Download Lesson plan 10 Proportional reasoning

ReflectionsonPractice
LessonPlanfor[SecondYear,Proportionalreasoning]
Forthelessonon[25/03/2015]
At[St.Mary’sAcademy,Carlow],[Mr.O’Leary’s]class
Teacher:[Mr.O’Leary]
Lessonplandevelopedby:[CathyCradock,CaitrionaCronin,RobO’Leary]
1. TitleoftheLesson:Ratio and proportion - giving students an intuitive understanding through
problem-solving
2. Briefdescriptionofthelesson:Wewantstudentstounderstandproblemswhichinvolve
proportionalreasoning.Wewantstudentstolearnmethodsforsolvingsuchproblems
themselves.Aspartofthisprocesswewantstudentstorecognizetheconceptofcalculatingaunit
quantityandhowthisunderstandingcanbeappliedtomanydifferenttypesofproblems
includingpercentages.Thelessonisonehourinduration.
3. AimsoftheLesson:
Long‐range/thematicgoals:
I’dlikemystudentstodevelopapositivedispositiontowardsmathematics.
I’dlikemystudentstolearntobecomeeffectiveproblemsolvers.
I’dlikemystudentstobemoreindependentlearners.
I’dlikemystudentstoworkeffectivelyingroupsandtobecomfortableexplainingtheirideastoother
students.
I’dlikemystudentstorecognizethattheycandoalotofmathematicsthemselves.
I’dlikemystudentstounderstandtheimportanceoftheirthinkingprocessasopposedtobeingreally
focusedonananswer.
I’dlikemystudentstoenjoytheirmathematics.
I’dlikemystudentstodevelopanattitudeofperseverancetowardstheirmathematics.
Short‐termgoals
I’dlikemystudentstoapplyproportionalreasoning.
I’dlikemystudentstorecognisethattherearedifferentwaysinwhichtotackleproblemsbasedon
proportionalreasoning.
I’dlikemystudentstorecognisetheimportanceofunitquantityinsolvingproportionalproblems.
I’dlikemystudentstounderstandhowtheoperationsofmultiplicationanddivisionfitinto
proportionalreasoning.
I’dlikemystudentstorecogniseproblemsinvolvingpercentagesgreaterthan100%.
4.LearningOutcomes
Asaresultofstudyingthistopicstudentswillbeableto:
 Understandtheconceptofproportionalreasoning
 Solveproblemswhengiventhecostofonequantityandaskedforthecostofadifferent
quantity.
 Relatetheprocessofdivisiontofindingthecostofaunit.
 Relatetheoperationofmultiplicationtofindingthecostofseveralunits.
 Selectsuitablestrategiesforsolvingproblemsrelatingtoproportionalreasoning.
 Applyproportionalreasoningtoproblemsbasedaroundpercentages.
4. BackgroundandRationale
Manystudentsexperiencedifficultyinunderstandingtheconceptswhichunderlieproblems
associatedwithproportionalreasoning.Proportionalreasoningisacoreskillinmathematicsandis
usefulinallbranchesofmathematics.Atsecondlevelstudentsencounterproportionalreasoningall
thetime,infractions,inpercentages,inspeed,inareaandvolumeandmanymoresituations.
Hereisasimpleexampleofaproportional‐reasoningproblem:Thepriceofaticketis€88which
includesa10%bookingfee.Whatisthecostoftheticketalone?
Studentsoftensolvetheseproblemsbyfollowingroutine,withoutmuchunderstandingofwhythey’re
doingwhatthey’redoing.Accordinglywhentheyencountersuchproblemsindifferentsituationsthey
havelimitedabilitytodealwiththem.Wethinkthatbypresentingproportional‐reasoningproblems
inasimplebutspecificwaywecanletstudentsfigureouthowsolvesuchproblemsandthatby
makingsomeimportantconnectionswecanshowstudentsthatthistypeofreasoningisimportantin
lotsofdifferentcontexts.Thehopeisthatbydoingsostudentswillunderstandandretaintheskillfor
longer,theywillseethattheycandomathsthemselvesandtheywillbeexposedtotheideathata
singleapproachcanbeusedinmanydifferentsituations.
5. Research
TheJuniorCert.mathssyllabusmakesspecificreferencetoproblemsbasedonratioand
proportionality:
Havingexaminedanumberoftextbookswefeelthatnosingletextdealswiththissyllabuslearning
outcomeinawaythatpromotesdeepunderstandingoftheconcepts.
6. AbouttheUnitandtheLesson
Thelessonwillhelpstudentsrecogniseproblemsbasedonproportionalreasoningandsolvesuch
problems.
Studentswillbeintroducedtothelessonusingasimplepricingproblemandencouragedtoestimate
ananswertotheproblem.Bytheendofthelessonstudentsshouldrecognisethattheycannowdo
morethanestimatetheanswerbutthattheyunderstandhowtocalculatetheexactvalue.
Studentswillstartworkontwosimplematchingactivities.Thefirstactivityinvolvescardswith
certainmassesandprices.Usingproportionalreasoningstudentsshouldbeabletofindthemissing
priceonthedifferentcards.Thecardsaremadetodifferentsizestogivestudentsaphysicalfeelfor
theproportionalnatureoftherelationshipsinvolved.Thematchingtasksinthefirstactivityare
designedtoexposestudentstomoredifficultexamplesofproportionalrelationshipssothattheymay
gainadeeperunderstandingoftheassociatedconceptsandsothattheyarechallenged.Theaimofthe
firstmatchingactivityistogetstudentsdescribingdifferentwaystoapproachproportionalproblems
andtothenapplythenumberoperationsofdivisionandmultiplicationtosolvetheproblems.
Thesecondmatchingactivityisagainbasedaroundpairsofcards.Thistimetherelationshipsare
expressednotingramsbutinpercentages.Undertheguidanceoftheteacherstudentswillseethat
thesearejustanotherexampleofaproportionalproblem.Underthisguidanceitishopedthat
studentswillapplytheirnewly‐acquiredknowledgetosolvetheseproblems.
Finallytheclasswillrevisittheintroductoryproblemandstudentswillbegiventheopportunityto
recognisethisasyetanotherproportionalproblemandwillthengetthechancetousetheir
understandingtosolvetheproblem.
7. FlowoftheUnit:
#oflesson
periods
Lesson
Ratioandproportion
1

Distinguishbetweenabsolutecomparisonandrelative
comparison

Seeratiosascomparingparttopartandfractionsascomparing
parttowhole,wherethequantitiesbeingcomparedhavethe
sameunits.

Seeratesastheratiooftwoquantitieshavingdifferentunits.

Appreciatetheimportanceoforderwhendealingwithratios

Findequivalentratios

Divideanumberintoagivenratio

Recogniseaproportionasastatementofequivalentratios5:2=
10:4orsetupaproportiontofindxasin5:2=8:x
2

Distinguishbetweenproportionalandnon‐proportional
situationsrecognisingthemultiplicativerelationshipthatexists
betweenthequantitiesinproportionalsituationsasseenin
tables,graphsandalgebraicexpressions
3

Useavarietyoftechniquesincludingtheunitarymethod,factorof
scaleandtables,tosolveproportionaltasksandtorecognisethat
thesetechniquesareallrelated

Solveproblemsinvolvingproportionalreasoningindifferent
contexts

Howtodrawandinterpretscaleddiagrams
3x1hour
1x1hour
3x1hour
Thefirstof
whichisthe
researchlesson.
8. FlowoftheLesson
TeachingActivity
1.Introduction
Studentsarepresentedwiththefollowing
problem:Youaregivenatickettoaconcert.The
costoftheticketincludesa10%bookingfee.Ifthe
ticketcosts€88,howmuchdoestheticketcost?
Studentsareaskedtoestimateananswer.
2.PosingtheTask
Studentsarepresentedwithasimplematching
activitywhichconsistsofanumberofcardsof
differentsizeswithassociatedmasses(ingrams)
andprices.Studentsareaskedtodeterminethe
PointsofConsideration
Wewantstudentstobeengagedwiththelesson.
Wewantstudentstomakeanestimateofthe
ticketprice.
Dostudentsunderstandthattheticketprice
mustbelessthan€88?
Arestudents’guessesreasonable?
Dostudentshavearoughideaofthevalueof
10%inthiscontext?
Theteacherhandsoutthematchingactivityand
theaccompanyingworksheet.
Note:Theactivityhas10parts.Theteacher
shouldchoosewhichpartsaresuitablefortheir
costofdifferentmasses.
students.
Theteachercirculatestheroomtocheckthat
studentsareontask.
Arestudentsabletouseproportionalreasoning
tocalculatethemissingprices?
Canstudentsexplaintheirapproachto
calculatingthemissingquantities?
Dostudentsrecognizetheimportanceof
divisionforfindingthevalueofasub‐multiple?
Dostudentsrecognizetheimportanceof
multiplicationforfindingvalueofamultiple?
Canstudentsverbalisetheapplicationof
divisionandmultiplicationtosolving
proportional‐reasoningproblems?
3.AnticipatedStudentResponses
Studentsmaynotbeabletouseproportional
Itisimportantthatstudentsareencouragedto
reasoning.
explaintheirapproach.
Studentsmaybeabletoanswerthequestionsbut Itisimportantthatstudentsdon’tsimplytalk
finditdifficulttoexplaintheirthinking.
aboutmultiplicationanddivision,ratherthey
Studentsmayfindthefirstnumberofproblems
talkaboutfindingthecostofasmallerquantity
(whichinvolvedivisiononly)easytodealwithbut andusingthistofindthecostofalarger
findthelatterproblemsmoredifficult(which
quantity.
involvedivision,followedmymultiplication).
Itisimportantthatstudentsmakethe
Studentsmayfindthecostofdifferentsub‐
connectionbetweendivisionandmultiplication
multiplesandusethistoworkoutthenew
andtheprocessesinvolvedinproportional
multiple.
reasoning.
Studentsmayfindthecostofoneunitandusethis Theteacherasksstudentstoexplainwhyone
toworkoutthenewmultiple.
problemismoredifficultthatanother?
4.ComparingandDiscussing
TheteacherrepresentsproblemA1ontheboard
Wewantstudentstofocusonthereasoning
withadiagram.
behindsolvingtheproblem.
Theteacherasksstudentstoexplaintheir
Wewantstudentstoexplaintheirapproachin
approachtosolvingtheproblem.
theirownterms(asopposedtofocusingsolely
ontheoperationsofmultiplicationand
TheteacherrepresentsproblemE5ontheboard
division).
withadiagram.
Wewantstudentstodescribehowdivisionand
Theteacherasksstudentstoexplaintheir
multiplicationfitintotheprocessofdealingwith
approachtosolvingthisproblem.
proportionalreasoningproblems.
Wewantstudentstorecognizetherelevance/
TheteacherrepresentsproblemI9ontheboard
importanceoffindingthecostofoneunit.
withadiagram.
Wewantstudentstoidentifysituationswhereit
Theteacherasksstudentswhat’shardaboutthis
makessensetofindthecostofoneunit.
problemcomparedtothepreviousproblems?
Theteacherasksstudentstocommunicatetheir
ideasonhowtoapproachthisproblem.
Theteachermayaskstudentsiftheunitary
Theteachersummarisestheapproachoffinding
methodwouldhaveworkedforthefirsttwo
thecostofoneunitandthenfindingthecostofX
problemspresentedontheboard.
units,beingcarefultoexplainwhythisapproachis Dostudentsunderstandwhatproportional
neededforthisexample.Theteacheridentifiesthis reasoningmeans?
methodastheunitarymethod.
Theteacherexplainstothestudentsthatwhatthey
aredoingisknownasproportionalreasoningand
explainswhatthismeans.
5.PosingtheTask
Theteacherasksstudentsiftheythinkthatthis
typeofproblemandapproachtosolvingitonly
applytoscenariosinvolvinggramsandeuro.
Theteacherpresentsstudentswiththeirsecond
matchingactivity.Thisoneisbasedon
percentages.
Theteacherasksstudentstolookatthefirstpairof
cardsA1andthenasksthemwhattheythinkof
thisproblem.
Theteacherexplainsthatthisissimplyanother
exampleofproportionalreasoning.
TheteacherdrawsthefirstpairA1ontheboard
andasksstudentstomakeastatementaboutwhat
weknow.
Theteacherasksstudentstomakeastatement
aboutwhatwearetryingtofindout.
Theteacherasksstudentstodiscusswhatwecould
calculatewhichmightbeuseful.
Theteacherwritesdetailsofstudents’approaches
ontheboard.
Theteacherasksstudentstomakeastatement
abouthowtosolvetheproblem.
Theteacherasksstudentstoattemptaselectionof
additionalproblemsontheworksheetintheir
groups.
6.Anticipatedstudentresponses
Studentsmightn’tseethelinkbetweenthisactivity
andthepreviousone.
Studentsmightimmediatelyturnoffbecauseofa
dislike/fearofpercentages.
Studentsmighthavedifficultyverbalisingwhat
theyknowabouttheproblemandwhattheyare
beingaskedtofindout.
Studentsmaygiveseveraldifferentapproaches.
Forexampletheymightfindwhat50%isworth
andthenfindwhat100%isworth.Theymightfind
what10%isworthandthenfindwhat100%is
worth.
Studentsmightfindthepairsatthestartofthe
worksheetstraight‐forwardbutmayfindthe
othersquitedifficult.
Studentsmayhavedifficultycommunicatingtheir
approachtosolvingeachproblem.
Studentsmaytrytodivideandmultiplyinanad
hocmannerwithouttryingtounderstandwhat
theyaredoing.
7.Comparinganddiscussing
TheteachersketchespairC3ontheboard,and
asksdifferentstudentstoexplainwhattheyknow,
whattheywanttofindoutandhowtheymightgo
aboutdoingthis.
Canstudentsidentifyothersituationswhere
proportionalreasoningmayapply?
Theteacherdistributescopiesofthesecond
worksheet.
Waittimeisimportanthere.Studentsneeda
minutetomatchthecardsandthinkaboutthe
problem.
Canstudentsmakestatementsoftheform“We
knowthat150%isworth€300”?
Canstudentsmakestatementsoftheform“We
wanttoknowhowmuch100%isworth”?
Canstudentsidentifyusefulsub‐multiplesof
150%?
Canstudentssuggestsuitablestrategiesfor
tacklingthisproblem?
Canstudentsmakestatementsoftheform“50%
mustbeworth€100so100%mustbeworth
€200”?
Itisimportantthatstudentsaregiventhe
chancetorecognizethelinkbetweenthis
activityandthepreviousone.Thisshouldbe
donebygettingstudentstoverbalisewhatthey
know,whattheywanttofindoutandhowthey
mightgoaboutdoingthis.
Ifdifferentapproachesarepresenteditis
importanttoemphasisethemeritsofeach
approachandshowthattheyareequivalent.
Canstudentsverbalisetheirideas?
CanstudentsexplainwhyY102isamore‐
difficultproblem?
Theteacheremphasisesthefactthatthisisa
proportionalproblem.
TheteachersketchespairY102ontheboardand
asksstudentswhythisismoredifficultthanthe
previousexample.
Theteacherasksstudentstosuggesthowthey
couldsolvethisproblem.
Theteacherreinforcestheideaoftheunitary
methodandwhatitmeansandwhereit’suseful.
8.Posingthetask
Theteacherrevisitstheintroductorytaskandasks
studentsiftheyhaveanysuggestionsonhowthey
mightsolvethisproblem.
Theteacherrepresentsthecostoftheticketalone
asasquareontheboardandidentifiesthissquare
asrepresenting100%.Theteacheridentifiesthe
priceofthissquareaswhatwearelookingfor.
Theteacherdrawsthesamesquareagainandthis
timeaddsinanextrapiece.
Theteacherasksstudentstoidentifywhat
percentageeachpiecerepresents.
Theteacherwritesin100%onthesquareand10%
ontheextrapiece.
Theteacheraskshowmuchthis100%costsand
marksin€88onthediagram.
Theteacherasksstudentstocalculatethecostof
theticketalone.
Dostudentsunderstandtheunitarymethodand
whereitisuseful?
Itisimportanttodrawrelativelyproportional
shapes.
Theteachermayidentifythe100%squareas
thepricewearelookingfor.
Differentapproachesaretobecommendedas
theyshowthatstudentsarethinkingfor
themselves.
Theunitarymethoddoesnothavetobeused
here.Forsomestudentsitmaymakemoresense
tofindthecostof10%andusethistocalculate
thecostof100%.
Theteachershouldtrytogetstudentstopresent
differentapproaches.
Itisgoodforstudentstoreflectontheiranswer
andhowitcomparestotheirestimatefromthe
startofthelesson.
9.Anticipatedstudentresponses
Studentsmayfindithardtounderstandthatthe
finalcostoftheticketis100%oftheactualcost.
Somestudentsmayworkoutwhat10%costsand
thenscalethisupto100%.
Somestudentsmayrequiresupporttoapplythe
unitarymethodtosolvingtheproblem.
10.Comparinganddiscussing
Theteacherasksstudentstowritetheiranswers
ontheirshow‐meboardsandtoholdthemup.
Theteacherasksstudentstoexplainhowthey
tackledtheproblem.
Theteacherasksstudentstocomparetheiranswer
totheirguess.
5.Summingup
Theteacherasksstudentstoexplainwhatthey
havelearnedtoday?
Theteacherrecapsontheconceptofproportional
reasoning.
Theteacherstressesthattherearemanywaysto
solveproportionalproblemsbutthattheunitary
methodwillworkinanysituation.
Studentsareaskedtomakeuptwoproportional
problemsfortheirhomework.
9. Evaluation
Therewillbethreeobserversinthelessonaswellastheteacherteachingthelesson.
Observer1willtakepicturesofstudentwork.
Observer2willrecordstudentbehaviourusinganassessmentwheel.Thiswillincludelookingfor
evidenceofstudentscommunicatingwitheachothereffectively,studentsunderstandingthemain
conceptsofthelesson,studentsaskingquestionsofeachotherandtheteacherandthelevelof
motivation.
Observer3willrecorddetailsoftheteacher‐studentinteraction.
10. BoardPlan
11. Post‐lessonreflection
Thelessonwasverymuchasuccesswithsomeareaswhereimprovementcouldbemade.
Whatworkedwellinthelesson:
 Studentsweremotivatedtoestimateananswertotheintroductoryproblem.
 Moststudentestimateswerereasonableinthattheywerelessthanthetotalcostoftheticket.
 Moststudentsworkedwelltogetheringroups,cooperatedwitheachother,helpedeachother
anddiscussedtheirmaths.
 Moststudentsweremotivatedtotrytosolveproblems.
 Moststudentswerewillingtooffersuggestionsonhowtosolveaproblemortodescribehow
theysolvedtheproblemthemselves.









Somestudentssuggestedalternativeapproachestosolvingaproblemthantheonesuggested
byotherstudents.
Studentsusedtheirshow‐meboardswhenaskedtodisplayananswertoaproblem.
Studentsusedanappontheiripadstohelpthemdivideandmultiplyquantities.
Moststudentswereinterestedinlearningandwerecontinuouslyengagingwiththeteacherto
checktheirworkandtoaskforhelp.
Inthecomparinganddiscussingpartsofthelesson,theteachermadesuretoinvolveall
studentsinfeedbackandgavedifferentstudentstimetodescribetheirapproachtosolvingthe
problem.Wherestudentsfocusedonanswersonly,theteacherencouragedthemtodescribe
theirapproach.
Somestudentsdemonstratedexcellentabilityinproportionalreasoning.Forexamplewhen
tacklingtheproblemoffindingthecostof100ggiventhat150gcost€30onestudent
explained“Because150gisworth€30,thismeansthat50gmustbeworth€10and100g
mustbeworth€20”.Withsomeencouragementthisstudentexplainedhisthinkingtotherest
ofhisgroup.
Theteacherencouragedstudentstodescribetheoverallapproachtheywereusingfromone
questiontothenext.Thishelpedstudentssolidifywhattheywerelearning.
Somestudentsrecognizedtheimportanceofdivisionandmultiplicationtothesolvingof
proportionalproblems.
Inoneofthecomparinganddiscussingsessionsstudentswereaskediftheythoughtthis
approachtosolvingproportionalproblemswouldonlyworkformassandprice.Students
identifiedlotsofotherareaswherethismethodwouldbeuseful,includingsomeareasinother
subjectstheystudy.
Whatwewouldchangeinthelesson:
 Wetriedtodotoomuchwiththegroupofstudentsthiswastriedwith.Wefeltthatspending
moretimeontheactivityrelatingmassandpricemayhavehelpedmorestudentsdevelopa
deeperunderstandingofproportionalreasoning.Thescopeofthelessonverymuchdepends
onthestudentswhositinfrontofyou.Forsomestudentswewouldrecommendreducingthe
scopeofthelessonwhileforbetterstudentswewouldtrytocoverallthecontentpresentedin
thelessonplan.
 Atthestartofthelessonstudentsreallyfocusedontheiranswersasopposedtotheir
approach.Itisimportantthatstudentsunderstandthatadescriptionoftheirapproachisthe
mostimportantpartoftheactivity.
 Somestudentsseemedintimidatedbytheextraadultsintheroom(includingafilmcrew).This
preventedthemfromengagingproperlywiththelesson.Thisshouldn’tbeanissuewithfuture
lessons.
 Wecouldhavespentalittlemoretimeatthestartexplainingthefirstactivity.Studentsdidn’t
realisethatthecardswerespecificallycreatedwithrelativesizestohelpthemunderstandthe
proportionalnatureoftheproblem.Bytakingthefirstpairinthefirstactivityandasking
studentsiftheythoughtthemissingpricewouldbemoreorlessthantheonegiven,thisidea
couldhavebeenteasedout.
 Studentstendedtofocusonthenumberoperationswhichprovidedthemwithsolutions.For
examplewhenaskedtodescribewhattheydidsomestudentsreplied“Idividedby…and
multipliedby…”.Wereallywantstudentstodescribetheprocessineverydayterms.For
examplestatementsoftheform“IfoundthepriceofXgramsandthenIusedthistofindthe
priceof3Xgrams”wouldshowadeeperlevelofunderstanding.
 Somestudentstendedtolookforaneasysolutionasopposedtothinkingtheproblemthrough
logically.Forexample,onestudentwhoobtainedacorrectanswertoaproblemexplainedhis
methodas“knockingazerooffbothofthem”.Thishighlightsthedangerofstudents
attemptingtomovestraighttosomeformofnumberoperationwithoutunderstandingwhat
theyaredoing.




Studentstookalongtimesortingthepairsofcards.Thisreducedvaluablethinkingtime.
Perhapsthereisabetterwaytopresenttheactivities.Alternativesincludepresentingthepairs
ofcardsonasheetofpaper.Ontheflipsideitshouldbesaidthatstudentsseemedtoenjoy
matchingthecardsandthisseemedtogetthemmoreinvolvedintheactivity.
Studentsdidn’tnaturallywritedownanexplanationofhowtheysolvedeachproblem.Itis
importanttoconstantlyremindthemoftheimportanceofdoingso.
Studentsmayneedextrasupportwhenmovingfromthemass‐priceactivitytothe
percentages‐priceactivitytoletthemrecognizethattheunitarymethodmayalsobeusedhere.
Wefoundthatassoonasstudentssawpercentages,manyofthemconsideredtheproblems
muchtoohardwhereasinrealitytheywerepracticallyidenticaltothefirstactivity.
Inthecomparinganddiscussingsessionitisimportantthatstudentsareencouragedtoexplain
whytheyusedtheapproachtheyused.Thisexplanationshouldnotimmediatelyfocuson
divisionandmultiplication.
Summary:
Wefoundthelessontobesuccessfulbutwithareaswhereitmaybeimproved.Wedesignedafairly
generallessoninproportionalreasoningbutpresentedittoagroupofstudentswhooftenstruggle
withtheirmaths.Itisimportantwhenusingalessonplantoadaptitforthestudentswhositinfront
ofyouinagivenlesson.
Whilethestudentsintheclasshaddifficulties,groupworkworkedverywell.Thisshowedtousthat
groupworkisn’tjustsomethingforthebeststudentsinayeargroup.Itcanworkwellforallstudents
butonlyiftheworkisappropriatetothosestudents’level.
Itisimportantthatstudentshavesomeeverydayunderstandingofwhattheyaredoingbefore
applyingnumericaloperationstosolveaproblem.Ifstudentsfocusonproceduresandoperationstoo
soontheyarelikelytostrugglewithretainingwhattheyhavelearnedandwhensimilarproblemsare
presentedinadifferentcontexttheyarelesslikelytobeabletodealwiththem.
CARD K
100 g
€60
CARD 11
117 g
€??
CARD G
150 g
€20
CARD 7
100 g
€??
CARD H
150 g
€60
CARD 8
100 g
€??
CARD L
120 g
€90
CARD 12
109 g
€??
CARD A
1000 g
€40
CARD B
1000 g
€20
CARD C
1000 g
€60
CARD 1
500 g
€??
CARD D
1000 g
€5
CARD E
1000 g
€80
CARD F
1000 g
€25
CARD 2
500 g
€??
CARD 3
250 g
€??
CARD 4
250 g
€??
CARD 5
300 g
€??
CARD 6
300 g
€??
CARD I
250 g
€80
CARD 9
100 g
€??
CARD J
250 g
€25
CARD 10
100 g
€??
CARD 7
100 %
€??
CARD 8
100 %
€??
CARD 9
100 %
€??
CARD G
167 %
€500
CARD I
115 %
€800
CARD H
113 %
€800
CARD J
130 %
€250
CARD 10
100 %
€??
CARD K
200 %
€45
CARD 11
100 %
€??
CARD L
200 %
€70
CARD 12
100 %
€??
CARD A
150 %
€300
CARD 1
100 %
€??
CARD 5
100 %
€??
CARD B
150 %
€600
CARD 2
100 %
€??
CARD 6
100 %
€??
CARD E
120 %
€600
CARD C
250 %
€800
CARD 3
100 %
€??
CARD D
250 %
€250
CARD 4
100 %
€??
CARD F
120 %
€900
Percentages Worksheet:
Find the cost of the quantity given on the smaller card
Card Letter
A
Card Number
1
What is the question asking?
Answer:
Explanation:
Card Letter
B
Card Number
2
What is the question asking?
Answer:
Explanation:
Card Letter
C
Card Number
3
What is the question asking?
Answer:
Explanation:
Card Letter
D
What is the question asking?
Card Number
4
Answer:
Explanation:
Card Letter
E
Card Number
5
What is the question asking?
Answer:
Explanation:
Card Letter
F
Card Number
6
What is the question asking?
Answer:
Explanation:
Card Letter
G
What is the question asking?
Answer:
Card Number
7
Explanation:
Card Letter
H
Card Number
8
What is the question asking?
Answer:
Explanation:
Card Letter
I
Card Number
9
What is the question asking?
Answer:
Explanation:
Card Letter
J
What is the question asking?
Answer:
Explanation:
Card Number
10
Card Letter
K
Card Number
11
What is the question asking?
Answer:
Explanation:
Card Letter
L
What is the question asking?
Answer:
Explanation:
Card Number
12
Grams Worksheet:
Find the cost of the quantity given on the smaller card
Card Letter Card Number
A
1
What is the question asking?
Answer:
Explanation:
Card Letter
B
Card Number
2
What is the question asking?
Answer:
Explanation:
Card Letter
C
Card Number
3
What is the question asking?
Answer:
Explanation:
Card Letter
D
Card Number
4
What is the question asking?
Answer:
Explanation:
Card Letter
E
What is the question asking?
Answer:
Card Number
5
Explanation:
Card Letter
F
Card Number
6
What is the question asking?
Answer:
Explanation:
Card Letter
G
Card Number
7
What is the question asking?
Answer:
Explanation:
Card Letter
H
Card Number
8
What is the question asking?
Answer:
Explanation:
Card Letter
I
What is the question asking?
Answer:
Explanation:
Card Number
9
Card Letter
J
What is the question asking?
Answer:
Explanation:
Card Number
10