvingthesetwotrees,theratiowouldbe6by2,or6:2(i.e.,sixtotwo).Theresultofdividing6by2(6÷2),3(quotient),is

calledthevalueoftheratio6:2,where6iscalledthefrontterm(comparedquantity)oftheratioand2iscalledthebackterm(basequantity)oftheratio.Thisideaisthesameassaying“6is

3timesasmanyas2.”Inotherwords,thevalueoftheratio6:2

describes themultiplicative relationship between the 6-ft tree

(comparedquantity)andthe2-fttree(basequantity).

Teacher: Ihaveintroducedsomenewwordstodescribecomparisonsbetweenquantities.Let’sdoanother

exampletopracticeusingthesewords.

SAMPLE



(DisplayExample1.7)

Example1.7

Hereisapictureoftwodesks.Whenyoumeasurethesepicturesoftheteacherandstudent

desksinpaperclips,theteacherdeskis4paperclipslongandthestudentdeskis1paperclip

long.

Teacher: Iwantyoutolookatthepictures(pointtopictures)oftheteacherandstudentdesksanddothe

following (point to statements on the teaching transparency): (1) Represent the relationshipbetween the length of the two desks as a ratio (i.e., a comparison that expresses amultiplicativerelationshipbetweenthetwoquantitiesormeasures),(2)writethevalueoftheratio,(3)labelthefrontterm(comparedquantity)andthebackterm(basequantity),and(4)describetherelationshipbetweenthetwoquantitiesinwords.

(Give studentsa fewminutes tocomplete these4 tasks, individually. If studentsare sitting in

groups,considergivingthegroupstimetogoovertheiranswersbeforeyougooverthesewith

theclass.Reinforcethataratiovalueisthevaluefoundwhenyoudividethefronttermbythe

backterm).


Representthetwoquantitiesasaratio. 4:1 Eitherresponseis

correct;however,the

ratiosrepresent

different

comparisons,sothe

ratiosarenot“the

same.”Ifstudents

askwhytheyare

different,atthis

point,simplyrespond

thattheyare

differentbecause

theyhavedifferent

frontandbackterms.

Verygood!Thisratiousesamultiplicativerelationship(4:1)

tocomparethelengthoftheteacher’sdesktothelengthof

thestudent’sdesk.

1:4 Great - you thought of a different ratio, 1:4. This ratio is

different,becauseitinvolvesamultiplicativecomparisonof

the length of the student’s desk to the length of the

teacher’sdesk.Bothratiosof4:1and1:4correctlydescribe

thissinglesituationinvolvingthelengthsofthesetwodesks

usingamultiplicativerelationship.

SAMPLE




Writethevalueoftheratio.

4÷1=4

Eitherresponseis

correct;however,

becausetheyare

differentratios,they

alsohavedifferent

ratiovalues.The

differentratiovalues

provideinformation

aboutthe

relationshipbetween

thelengthsofthe

twodesks.

Reinforcethataratio

valueisthevalue

foundwhenyou

dividethefrontterm

bythebackterm.

Perfect!Tofindthevalueoftheratioyoudividethefront

termbythebackterm.

1÷4= 14 or0.25

Wonderful!Youdividedthefronttermbythebacktermto

get the ratiovalueof 14 or0.25.Because the ratio4:1 is

different than the ratio 1:4, you also found that theseratioshavedifferentratiovalues.Intheratio4:1,theratiovalueof4 tellsyou that the teacher’sdesk is4 timesaslongasthestudent’sdesk.Intheratio1:4,theratiovaluetells you that the student’s desk is

14 the size of the

teacher’sdesk.

Labelthefrontterm(comparedquantity)andthebackterm(basequantity).

4isthefrontterm

(comparedquantity)and

1isthebackterm(base

quantity).

Yes! For the ratio 4:1, 4 is the front term (compared

quantity)and1isthebackterm(basequantity).

1isthefrontterm

(comparedquantity)and

4isthebackterm(base

quantity).

Youaredoingagreatjob!Yes,fortheratio1:4,1isthefront

term (compared quantity) and 4 is the back term (base

quantity).

Describetherelationshipbetweenthetwoquantitiesinwords. Theratioofthelength

oftheteacher’sdeskto

thelengthofthe

student’sdeskis4:1.

Allresponsesare

correct;however,the

wordingoftheratios

emphasizesthatthe

orderofthenumbers

intheratioisvery

importantanda

differentorderwill

communicate

differentinformation

aboutthe

Excellent!Thiswordingemphasizeswhichdesklengthisthe

compared quantity (i.e., teacher’s desk) and which desk

lengthisthebasequantity(i.e.,student’sdesk).

Thelengthofthe

teacher’sdeskis4times

longerthanthelength

ofthestudent’sdesk.

Way to go! This wording describes the multiplicative

relationship between the lengths of the two desks, and

indicateshowmuch longer the teacher’sdesk (compared

quantity)isthanthestudent’sdesk(basequantity)forthese

twospecificdesks.

SAMPLE



Theratioofthelength

ofthestudent’sdeskto

thelengthofthe

teacher’sdeskis1:4.

relationshipbetween

thedesks'lengths.

Youaredoingsuchagoodjob!Thiswordingidentifiesthe

lengthofthestudent’sdeskasthecomparedquantityand

thelengthoftheteacher’sdeskasthebasequantity.

Thestudent’sdeskis 14

thelengthofthe

teacher’sdesk.

Wonderful! With this wording, you are highlighting the

multiplicativerelationshipbetweenthelengthsofthetwo

desks in this situation,which indicateshowmuchsmaller

thestudent’sdeskisthantheteacher’sdesk.

Teacher: Ratio problems describe a multiplicative relationship between two quantities in a single

situation.Forexample,youcouldfindtheratioofa12oz.(small)waterbottleanda16oz.(large)

waterbottle fromthevendingmachine,oryoucould findtheratioofthenumberofRrated

moviestothenumberofPGratedmoviesatthemovietheater.Ineachoftheseexamples,we

aretalkingaboutonesetting,thenumberofwaterbottlesinaspecificvendingmachineorthe

number of movies at a specific theater. Let’s look at another example, where we are

multiplicativelycomparingtwoquantitiesinonesituation.

TheMeaningoftheRatioValue

(DisplayExample1.8)

Example1.8

Lisaandherbrother,Tim,wenttothestoretodayandboughtsomebrownies.Lisabought8

browniesandTimbought2brownies.Answerthefollowingquestions:(1)Whatistheratioof

thenumberofLisa’sbrowniestothenumberofTim’sbrownies?(2)Thenumberofbrownies

LisaboughtishowmanytimesthenumberofbrowniesTimbought?(3)Whatistheratioofthe

numberofTim’sbrowniestothenumberofLisa’sbrownies?(4)ThenumberofbrowniesTim

boughtishowmanytimesthenumberofbrowniesLisabought?Forallsolutions,representthe

ratiorelationshipusingadiagram.

Discussionpoints:Callonstudentstosharetheirsolutionsandrepresentations.Studentsmaynot

havedifficultysolvingtheproblem,butmayencounterdifficultyrepresentingtheratios.Usethe

followingrepresentationtoaccompanythediscussionofratios8:2and2:8.

Teacher: (Write on board as you discuss the solution.) The answer to the first question is 8:2, which

represents the ratioof thenumberof Lisa’sbrownies to thenumberof Tim’sbrownies.Thesolutiontothesecondquestionis8÷2=4.Tosolvethisproblem,youneededtoidentifythebasequantity.Becauseyouareusingamultiplicativerelationship(8:2)tocomparethenumber

ofLisa’sbrowniestothenumberofTim’sbrownies,thenumberofbrowniesTimboughtisthe

basequantity(backterm).

Basequantity/backterm

Comparedquantity/frontterm

1 2 3 4

(Ratioof ,ratiovalueof4)SAMPLE



The answer to the third question is 2:8, which represents the ratio of the number of Tim’s

browniestothenumberofLisa’sbrownies.Inthissituation,youaremultiplicativelycomparing

thenumberofbrowniesTimboughttothenumberofbrowniesthatLisabought.Therefore,the

numberofLisa’sbrowniesisthebasequantity(backterm)forcomparison.Thesolutiontothe

fourthproblemis2÷8=28 =0.25.Youcanusebothfractionsanddecimalsfortheratiovalue.

Theseexamplesofdifferent ratios (8:2and2:8)arewithin thecontextofasinglesituationinvolving brownies made by Lisa and Tim and show us that a ratio is a multiplicativerelationship between two quantities. Also, notice that a ratio is a way to compare twoquantitiesusingthedivisionoperation.Therefore,theorderofthetwotermsinaparticularratioisimportant.Ifyounoticedthesolutionstothetwoquestions,itisclearthatthevalueofratio 8:2 (4) is not the same as the value of ratio 2:8 (0.25). Yet both ratio values tell usimportantinformationaboutthisspecificsituationwithLisaandTimbakingbrownies.

(DisplayExample1.9)

Example1.9

Ryan,abasketballplayer,is6fttall,andhisfriendSteve,whoisshorterthanRyan,is60inches

tall.RyansaysthattheratiobetweenhisheightandSteve’sheightis6:60.Is6:60thebestway

todescribetherelationshipbetweenRyanandSteve’sheights?

Discussionpoints:Somestudentsmayagreeandreasonthatwearecomparing6(fronttermor

comparedquantity,whichisRyan’sheight)to60(backterm,orbasequantity,whichisSteve’s

height).Model(think-aloud)howyouwouldsolvethisproblem. It is importanttomodelyourthinking(asthescriptbelowillustrates)ratherthantellstudentshowtosolvetheproblem.Also,modelthinkingthatmaynotbecorrectandthatwillrequireadjustingthestrategy,asisdone below. In this situation, show students the importance of forming a more meaningful

relationshipbyfocusingontheunitswhencomparingtwoquantities.

Teacher: 6:60isoneratiothatexpressesamultiplicativerelationshipbetweenSteve’sandRyan’sheights.

Iknowthataratiocomparestwoquantities,whereonequantityisthecomparedquantityand

theotheristhebasequantity.Inthisproblem,6isthecomparedquantityand60isthebasequantity,becausewearecomparingRyan’sheighttoSteve’sheight.Icanalsorepresentthissameratioas!

660 .Theresultof6÷60is!

110 or0.1.Thatis,Ryanis0.1timesastallasSteve.This

doesnotseemtomakesensetome,becauseweknowthatRyanistallerthanhisfriendSteve.I

know that I correctly used the base quantity for comparison. Letme read the problem and

underlineRyan’sandSteve’sheights.Ryan,abasketballplayer,is6fttall,andhisfriendSteveis

60 inches tall. It looks like thatweare comparing feet to inches. I think itwouldhelp ifwe

comparedthetwoheightsusingthesamemeasure(i.e.,feetorinches).WhatcanIdo?

ThisproblemgivesRyan’sheightinfeetandSteve’sheightininches.Onewaytomakeabetterratiowouldbe to convertbothheights to inches.Since thereare12 inches ina foot, I canconvert6feet(Ryan’sheight)toinchesbymultiplyinghowtallheisinfeetby12.So6times

12 is72, soRyan is72 inches tall.Sotheratiousingbothheights in incheswouldbe72:60.

(Ratioof ,ratiovalueof0.25)Comparedquantity/frontterm

Basequantity/backterm

SAMPLE



Alternatively, I canwrite a better ratio by converting both heights to feet. Ryan’s height isalreadyinfeet,soIjustneedtoconvertSteve’sheight.Steveis60inchestall,soIdivide60by12toconverttofeet.60dividedby12is5,soSteveis5feettall.Sotheratioin feet of Ryan’sheighttoSteve’sheightis6:5.(Ifthequestionarisesastowhetherthesetworatios,withbothquantities in feetorbothquantities in inches,are thesameaseachotheror thesameas the

original6:60ratio,saythatthetopicofwhatmakesoneratiothesameasanotherwillbetalked

aboutinthenextlesson.Butthepointhereisthatmanydifferentratioscanbewrittenforthe

samesituation,andeachoftheseratiostellsussomethingaboutthemultiplicativerelationships

thatarepresentinthegivenquantities.)

Justtomakesurethatweareallonthesamepage,let'sreturntothesituationinvolvingTimand

Lisa’sbrowniesandtrytowriteasmanyratiosaswecanthatdescribethissituation.Remember

thatTimhad2browniesandLisahad8brownies.Howmanybrowniesdotheyhavealtogether?

(10)Nowgivemeexamplesofdifferentratiosthatdescribethissituation.

Students: TheratioofthenumberofTim’sbrowniestothenumberofLisa’sbrowniesis2:8.Andtheratioofthenumberof

Lisa’sbrowniestothenumberofTim’sbrowniesis8:2.

Teacher: Whatotherratioscanyoucomeupwithinthissituation?

Students: TheratioofthenumberofTim’sbrowniestothetotalnumberofbrowniesis2:10.Andtheratioofthenumberof

Lisa’sbrowniestothetotalnumberofbrowniesis8:10.

Teacher: Aswe'lltalkaboutsoon,notalloftheseratiosareequivalent;2:10isnotequalto8:2isnotequal

to2:8.Yetalloftheseratiostellus informationabouttherelationshipbetweenthebrownies

thatLisahadandthebrowniesthatTimhad.Let'skeepexploringthisveryimportantideawith

anotherexample.

SAMPLE



(DisplayExample1.10)

Example1.10

Inasurveyof50seventhgraders,10choseOranginaastheirfavoritedrinkand40choseSprite

astheirfavoritedrink.Findthefollowingratiosandthevalueofeachratio,andthensaywhat

theratiomeansusingwordsandnumbers.

(1) Thenumberof7thgraderswhochoseSpritetothenumberof7

thgraderswhochoseOrangina

(2) Thenumberof7thgraderswhochoseSpritetothetotalnumberof7

thgraders

(3) Thenumberof7thgraderswhochoseOranginatothenumberof7

thgraderswhochoseSprite

(4) Thenumberof7thgraderswhochoseOranginatothetotalnumberof7

thgraders

(Note:Requiringstudentsto“saywhattheratiomeansusingwordsandnumbers”willnotbe

initially clear to them, so you may have to rephrase as follows: “quantity 1 is -- times as

large/smallasquantity2.”)


Thenumberof7thgraderswhochoseSpritetothenumberof7thgraderswhochoseOrangina(ratio,ratiovalue,andmeaninginwords)

Ratio:40:10Value:40÷10=4Meaning:The40studentswhochose

Spriteis4timesaslarge

asthe10studentswho

choseOrangina.

Emphasizethatthisratioisa

multiplicativecomparisonof

twopartsoftheseventh

gradepopulation–the40

studentswhochoseSprite

andthe10studentswho

choseOrangina.Thisiscalledapart-to-partcomparison,becauseitcomparespartofaset(the

numberofstudentswho

choseSprite)toanotherpart

(thenumberofstudentswho

choseOrangina)ofthesame

set(thetotalofallseventh-

gradestudentswhowere

surveyed).

Yes,thisratiodescribestwogroupsofstudents:40

seventhgraderswhochoseSpritecomparedto10

seventh graders who chose Orangina. The ratiovalue of 4 tells us that the number of seventhgraders(comparedquantity)whochoseSpriteis4 times the number of students who choseOrangina(basequantity).

Ratio:10:40

Value:10÷40=14 or

0.25

Meaning:The10studentswhochose

Oranginais14 aslarge

asthe40studentswho

choseSprite.

This is actually the answer to question #3. In

question #1 we are comparing the number of

students who chose Sprite (the front

term/compared quantity) to the number of

studentswhochoseOrangina(thebackterm/base

quantity).Remember,whenyousetupyourratio,

youhavetohavethecorrectfrontandbackterms.

Ifnot,theratiovaluewillnotbecorrect.Let’sthink

aboutthisratiovalue--doesitmakesensethatthe

40 students who chose Sprite is 14 of the 10

studentswhochooseOranginawhen40isgreater

than10?No,sotheratiovalueof 14 doesnotmake

sense.

SAMPLE




Thenumberof7thgraderswhochoseSpritetothetotalnumberof7thgraders(ratio,ratiovalue,andmeaninginwords)

Ratio:40:50Value:40÷50=!

45 or0.8

Meaning:The40studentswhochoseSpriteis!

45 as

largeasthe50students

surveyed

Emphasizethatthisratiois

amultiplicativecomparison

ofapartoftheseventh-

gradepopulation(students

whochoseSprite)toalloftheseventhgraders

surveyed.Thisiscalledapart-to-wholecomparison,becauseitcomparespartof

aset(thenumberof

studentswhochoseSprite)

tothewholeset(allofthe

seventhgraderssurveyed).

That’s right! We are using a multiplicative

relationship (40:50) to compare the number of

seventhgraderswhochoseSprite(thefrontterm

orcomparedquantity)toalloftheseventhgraders

surveyed (the back term or base quantity). Thisratiovalueof!

45 or0.8tellsusthatthenumberof

seventhgraderswhochoseSprite is !45 thetotal

numberofseventhgraderssurveyed.

Ratio:40:10,10:40Value:40÷10=4,10÷

40=!14 or0.25

With these ratios, we are still using a

multiplicative relationship to compare the two

parts of the whole group of seventh graders

surveyed (students who chose Sprite and

students who chose Orangina). The question is

asking us to compare one part of the seventh

graders(studentswhochoseSprite)toallofthe

seventhgraderssurveyed.Becausetheratiosare

not written in the correct order and/or do not

identify the correct quantities, you get a ratio

value that does not provide you with the right

informationtomakethecomparison.


54

or1.25

Thisratiousestherightnumbersbutinthewrong

order—we want to compare the students who

choseSprite(fronttermorcomparedquantity)to

the whole group of seventh graders surveyed

(backtermorbasequantity).Becausetheratios

arenotwritteninthecorrectorderand/ordonot

identify the correct quantities, you get a ratio

value that does not provide you with the right

informationtomakethecomparison.

SAMPLE



Thenumberof7thgraderswhochoseOranginatothetotalnumberof7thgraders(ratio,ratiovalue,meaninginwords)


15 or

0.2


Oranginais!15aslarge

asthe50students

surveyed.

Emphasizethatthisratio

isamultiplicative

comparisonofapartof

theseventhgrade

population(theOrangina-

choosingstudents)toall

oftheseventhgraders

surveyed.Thisiscalledapart-to-wholecomparison.

Perfect! This ratio uses amultiplicative relationship to

compare a part of the seventh graders (students who

choseOrangina)tothewholegroupofseventhgraders

surveyed. The ratio value tells you that thenumberof

studentswhochoseOrangina is !15 thetotalnumberof

seventhgraderssurveyed.


Thenumberof7thgraderswhochoseOranginatothenumberof7thgraderswhochoseSprite(ratio,ratiovalue,andmeaninginwords)

Ratio:10:40

Value:10÷40=14 or

0.25


Oranginais14 as

largeasthe40

studentswhochose

Sprite.

Emphasizethatthisratio

isamultiplicative

comparisonoftwoparts

oftheseventhgrade

population–the10

studentswhochose

Oranginaandthe40

studentswhochose

Sprite.Thisiscalledapart-to-partcomparison.

Perfect!Thisratiodescribestwogroupsofstudents:10

students who chose Orangina compared to the 40

studentswhochoseSprite.Theratiovalueof14 tellsyou

that thenumberof studentswho choseOrangina is 14

timesthenumberofstudentswhochoseSprite.

Ratio:40:10Value:40÷10=4Meaning:The40studentswhochose

Spriteis4timesas

largeasthe10

studentswhochose

Orangina.

Remember,youneedtobecarefulwhenwritingtheratio

--thisratio40:10comparesthenumberofstudentswho

chose Sprite to the number of students who chose

Orangina. The correct ratio uses a multiplicativerelationship to compare the number of studentswhochoseOrangina(comparedquantity)tothenumberofstudentswhochoseSprite(basequantity).Writingthe

ratiointhewrongorderforthecomparisongivesyouthe

incorrectratiovalue.Weknowthatfewerstudentschose

Orangina than Sprite, so the ratio value of 4 times

(meaning 4 times asmany students choseOrangina as

choseSprite)doesnotmakesense.

SAMPLE




Ratio:10:40,40:10Value:40÷10=4,10

÷40=14

With these ratios, you are still using a multiplicative

relationshiptocomparethetwokindsofseventhgraders

to each other, rather than comparing one part of the

seventh graders (students who chose Orangina) to all

seventh graders surveyed. Because the ratios are not

written in thecorrectorderand/ordonot identify the

correct quantities, you get a ratio value that does not

provide you with the right information to make the

comparison.

Ratio:50:10Value:50÷10=5

This ratio asks you to use amultiplicative relationship

(50:10) to compare part of the seventh graders (those

who chose Orangina) to all of the seventh graders

surveyed. You have the correct ratio terms but in the

wrongorder.Because the ratiosarenotwritten in the

correct order and/or do not identify the correct

quantities, you get a ratio value that doesnot provide

youwiththerightinformationtomakethecomparison.

SAMPLE



(DisplayChallengeProblem1.11)

ChallengeProblem1.11:Answer

TheamountoftimeLucindaspentonhomeworkonMondaytotheamountoftimeshespenton

homeworkonWednesday:

1.Inminutes:30:20,whichisaratioof3:2(30:20isthesameas

!

3020

,sowecansimplifyitto3:2).

2.Inhours:12 :

13

Answer:3:2inminutesor12 :

13 inhours.

(DisplayChallengeProblem1.12)ChallengeProblem1.12

Anastronautwhoweighs174lbonEarthweighs29lbonthemoon.IfStacyweighs102lbon

Earth,howmuchwouldsheweighonthemoon?

ChallengeProblem1.12:Answer

Astronaut:174lbonEarth

29lbonthemoon Stacy:

102lbonEarthx lbonthemoon

174lbonEarth

29lbonthemoon = 102lbonEarth

x lbonthemoon

174 x=102 29 174x=2,958

x=17

Answer:17lb.

ChallengeProblem1.11

Lucindahasbeenthinkingabouthowmuchtimeshespentonhomeworklastweek.Sheworked

onhomeworkforahalfhouronMondayand20minutesonWednesday.Comparethetime

LucindaspentonhomeworkonMondaytothetimeshedidhomeworkonWednesday.Write

tworatiosthatcomparethesetwotimes.

Challenge(optional)

Homework:pp.1-6

SAMPLE

TeacherGuide:Review:IdentifyingandRepresentingProblemTypes—Lesson19 Page394©2016AshaK.JitendraandJonR.Star.Allrightsreserved.

Lesson19:Review:IdentifyingandRepresentingProblemTypes

LessonObjectivesStudentslearntoidentifyandcategorizewordproblemsintoappropriateproblemtypes(e.g.ratio,proportion,percentandpercentofchange).

Vocabulary: interest, principal, simple interest, annual interest rate, balance, ratio, proportion, percent,percentofchangeCCSSM:Standardsincludedinlessons11-18

Teacher: Yesterdaywesolvedsimpleinterestproblems.Whataresomesituationswhenweusesimpleinterest?

Students: Youmightgetsimpleinterestifyoudepositmoneyinabankoryoumightpaysimpleinterestifyougetaloan.

Teacher: Exactly!Simpleinterestistherateyouearnonyourmoneyorpayforborrowingmoney.Isthesimpleinterestrateexpressedasadecimal,fraction,orpercent?

Students: Percent.

Teacher: Right.Whorememberswhatthetermisfortheamountofmoneyyoudeposit?Students: Principal.

Teacher: Right.Whenwethinkaboutsimpleinterestproblems,rememberthatyoumaybetryingtofindtheamountthatwasfirstdepositedorborrowed,thesimpleinterestrate,theamountearnedorpaidininterest,orthefinalbalance.Let’ssolvethisproblem.

(DisplayReviewProblem19.1)

Step1:FilltheinformationgivenintheproblemontotheRatioandChangediagrams.

ReviewProblem19.1

Youdeposit$600intoacertificateofdeposit.After1yearthebalanceis$630.Findthesimpleannualinterestrate.

Review(about10minutes)

SAMPLE


Step2:Solvefirstforthe“?”(changeamount)intheChangediagram.Remember,simpleinterestisalwaysaddedtotheprincipalamount.So,circlethe“+”inthechangediagramandthinkwhatnumberyouwouldaddto$600toget$630orsubtract$630from$600.$630− $600=$30.So,$30wastheamountearnedininterestinoneyear.

Step3: Crossout the “?” for the changeamount in theChangediagramandwrite in$30 toindicatetheamountofinterestearned.Also,crossoutthe“?”forthechangeamountintheRatiodiagramandwritein$30.

Compared

Change(Simpleinterest)

$?

Base

RatioValue

Original(Principal)

$600

New(Balance)

Original(Principal)


$600 $630

$?

SAMPLE


Step4:Solvefortheinterestratefor6monthsintheRatiodiagram.

!!

$30!$600!

=x

100

600÷100=6,so30÷6=5

Teacher: Whatisthesimpleinterestrateinthisproblem?Students: 5%.

Answer: Youwouldhaveearned5%simpleinterestonyourdeposit.

UnitReview

Teacher: Inthisunit,welearnedaboutfourtypesofproblems.Whocannamethem?Students: Ratio,proportion,percent,andpercentofchange(includingsimpleinterest).

(Note:Youmaywanttowritetheseproblemtypesontheboardsothatstudentscanrefertothemasthereviewgameprogresses.Helpstudentsseethatalloftheproblemscoveredinthe

$30

New(Balance)

Original(Principal)


$600 $630

$?

$30

Compared


$?

Base

RatioValue

Original(Principal)

$600

TeachingtheLessonSAMPLE


unit fit into these basic categories. For example, if students mention problem types likecommission or prediction, point out that these are basically percent problems. If they namemarkupordiscountproblems,pointoutthatthesearepercentofchangeproblems.Tipproblemsmaybeeitherpercentorpercentofchange.)

Welldone!Today,wearegoingtoplay“Jeopardy!”topracticesortingproblemsintoeachofthesecategories.Sometimesthemostdifficultpartofsolvingawordproblemisfiguringoutwhatkind of problem you have. This is something we've been working hard on in this unit andsomethingthattheDISCchecklisthelpswith.Sowearegoingtopracticesortingwiththisreviewactivity.

(Note:TheJeopardygameisinaPowerPointformat.TheruleswillbeessentiallythesameasagenericJeopardygame.Studentsshouldplayinteams/groups/partnersforabout15-20minutes.Each group will produce a response in “Jeopardy Talk” – e.g. “What is a ratio problem?” Awhiteboardforeachgroupwouldbeideal,butnotebookorpiecesofscratchpaperwouldalsowork.Aftertheproblemisdisplayed,eachgroupwillwriteananswer indicatingwhattypeofproblemtheysee.Youcanthenaskgroupstorevealtheiranswersandawardpointsaccordingtothepoint-valueofthequestion–e.g.“Shoppingfor30points”.Groupscankeeptrackoftheirpointsoryoucanappointascorekeeperfortheclass.ItisrecommendedtoplayregularJeopardyabout15-20minutes.Thereareintentionallymoreproblemsthancanbeplayedinaclassperiod.Theobjectofthegameistohavefunreviewingandsortingtheproblemtypes,sothereissomeflexibilityinthewayyouusetheJeopardyPowerPointwithyourclass.Notethatstudentsmayberesistant tomerely sortingproblemsandnot solving them. This activity is about sorting, andsolvingpracticewillbedonelaterinthelesson,inFinalJeopardy.)

SortingGame

(SeeJeopardyPowerPoint) OurtimeisupforourroundofJeopardy.NowwewillgetreadyforourroundofFINALJEOPARDY!(Note:Thisactivityisabout15minutes.)DuringJeopardy,youdidaverygoodjobofsortingtheseproblemsintoratio,proportion,percent,andpercentofchangecategories.Whenyouworkedontheseproblemtypes,you learnedtousediagramsthathelpedyoutorepresentandsolvethem.Sometimes,youwillbeaskedtosolveproblemsbutwillnothavethesediagramsavailable.We used the diagrams to represent information in the problem and to understand therelationshipsbetweendifferentelementsintheproblems.Whenyousolveproblems,youdonothavetousetheexactdiagramsweusedinclasstosetuptheproblems.Instead,youcanuseyourowndiagramsthatareefficientinrepresentinginformationintheproblemandusefulinsolvingthedifferentproblems.ThisiswhatwearegoingtodoinFINALJEOPARDY.

RulesforFINALJEOPARDY:Firstyouwillseeaproblemanddecidetheproblemtype,justlikeyoudidinthefirstroundofJeopardy.Next,youwillworktogethertorepresenttheproblem.(Note:Statesomethingaboutcomingupwithadiagramthatisusefulandquicktodo.)Theremaybedifferentwaystoset-uptheinformationinaproblemthatyouwillsharewiththeclass.Let’slookatoneproblemtogether.

SAMPLE


(DisplayExample19.2)

Example19.2

TheratioofA’stoB’sthatSheetalreceivedonherreportcardwas3:1.IfSheetalreceived2B’s,thenhowmanyA’sdidshereceive?

Teacher: Whatistheproblemtype?Students: Itisaratioproblem?

Teacher: Howdoyousaythisin“Jeopardytalk”?Students: Whatisaratioproblem?

Teacher: Right.NowtoearnyourFINALJEOPARDYpoints,youneedtosetuptheproblemusingyourowndiagram/representationthatwouldhelpyoutosolvetheproblem,andthensolvetheproblem.

(Note:Walkthroughthisproblemwiththestudentswiththepurposeofshowingthestudentshowtosetupthisproblemwithoutateacher-directeddiagram.ItisrecommendedtoplayFinalJeopardyforabout15minutes.)

Agoodquestiontoaskyourselfis,“Whatistheproblemaskingmetosolve?”So,tellmewhatdoyouhavetosolveinthisproblem?

Students: WehavetosolveforthenumberofA’sSheetalearnedonherreportcard.

Teacher: Excellent.Workwithyourpartnertoshowhowyouwouldrepresenttheproblemandthensolveit.

(Note: Circulate among the student groups giving guidance as necessary. Theirwork shouldinclude the use of correct units to align with the appropriate quantities. The following is anexample:

!!

x !A's!2!B's!

=3A's1!B

(Ifstudentsareworkingslowlyoryouarepressedfortime,itisnotnecessarytohavestudentssolvethisandotherFinalJeopardyproblems-youcaninsteadaskthatstudentsmerelyset-uptheproblemandnotsolveit.)Aftermoststudentshaverepresentedtheproblem,callonstudentstosharetheirwork.Discusshoweachstudentexampledoesordoesnotaccurately representinformationintheproblem.Remindstudentsthattheyneedtohaveagoodunderstandingoftherelationships in the problem to solve it correctly, but that they do not need to use the exactdiagramsusedininstruction.)

SAMPLE


(DisplayFinalJeopardyproblems)

Problem19.3

AnofficialU.S.flaghasalength-to-widthratioof19:10.TheU.S.flagsatMarthaWashingtonElementary School measure 380 ft. by 210 ft. Are the U.S. flags at Martha WashingtonElementarySchoolofficialU.S.flags?

Problem19.3:Answer

Problemtype:Whatisaratioproblem?

Possiblestudentrepresentation:

!

19!10!

= ? ! ≠380210

Answer:No.

Problem19.4

Jihoonearns10%moreremovingsnowforpeopleinhisneighborhoodthanSamearnsinhisneighborhood.IfSamearns$20foreachdrivewayheclearsofsnow,howmuchdoesJihoonearn?

Problem19.4:Answer

Problemtype:Whatisapercentofchangeproblem?


!

$?$20

! = !10!100!

$20+$?=$x(i.e.,total$Jihoonearnsforeachdrivewayheclearsofsnow)

Answer:$22perdriveway.

Problem19.5:Answer

Problemtype:Whatisaproportionproblem?


=Model 4 1:Table 36 9

Answer:1:9.

Problem19.5

AcarpentermakesminiaturereplicasofthefurnitureintheWhiteHouse.Thescalemodelofatablethathemadeis4incheslong.Thefull-sizetableis36incheslong.Whatisthemodel’sscale? SAMPLE


Problem19.6

Angiewent shopping for a new comforter for her bed. She found an entire set of bedding(sheets,pillowcasesandcomforter)onsalefor40%off.Theoriginalpricewas$120.Whatisthesalepriceofthebedding?

Problem19.6:Answer

Problemtype:Whatisapercentofchangeproblem?


!

? !120!

=40100

120-?=$x

Answer:$72.

pp.22-30If students did not complete solving any of the problems that they represented during FinalJeopardyusingtheirowndiagramsinclass,havethemsolvethoseproblemsforhomework.

.

Homework:pp.175-184

SAMPLE

TeacherGuide:JeopardyDirections–Lesson19 Page401©2016AshaK.JitendraandJonR.Star.Allrightsreserved.

JeopardySortingGame

DirectionsforUsingthePowerPoint

RegularJeopardy1. OpenJeopardySortingGameinPowerPoint.

2. Clickslideshowtab.3. ClickFromStartIcon.

4. Clickthescreentobegin. 5.Clickondesiredpointvalue.

6. Afterstudent(orteam)hasresponded,clickthescreentorevealthecorrectansweronthenextslide.

7. Toreturntocategoryselection,clickthescreenwiththecorrectanswer.ThePowerPointwillautomaticallyreturntotheCategoryscreen.

8. Clickondesiredpointvaluefornextproblem.Repeatsteps5-7tocompletetheRegularJeopardygame.

©2014&Regents&of&the&University&of&Minnesota.&All&rights&reserved.&&&

SPORTS SCHOOL SHOPPING FOOD / COOKING ENTERTAINMENT MISC.

10 Points 10 Points 10 Points 10 Points 10 Points 10 Points





Rosie played 3 games of tennis

and 1 round of golf. Compare the

games of tennis she played to the

rounds of golf.

WHAT TYPE OF PROBLEM IS THIS?!

SAMPLE

TeacherGuide:JeopardyDirections–Lesson19 Page402©2016AshaK.JitendraandJonR.Star.Allrightsreserved.

FinalJeopardyAfterallquestionshavebeenanswered,ortimehasrunout,proceedtoFinalJeopardy:1. Clickonthewords“FinalJeopardy”onthebottomofthecategoryselectionscreen:

2. AllowthestudentstochoosefromoneofthefourfinalJeopardychoices.Clickonthechoiceselected(e.g.,clickthewords“Choice2”).

ThiswillrevealthefinalJeopardyquestion.Clickthescreentorevealtheanswer.Clickingontheanswerscreenwillbringyoubacktothetitlescreen.

3.ToendJeopardyGame,presstheescapebuttononkeyboard.

SPORTS SCHOOL SHOPPING FOOD / COOKING ENTERTAINMENT MISC.






Choice 2 Choice 3 Choice 4 Choice 1

SAMPLE

Jeop

ardy

Answers

Teache

rGuide

:Jeop

ardyAnswers–

Lesson

19

Page403

©201

6Asha

K.Jite

ndraand

JonR.Star.Allrightsreserved.

SPORT

SSCHO

OL

SHOPP

ING

FOOD/

COOKING

EN

TERT

AINM

ENT

MISC.

10POINTS

Rosie

played3gamesof

tenn

isan

d1roun

dofgolf.

Compa

reth

egamesof

tenn

issheplayed

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eroun

dsofg

olf.

Terren

cestud

iedfor3

0minutesand

relaxed

for1

0minutes.

Compa

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eTerren

cestud

iedtoth

etim

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Saman

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tshop

ping

and

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shirtsa

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socks.Co

mpa

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enu

mbe

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pairsofsocks.

Dominick

wan

tsto

ha

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ughwingsso

eachboyca

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.Th

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boys

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Howm

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wingssh

ouldDom

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bring?

Theirtick

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re$60

each,and

thereisa2%

surcha

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eticketb

roker.Wha

tis

thetotalcostforone

ticket?

Hehasearne

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per

hour.Thisy

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received

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increaseinhispa

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Howm

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3:1

3:1

3:5

66wings

$61.20

$7

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20POINTS

Shaylausuallyplays3

gamesoften

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roun

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wee

kend

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gamesoften

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Eachclassroo

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ol

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3stud

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Thebillwith

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service

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30POINTS

Thefirstlapofanau

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raceis100

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%ofthe

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Afund

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Denver?

Scotta

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.Wha

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Maintaining

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Prob

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47

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37.5minutes

SAMPLE

Jeop

ardy

Answers

Teache

rGuide

:Jeop

ardyAnswers–

Lesson

19

Page404

©201

6Asha

K.Jite

ndraand

JonR.Star.Allrightsreserved.

SPORT

SSCHO

OL

SHOPP

ING

FOOD/

COOKING

EN

TERT

AINM

ENT

MISC.

40POINTS

Mike’sb

asketballteam

won

87%

ofthe

gam

es

theyplayedoverth

epa

st

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s.Iftheyplayed

58gam

es,h

owm

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eywin?

Thecheerle

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50POINTS

LastyearV

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increased13

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hatis

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Aaronreceived

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Wha

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Howm

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iceKrispies

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Compa

reth

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ofm

arshmallowsto

RiceKrispies.

Inhiscollection,Ben

ha

s5actionDV

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revery2musica

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nha

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nDV

Ds,h

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any

musica

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FINALJEOPARDY

Anofficia

lU.S.flagha

saleng

th-to

-widthra

tioof1

9:10

.Th

eU.S.flags

atM

arthaWashing

tonElem

entary

Scho

olm

easure380

ftby21

0ft.A

re

thefla

gsatM

arthaWashing

ton

Elem

entaryofficia

lU.S.flags?

Jihoo

nearns1

0%m

oreremoving

snow

forp

eopleinhisne

ighb

orho

od

than

Sam

earns.IfSam

earns$20

for

eachdriv

ewayhecle

arso

fsno

w,

howm

uchdo

esJiho

onearn?

Acarpen

term

akesm

iniaturere

plica

softh

efurnitu

reinth

ewhitehou

se.

Thescalemod

elofa

tablethathe

mad

eis4incheslong

.The

full-siz

etableis36

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SAMPLE

©2016AshaK.JitendraandJonR.Star.Allrightsreserved. DISCRatio,Proportion,andPercentChecklist–Page405

RATIO,PROPORTION,andPERCENTPROBLEMCHECKLISTS

Step1:Discovertheproblemtype

§ Readandretelltheproblemtounderstandit.§ Askiftheproblemisa…

RATIOPROBLEM

PROPORTIONPROBLEM

PERCENT,PERCENTOFCHANGE,or

SIMPLEINTERESTPROBLEM

Does this problem have a part-to-part orpart-to-whole comparison? Look forsymbols, words, and phrases such as: “theratioofatob,”“a:b,”“aperb,”“aforb,”“aforeveryb,”“foreverybtherearea,”“ntimesasmany/muchas,”“nthof,”“aoutofb,” to see whether there is a ratiostatement that tells about a multiplicativerelationship between two quantities in asinglesituation.

Does the problem describe an “If…Then”statement of equality between tworatios/rates that allows us to think aboutthewaysthattwosituationsarethesame?That is, the If statement describes arate/ratio between two quantities in onesituationand theThen statement involveseither an increase or decrease in the twoquantities in another situation, but withthesameratio.

Lookforsymbolsorwordssuchas“%,”“percent,” “percent of change,” or“simple interest,” to see whetherthere is a percent or percent ofchange statement that tells about amultiplicative relationship betweentwoquantities.

§ Askifthisproblemisdifferentfromorsimilartoanotherproblemthathasalreadybeensolved.

Step2:Identifyinformationintheproblemtorepresentinadiagram(s)

§ Underlinethe…

ratioorcomparisonstatement. twoquantitiesthatformaspecificratio/rate.

percentorsimpleintereststatement.

§ Write…

➔ compared and base quantities and unitsinthediagram.

➔ value of the ratio between the twoquantitiesinthediagram(ratiovalue).

➔ “x” forwhatmustbesolved.

➔ names of the two quantities thatformaratiointhediagram.

➔ quantitiesandunitsforeachofthetworatios/ratesinthediagram.

➔ “x” for what must besolved.

➔ information (part, whole, or ratiovalue; change, original, ratio value,or new) in the problem in thediagram(s).

➔ “x”forwhatmustbesolved.

Step3:Solvetheproblem

§ Trytocomeupwithanestimatefortheanswer.§ Translatetheinformationinthediagramintoamathequation.§ Planhowtosolvethemathequation.

§ Solvethemathequation,andwritethecompleteanswer.

Step4:Checkthesolution

§ LookbacktoseeiftheestimateinStep3isclosetotheexactanswer.§ Checktoseeiftheanswermakessense.

a:b If…Then %

DISC

If ThenSAMPLE

Documents

SAMPLE - dibels.uoregon.edu• Review equivalent fractions and related word problems. • Review simplifying fractions. • Define ratio as a multiplicative relationship. A ratio is