QuizQuizTradeCardsforMath
Grade5
Purpose:Togivestudentsanopportunitytoreviewmaterial,teachandexplainideas,usecritical
vocabulary,andmoveabouttheclassroomworkingonsocialskills.
Prepare:Useindexcardsorthetophalfofafullsheetofpapertocreateonequestionforeach
studentinyourclass.Theanswershouldbeonthebackofthecardoronthebottomhalfofthesheet.
Answersshouldbeclear,accurate,andstudentfriendly(showingallsteps,answerincorrectform…).
Thequestionsshould:
1. Emphasize process over computation (How would you find…? Estimate the answer… explain error)
2. Include academic verbs: explain, show, identify, indicate, (shade, select, click, drag) express, solve,
compute, calculate, evaluate, estimate, approximate, claim, reason, prove, interpret, evidence,
critique, reasoning, justify…
3. Include math related vocabulary: pattern, variable, sum, difference, product, coordinates…
4. Ask students generally about the graphic: key information given, questions likely asked, related
vocabulary…
5. Ask students to imagine or identify a common error or analyze a given type of error
6. Include multiple parts (often an easier part then a more difficult part)
7. Make students: generalize (What does area mean?); work backwards (Given the area, what is
length?); use variables (find perimeter of square with side n inches long); ask “What if?” (what if it
was hexagon); explain a pattern; explain why; explain more than one way to solve…
8. If the question uses an already formed test question from a state test, then pose a different question
that goes beyond the given question (Why is answer choice C definitely wrong? What choices can
you easily eliminate? Why is D tempting? Why is this problem tricky? What else could they have
asked? Explain how you know you are correct…)
9. Make questions easy to read, not too long, not too open-ended (it’s hard to list all the possible
solutions)
10. Include answer in a form that matches your expectations (formula is presented empty then filled in…)
11. Include an answer that might show two ways to solve the problem (one visual, one with a graph etc.)
Remember,studentsarewalkingaroundandthinkingontheirfeet.Theywon’tbeabletodocomplex
calculations.Askforestimations,approximations,howwouldyou,why,etc.(Whyis3÷¼=12?;Can
youestimatethevolume,foraprismexplainwhytheformula:areaofbasetimesheightisthesameas
(l)(w)(h)?Whatisthedifferenceinthesewordproblemsandhowarethenumbersentences
different?(i.e.oneasksmissingtotalandoneasksformissingfactor…)
ExplaintoStudents:
“TodaywearegoingtouseQuizQuizTradeCards.Thesewillhelpyouto:explainyourideasbetter,
reviewkeymaterial,practicegoingfromstrandtostrand,gettoknowyourclassmates,learnhowto
study,getexercise,anddomentalmath,andteachothers.QuizQuizTradeCardsarelikeadvanced
flashcards.Thereisaquestiononthefrontandtheanswerisontheback.Oftenthefronthasatwopartquestionoraquestionthatneedsanexplanation.QuizQuizTradeCardsworklikethis:(model
thispartwithastudent)
Whenyougetyourcardreviewbothsides.Onmysignal,standupandfindsomeonewhois
lookingforapartner.BENICE!Findapartner,standshouldertoshoulder.Askyourquestion.If
1
yourpartnerdoesn’tknowtheanswergiveahint,anotherhint,thentellthem.HINT,HINT,TELL.
(Ifyourpartnerisreallystrugglingyoucanskipthesecondpartofquestions.)Thenhavethe
otherpersonaskyouhisorherquestion.Whenyouarefinished,tradecards.Thenheadout
andlookforanotherperson.Youcanraiseyourhanduptoshowyouareavailable,sootherscan
seeyou.Ifyougetthesamequestiontwice,justbeanexpertandansweritbetter.Threerules:
Spreadout;keepyourvoicesdown;andbenice.(Youwillhavetositdownifyoudonotplaywell
withothers).
Passoutthecards.Afteraminute,allowthestudentstomoveaboutfor8-10minutesminglingwith
others.Encouragethemtogettoasmanydifferentquestions/peopleastheycan.Tellstudentsthat
it’sfineiftheyencounterthesamequestiontwice.Whenseeingacardforthesecondtimetheyshould
beanexpertonthatquestion.
Afterthetimeexpires,collectthecardsandhavestudentsreturntoseats.Askoneofthefollowing
questionsforaquickwrite:(don’tforget:quotaplustimelimit…2minutes)
1. What was good about this activity? (Suggestions to make it better? Especially for 1st time)
(write4linesormore.)
2. Draw and write about (list) as many cards as you can remember seeing. (Get at least 3)
3. List as many math words that you encountered. (List at least 5)
4. Describe one thing or more that you learned or reviewed. (write 3+ lines)
5. Describe one easy question and one harder question. (What was the hardest question you got?) (3
lines or more)
6. How good a teacher were you? (on a scale of 1-10) Explain your score. How could you be better?
After:
Studentswillnothaveseenallthecardsbutyoucanputupsomeofthecardswiththedocument
cameraandsolvethemtogetherorhavestudentssolvethemordiscuss/reviewthem.Tellstudents,
“WewilluseQuizQuizTradecardsfrequentlythisyear.Iwillbeaddingandretiringcardsaswe
becomemoreskillful.InthefutureyouwillhaveopportunitiestomakecardsfornewQuizQuizTrade
sessions.”TellthemtheymayseeaQuizQuizTradecardasashortquizinthedaysahead.
DifferentiatedStrategies:
1.Showthecardstothestudentswhomightstrugglebeforehand.Letthempracticetheanswersso
theyfeelmoreconfident.
2.Usewithafewernumberofcardsbyusingduplicatecards.Whenstudentsseeacardtheyhave
alreadyseen,theyfeelmoreconfident.Therecanbebonusquestionstokeepitchallenging.
3.Considerplayingwithtwodifferentsetsofcardsthatarecolor-codedbydifficulty(i.e.greeneasier,
blueharder).Tellstudentstodecidewhichlevelofchallengetheyareupfor.Theycanmoveupor
downbasedonhowconfidenttheyarefeeling.
4.Eachcardcouldhaveabonusquestiononbottomforstudentswhowantmoreofachallenge.
5.Ifclassmanagementisaproblemconsiderputtingstudentsintotwolines,eachpersonfacinga
partnerabout1meterapart.Makethequestionsshorterwithsimpleranswers.Then,havestudents
2
Quiz,Quiz,Trade.After1minute,ringabell.“Finishedornot,tradecards”(orkeepthesamecard).
Onelineofstudentsmovesdownoneperson,soeveryonefacesanewpartner.Repeat.
Thismethodeliminateswanderingstudentsanddowntime.However,it’simportanttotryandmake
thecardshaveasimplepartandthenabonuspart.Maybebothstudentscangettothesimplepart,if
thereistime,goontobonuspart.
6.StudentscanmakeaQuizQuizTradeCard.
FocusAreas:
a. Include 1-2 clear, solvable, easy to read question(s)
b.Include1questionthat:
1. Asks why or explain
2. Asks “What if” questions…
3. Attacks common mistakes
4. Uses a variable or pattern
5. Makes one work backwards
6. Uses math and/or academic vocabulary (list should be provided)
7. Generalizes the problem by asking about what might be asked, what vocabulary is related,
what mistakes should be avoided
8. Emphasizes process over answers: how would you find, estimate and explain…
c.Answersareclear,accurate,andeasytoread
3
Q
ExplainwhyBiscorrectandAisincorrect.
A
Biscorrectbecausethevalueofthesixin26.495is6
tens.Thevalueofthesixin17.64is6tenths.
6ones(wholeunits)is10timesgreaterthansix
tenths.
Inournumbersystemeachplacevaluepositionis
tentimesmorethanthepositionontheright.
Sointhisproblem,thevalueis10timesgreaternot
1/10asAincorrectlysuggests.
4
Q
Thisshowshowtoenter
anansweronone
Standardizedtest.
Whymightthisbe
confusingforsome
students?
A
Onthistest,youmustenternumbersfrom
lefttoright.
It’strickybecausetheonesplaceisusually
thefarrightposition.
5
Q
A.Howwouldyoufindthevolumeofthecerealbox?
Explainyourthinking.
B.Whywillthisbetrickyforsomestudents?
A
A. To find the volume of a box or prism, you find the area of
the base (bottom layer). Then, you multiply by the height
(number of layers).
Forthisproblem,youaregiventheareaofthebase,so
justmultiply160cm2x32cm.
B. It’s tricky because some students think the only formula
for the volume of a box V = (l) (w) (h) so they are looking
for a third number to multiply.
6
Q
Onthiscalculator,whichkeyswouldyoupresstoenterafraction?
Whichkeydoyouusetoenteradecimal?
Whichkeytodelete?
A
Deletekey
Fractionkey
Decimalkey
7
Q
Explainhow
youknowyou
arecorrect.
A
Iknowthat(6,4)is6
unitsoverbecausethe
firstnumberisthex
coordinateandxisthe
horizontalline(axis).
XcomesbeforeY!
Onememorytrickis:you
mustwalkovertothe
elevatorbeforegoingup.
8
Q
3 ⋅ 8 + 16 ÷ 4=?
Bobsolvedthisproblembydoingthis:
3⋅8+16÷4=?
24+16÷4=?
40÷4=?
10=?
WhatmistakeisBobmaking?
Describethestepsneededsolvethisproblem.
3 ⋅ 8 + 16 ÷ 4=?
A
Bobisjustgoinglefttoright!
Heneedstofollowtheorderofoperations!
1.Parenthesis(groupingsignals)
2.Exponents
3.MultiplicationandDivisionfromlefttoright
4.Additionandsubtractionfromlefttoright
3⋅(8+16)÷4=?
3⋅(24)÷4=?
72÷4=?
18=?
9
Q
WhatmistakeisLenmaking?
Howdoyouknowhisansweriswrong?
Whatwouldbeabetteranswerorestimate?
A
3/10+2/5=5/15
Lenthinkstoaddfractionsyoujustaddthenumeratorsand
denominators.
Thesum5/15makesnosensebecause2/5isalmosthalf.Ifyouadd
3/10itwouldbeover1/2.ThesumLengave,5/15,islessthan1/2!
Tofindthesum,findequivalentfractionsthathavethesame
denominator.
2/5=4/10Nowadd:3/10+4/10=7/10Thisanswermakessense!
10
Q
A.Whatisthekeyinformationintheproblem?
B.Whatkeyinformationdoyouneedtoknowaboutliquid
measurementthat’snotgivenintheproblem?
(Hint:gallons…ounces…)
A
A.Thekeyinformationfromtheproblemis:
1.Thetankholds5gallonsofwater
2.Tomfills6bottlesandapitchertotakewaterfromtank
3.Eachbottleholds16ounces
4.Thepitcherholds½gallon
B.Whatyouneedtoknowisthatthereare128fluidouncesinagallon!
(8ounces=cup;16ounces=pint;32ounces=quart64ounces=½gallon)
11
Q
Tomhasawatertankthatholds5gallonsofwater.
IfTomdrinks4pintsofwateraday,howmanyfull
tanksofwaterwilldrinkin30days?
A.TofindhowmanypintsTomdrinksin30days,what
equationcouldyouuse?
B.Whatequationcouldyouusetofindhowmany
gallonsequals120pints?(Canyouuseabarmodel?)
A
A.4pints/eachdayx30days=120pints
4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
B.8pints=1gallon(2pt.=1qt.4qt.=1gal.)
120pints
8
(1
ga
ll
8
8
8
Howmany8’s(each8=1gallon)willittaketomake120?120÷8=40g.
12
Q
Explainhowyouknowyouareright.
5.051
A
5.05
5.06
Theseare
thousandths!
5.07
5.08
5.09
5.10
5.11
5.12
5.108
5.066
5.074
5.117
Whenroundingtothenearesthundredth,it’simportanttoknowhowmanythousandthsthere
are.Thengotonearesthundredth!Seenumberline!
A.5.066roundsto5.07(closerto5.07becausethereare6thousandths)CORRECT
B.5.074roundsto5.07(closerto5.07becausethereareonly4thousandths)
C.5.117roundsto5.12(closerto5.12becausethereare7thousandths)
D.5.108roundsto5.11(closerto5.11becausethereare8thousandths)CORRECT
13
Q
Whichiscorrect?
Explainthedifferencebetweeneachexplanation.
A
Aiscorrect.Parallelogramshave2pairsofparallelsides!
BisalmostthesameasAexceptitstatesparallelograms
haveexactly1pairofparallelsides.
Thisisthedefinitionofatrapezoidnotaparallelogram.
14
Q
A.Whatdoyou
thinkthis
questionwillask?
B.Whatequation
couldyouuseto
solve?
A
A.Itwillprobablyask,“Howmanytoyanimalsinacrate?”
B.36inabagx48bagsinaboxx18boxesinacrate=total
36x48x18=t
Or“Ifyouhave100,000toyanimals(orsomenumber)how
manycrateswouldyouneed?”
100,000÷totalin1crate=n
15
Q
Givetheequationyouwouldusetofindthevolumeof
thisprism.
Explainwhythisequationworks.
A
Theformulaforvolumeofaprismisareaofthebasexheight.
Theareaofthisbaseis5x3(it’sarectangle)
Theheightis2
(5x3)x2=30cubicunits
Itworksbecauseyoumustfindthecubesonthebottomlayer:
5x3.Thereare2layerssomultiplythatnumberby2(theheight)
16
Q
Whichansweris
correct?Explainhow
youknow.
A
5ft
Emmaiscuttinga5footboardinto6equalpieces.Sheis
dividingitinto6equalparts.
Thedenominatorofafractiontellsyouhowmanypartsyouare
dividingsomethinginto.
5÷6means5/6
Also,ifshehad6feetofboardanddivideditinto6piecesthe
pieceswouldbe1footeach.Inthiscasesheonlyhas5feetof
board,sothepiecesaregoingtobealittlelessthan1footeach!
17
Q
Bobthoughtallofthesecouldberectanglessohe
choseA,B,CandD.Whyishewrong?
A
Bobisn’treadingthequestioncarefully.Itsays,
“Whichfigureisalwaysarectangle.”Itdoesnotsay,
whichfigurecouldbearectangle.
Thesquaremusthaverightanglessoitistheonly
shapethatisalwaysarectangle!
Parallelogram
(withoutrightangles)
square
ordinary
quadrilateral
Rhombus
(withoutrightangles)
18
Q
Explain
your
thinking.
A
Volumeisareaofthebasetimestheheight.(the
numberonthebottomlayertimesthenumberof
layers)
Theareaofthebaseis4x5(countcarefully!)
Theheightis3(3layersof20)
Volumeis(4x5)x3=60cubicunits
19
Q
*
,
Nickthinks ismorethan because:
+
3ismorethan1and8ismorethan2.
Correctthemistakeinhisreasoning.
A
½
Nickisincorrectbecausealargedenominatordoesnotmakeafraction
large.The8meansthefractionisdividedinto8equalpieces.The
numeratortellsyouhowmanyofthose8piecesyouhave.
Inthiscase3/8islessthanhalf.4/8=½3/8<1/2
20
Q
Explainyour
thinking.
Usethedrawing
tofindthe
productof
4x2/3
A
-
-
Cisthebestrepresents4x becauseitshows4groupsof *
*
2 2 2 2
8
+ + + = 3 3 3 3
3
+
-
*
*
Ifyouputthethirdstogether … =2 21
Q
A.Whatistrickyaboutthisproblem?
B.What2stepswillyouneedtotaketosolveit?
A
A.Whatistrickyaboutthisproblemistheunitsareinmeters,but
theanswermustbeincentimeters!
1ststep:Findtheperimeterbyaddingupallthesidelengths
2ndstep:Convertmetersintocentimeterbymultiplyingby100
Eachmeter=100centimeters
Youcandothestepsineitherorder!
Remember2.57x100=257
22
Q
Whatisthe
orderedpair
thatdescribes
thelocationof
pointA?
Explain.
A
Theorderedpairis(2,7)
Youknowthisiscorrectbecausethefirstcoordinatetells
youtogoover2onthexaxis.
Thesecondcoordinatetellsyoutogoup7ontheyaxis.
23
Q
Whatequationcanyou
usetodeterminethe
heightofthewaterin
thetank?
Explainyourthinking.
A
Volume=(areaofthebase)⋅height
Thevolumeisgiven=1050cubicinches
Thelengthandwidtharegiven.
length=30incheswidth=7inches
1050in3=(30in⋅7in)⋅hin
24
Q
Whataresome
numbersthat
wouldmakethis
inequalitytrue?
A
Youneedtomakeafraction
thatislessthan1.
4x1=4soanyfraction
lessthan1willbecreatea
productlessthan4.
Tomakeafractionless
than1,makethenumerator
smallerthanthe
denominator…
1 1 1 2 3 4
, , , , , …
2 3 4 3 5 9
,
4x <4
-
25
Q
Whataresome
numbersthat
wouldmakethis
inequalitytrue?
A
Youneedtomakeafraction
thatismorethan1.
4x1=4soanyfraction
morethan1willbecreatea productmorethan4.
Tomakeafractionmore
than1,makethenumerator
greaterthanthe
denominator…
2 3 5 8 9
, , , , , …
1 2 3 4 5
6
3
4x >4
26
Q
What
mistakedid
Bobmake?
Explain.
A
Thesesides
notparallel!
Thesesides
notequalin
length
Bob’smistakeisthatthetrapezoiddoesnothave
bothsetsofoppositesidesparallel.Itonlyhasone
setofoppositesidesparallel.Also,tobea
parallelogram,bothoppositesideshavetobe
equalinlength.Thisisnottrueoftrapezoids.
27
Q
What2stepscanyoutaketofindthetotalmassoftheboxesonthetruck?
Whatequationscanyouuse?
A Thenumberofboxescanbefoundbyusingthevolumeformula.
Volume=(areaofthebase)xheightv=5x4x4v=80boxes
Then,multiplythenumberofboxesbythemassofonebox.
Totalboxesx22.5=totalmass
80x22.5=totalmass
80x(20+2+.5)=totalmass(thisisthedistributiveproperty!)
1600+160+40=totalmass
1800=totalmass
28
Q
Explainhowyouknow
youhavethecorrect
answers.
A
Areaofbasexh=volume
lxwxh=volume
29
Marysaidtofindtheareajustmultiply
, ,
,
,
4x8=32and-x-=BFinalarea=32B
Whatisthemistakeinherreasoning?
A
8cm
1/2cm
32cm2
4cm
½cm
2cm2
A=32+4+2+¼
A=38¼cm2
¼cm2
4cm2
Marydoesn’tunderstandhowtomultiplynumbers.Tomultiply
sheneedstobreakthefractionsintotwopartsanduseanarea
model.Orshecanchangethefractionsintoimpropernumbers.
,
,C
,
D
,C
D
,E*
-
-
-
-
-
-
-B
8 = 4 = x =
,E*
-B
,
=38 cm2
B
30
Q
Whatnumbergoesinthe?spot.Explainhow
theareamodelworks.
A
4x60=240
Inthisareamodel,thedividend(theproduct…whatdividedby4=363?)isrepresented
bytheinside(area).Onedivisor(factor)is4(thewidth)andtheotheris363(length).
Now,youcanworkbackwards:363x4=?Thiswillfindthearea.
Breaking363downinto300+60+3andmultiplyeachpartby4.
The
=240
31
Q
What!keys!would!you!push!to!solve!this!problem?!!
!!
Why!is!this!tricky?!
A
(8x2)–4=
(8x2)–4
Thinkcarefully!4yearslessthantwicehisage.Eventhoughit
It’strickybecauseitsays“Olivia’sageis4yearslessthan
seemslikeyoushouldsubtractfourfirst,youactuallyneedtodouble
theagefirst!Youdon’tknowwhattosubtractfromuntilyoudouble
twiceTyler’sage.”Youhavetomultiplyfirsttogethisage,
theage!
thensubtracttofindOlivia’sagewhichis4yearsless!
32
MakeaQuizQuizTradeCard
FocusCorrectionAreas:
1.Include1-2clear,solvable,
question(s)
3.Answersareclearandaccurate
4.Include1questionthat:
a.Askswhyorexplain
b.Asks“Whatif”question…
c.Attackscommonmistakes
d.Usesavariableorpattern
e.Makesoneworkbackwards
f.Usesmathvocabulary
33
Q
A
34
Q
A
35
Q
A
36
Q
A
37
Q
A
38