Mathematics:NumberandOperationsinBaseTen
ClusterHeading:Understandplacevalue
1.NBT.2
ContentStandard:Understandthatthetwodigitsofatwo-digitnumberrepresentamountsoftensandones.
PracticeStandard:MP6Attendtoprecision,MP7Lookforandmakeuseofstructure
Problem/TaskSuggestionsFormativeAssessmentSuggestions
Numbers,Numbers
Eachstudentreceives3 numbercards.
Choose2cardstomakethelargest2-digitnumber.
497
Now,choose2cardstomakethesmallest2-digitnumber.
Recordyouranswerandexplaintoa partnerhowyoufoundyouranswer.
Differentiation: Supports:
•Providearecordingsheetwith2 blankrectanglesforthelargestand smallest2-digitnumber.
•Provideanumbergrid.
Extensions:
•Createawordproblemthatusesthetwo2-digitnumbers.
•Howwouldhaveacardthatsayszerochangeyouranswer?Couldyouget abiggernumberorsmallernumberwithazeroandusing2 cards?
Solutions:
•Largestnumber:97,smallestnumber:7.
•Inordertomakethelargestnumber,thelargestnumeralhastogoin thetensplaceandthenextlargestintheonesplace.
•Inordertomakethesmallestnumber,thesmallestnumeralhastogo inthetensplaceandthenextsmallestintheonesplace.
ObservationofStudents
•Dotheyrecognizeplacevalue?
•Cantheyexplaintheirstrategy?
•Dotheyunderstandwhattheproblemis askingthemtodo?
•Cantheyreadthenumberoutloud?
QuestionstoGuideStudentThinking:
•Whatisa wronganswer?Howdoyouknowitiswrong?
•Canyoureadthenumberoutloud?
•Whatpartofthenumbercanyouchangetomakeitgreater/smaller?
Misconceptions
Studentsmay:
•Reversethetens/ones.
•Usenumbersnotgiven.
•Notuseall3 numbers(useonlythe2 numbersfromthelargest numbertomakethesmallestnumber).
VocabularyConsiderations
Greater,greatest,smaller,smallest,placevalue,tens,ones
Larger/largest
Createdby:SharonHolt,LauraParat,LauraRhoneyforAuroraUniversity’sOEDC5204
2.MD.8
ClusterHeading:Workwithtimeandmoney.
ContentStandard:Solvewordproblemsinvolvingdollarbills,quarters,dimes,nickelsandpennies,using$ and¢ symbolsappropriately.
PracticeStandard:MP1Makesenseofaproblemandpersevereinsolvingit.
Problem/TaskSuggestionsFormativeAssessmentSuggestions
HowCanYouMake25Cents?
Whatareall thedifferentwaysyoucanmake25cents?
(Givestudentsplentyofplay/realmoneyanda blanksheetofpaperfor
recording.Youmaywantstudentstoworkwitha partner.)
Differentiation
Supports
•Reada booksuchas“AQuarterfromtheToothFairy”thatlistsfour combinationsaspartofthestory.Thisgivesstudentsexamplesof solutionsandaplacetostart.
•Askafewquestionsofstrugglingstudentstodetermineif thestudent knowsthevalueofeachcoin.If he/shedoesnot,givethechild experienceswithcoingamesandactivities,suchasmatchinggames (coinstovalues),raceforadollar(rollingdice,takingdesignated penniesandtrading),playing“fish”or“concentration”wheresome cardshavepicturesofcoinsandothercardshavevalues.
•Askstudentstothinkofawaytomake25centswithonlypenniesand onlynickels,andaskthemiftheycouldtradeanyofthecoinsintheir combinationforacointhatwouldhavethesamevalue.Thiswould generateanothercombination,whichtheycouldwritedownontheir list.Ask,“Doyouthinktradingwillgiveyouothercombinations?”
•Providealistofvaluesofeachofthecoinstouseasareferenceor havethestudentcreatehis/herownreferencelistforcoins.
Extensions
•Pickupsomecoinsandhidethem.Haveyourpartneraskyouyes/no questionsaboutyourcoinstofigureouthowmanyandthevalue.
•Askaboutcombinationsofcoinstomake50centsoradollar.
Solution
13 ways:1quarter,25pennies,2dimes,1nickel,1 nickeland20pennies,2
dimes,5 pennies,2nickelsand15pennies,1dime,3nickels,3nickelsand
10pennies,1 dime,2nickelsand5 pennies,4nickelsand5 pennies,1
dime,1 nickeland10pennies,5nickels,1dimeand15pennies
Createdby:IllinoisStateBoardofEducationContentAreaSpecialists
Observationof theStudents
•Isthestudentabletorecognizewhattheproblemis asking?MP1
•Doesthestudentknowthevalueofeachofthecoins?
•Isthestudentabletousementalmathtodosimplecomputationsordo theyneedtouseanothertool?MP5
•Doesthestudentrecognizethatmultipleanswersarepossible?
•Canthestudentexplainhis/herprocesstootherstudents?MP6
•Isthestudentabletofindall13waystomake25cents?
QuestionstoGuideStudentThinking
•Isthereanotherway?
•Howareyoucertainthattherearenootherpossibilities?
•Whenprocessingtheproblemwiththewholegroup,askthestudents withfewermethodstopresentfirstandthenhavetheotherstudents addonsothateveryonecanparticipateintheconversation.
Misconceptions
Studentsmay
•Stopafterfindingonlyoneortwoways.
•Thinkthatlargersizedcoinsareworthmoreinvalue.
Vocabulary
•Cents,quarters,dimes,nickels,pennies,equal,value
2.OA.1
ClusterHeading:Representandsolveproblemsinvolvingadditionand subtraction
ContentStandard:Useadditionandsubtractionwithin 100tosolveone- andtwo-stepword problemsinvolvingsituationsof addingto, takingfrom, puttingtogether,takingapart,andcomparing,with unknownsinallpositions
PracticeStandard:MP1Makesenseof problemsandpersevereinsolvingthem.
Problem/TaskSuggestionsFormativeAssessmentSuggestions
AllRoadsLeadto100.
Writetwomathwordproblemswherebothanswerswouldbe100.Writethe equationthatgoeswitheachofyourstoriesandshowyourcomputation.Putan “E”bytheeasyproblemandan“H”bythehardproblem.Explainwhatmakes the easyproblemeasyandthehardproblemhard.
Differentiation
Supports
•Changethesuminthetaskto20insteadof 100
•Askstudentswhoare strugglingtowritea word problem.
•Scribeforthe studentas he/shedictatesverbally.
•Provideaprompttogetthe student startedsuchas “Astudentwasfilling boxeswithblocksand…” or“Iamthinkingof somenumbersthat…”.
•Askthestudenttodrawa pictureorfindapictureina magazine,andthen writeastoryaskingabout thenumberof itemsinthepicture.
•Underlinewordsintheproseof thestoryandshowthestudenthow to representthephraseusinganumberand/orsymbolfortheoperation.
Extensions
•Increasethe numberof storyproblemsthestudentshouldwrite.
•Havestudentswriteeachof their storyproblemsonaseparateindex card withtheir namebutno “E” and“H” indicated.Studentsexchangecardswith another student,solvetheproblemsonthecardsandthenindicatewhich problemtheythoughttheauthorwould havemarked“H” andwhy. Students would thencheckwiththeauthorto seeif theyagreedonthemostdifficult problem.
Solutionswill varydependingonthe storywritten.All shouldhavethesameanswer of 100. Someproblemsmayhaveonly1operationandonly twonumbersbut others could have multiplenumbersandbothadditionandsubtractionincluded.For instance,“The teacherput 85coloredcandiesin theclass candyjar.15studentseach tookapiecefromthebowl as anaward forgood work.Aparentbroughtinanother bagof 30piecesof candyandadded it tothejar. Howmanypiecesof candyarein
thejarnow?”(85–15+30= 100)
Createdby:IllinoisStateBoardofEducationContentAreaSpecialist
ObservationofStudents
•Arethesolutionstoeachofthewordproblems100?
•Iftherearecomputationerrors,aretheanswerscloseorarethere majorerrors?
•Aretheequationscorrectforeachofthestories?
•Doestheproblemhaveonlytwonumbersormultiplenumbers?
•Doesthestudentuseonlyaddition?Justsubtraction?Both
•Doestheexplanationforselectionofthehardestandeasiest problemmakesense?
•Doesthecomputationworkindicatethestudentusedmultiple strategiestofindtheirsolutions?
QuestionstoGuideStudentThinking
•Canyouthinkofalistofnumbersthataddupto100?
•Doyouknowasubtractionproblemwheretheansweris100?
•Haveyouconsideredjustusingnumbersthatendinzero?
•Canyouthinkofcoinsthatadduptoadollar?Couldyouuse thatinformationtowritea wordproblem?
•IfIgaveyouanequationcouldyouwriteawordproblemtogo withit?
Misconceptions
Studentsmay
•Thinktheycanonlyusetwonumbersintheirstory(and equation)
•Thinkthattheycanonlyuseadditionanddon’tconsider subtractionproblemsthatresultin100.
VocabularyConsiderations
-Solution,variable,equation,computation
Mathematics:OperationsandAlgebraicThinking
ClusterHeading:Representandsolveproblemsinvolvingadditionandsubtraction.
ContentStandard:Useadditionandsubtractionwithin100tosolveoneandtwo-stepwordproblemsinvolvingsituationsofaddingto,taking
2.OA.1
from,puttingtogether,takingapart,andcomparing,withunknownsinall positions,e.g.,by usingdrawingsandequationswitha symbolfor theunknownnumbertorepresenttheproblem.
PracticeStandards:MP1Makesenseofproblemsandpersevereinsolvingthem,MP2Reasonabstractlyandquantitatively.
Problem/TaskSuggestionsFormativeAssessmentSuggestions
BetheMathematicsAuthor
Writeawordproblemfor34–16=
Giveeachstudentan8.5”x11”recordingsheetthathasthemathequationat thetop.Leavehalfthepageforhim/hertowritethewordproblem.
Solvetheproblemusingpictures,words,numbers,andmathematicaltools thatmakesensetoyou.
Leavethebottomhalfofthepageblankforeachstudenttorepresentordraw his/hersolutions.
Differentiation
Support
•Askthestudentstodescribethewordproblemanddecideif theyagree thatitmatchestheoriginalmathsentence.
Extensions
•Writeyourownmathsentenceandwordproblemandaska classmateto solveit.
•Askthestudentstosolvea problemsuchas34- = 29
Solutions
Anyreasonablestoryandpictorialrepresentationleadingto34 –16=18.
ObservationofStudents
•Doeseachstudentunderstandthetask?
•Howdoeseachstudentrepresenthis/herthinking(counters/physical model,pictures,words,hundredschart,open-numberline)?
•Iseachstudentabletocommunicatehis/herideastoothers?
•Iseachstudentwillingtoshare-individually,smallgroup,orwhole group?
Examinestudent’swrittenwork
Doesthestudent:
•Haveastorythatmakessensewiththenumbersintheequation?
•Includeaccuratecalculations?
•Usecorrectnotation?
•Istherea correctlabeltogowiththeproblem?
QuestionstoGuideStudentThinking
•Whatdoesthe3in34mean?Theotherdigits?
•Couldyousolveorrepresenttheprobleminanotherway?
Misconceptions
•Student’sstorymayindicateanadditionprobleminsteadofa subtractionproblem.
•Studentsmayadd34+16.
•Studentsmaynotuseplacevalueunderstandingintheircalculation.
•Studentsmaycalculateananswerof28or22.
Adaptedfrom:HowtoAssessWhileYouTeachMath:FormativeAssessmentPracticeandLessons,GradesK-2:A MultimediaProfessionalLearningResource, byDanaIslas,MathSolutions,ISBN:978-1-935099-17-8
Mathematics:CountingandCardinality
ClusterHeadings:Counttotellthenumberofobjects.Comparenumbers
K.CC.4a
K.CC.6
ContentStandards:Understandtherelationshipbetweennumbersandquantities;connectcountingtocardinality.a.Whencountingobjects, saythenumbernamesinthestandardorder,pairingeachobjectwithoneandonlyonenumbernameandeachnumbernamewithoneand onlyoneobject.Identifywhetherthenumberofobjectsinonegroupisgreaterthan,lessthan,orequaltothenumberofobjectsinanother group,e.g.,byusingmatchingandcountingstrategies.
PracticeStandard:MP6Attendtoprecision,MP1 Makesenseoftheproblemandpersevereinsolvingthem.
Problem/TaskSuggestionFormativeAssessmentSuggestions
RollingaNumberCube
Givepairsofstudentsseveralunifixcubesandanumbercubewithnumerals
oneachside.Adjustthenumeralsonthenumbercubestoaddressthecurrent needsofthestudents.Studentstaketurnsrollinga numbercubeandcounting outthenumberofunifixcubesindicated.Thechildthensnapsthecounted cubesintoa trainandcompareshis/hertraintoa partnertoseewhohas
more.
Aftereachchildhashad5 turns,havehim/herlookatthefiveindividualtrains andtrytoseewhowouldhavethemostif theysnapthetrainstogether.After estimatingwhomayhavemoretheyeachsnaptheir5trainstogetherandlay thembesideeachothertoseewhichislonger.Finallytheymaycounttosee howmanyareineachlongtrain.
Differentiation
Support
•Usealargefoamrubbernumbercubewithdotsratherthannumerals.
Whenthestudentrollsthenumbercube,he/sheplacesaunifixcubeon
eachdot,thensnapsthemtogether.Nextstepistouseanumbercube withdotsandnumeral
Extensions
•Rolltwonumbercubesandfindthesumtodeterminethenumberof unifixcubestosnaptogetherandcompare.
•Determinenotonlywhohasmorebuthowmanymore.
ObservationofStudents
Doesthestudent
•Demonstratetheverbalcountingsequence?
•Recognizetherollednumeralandtakethatmanycubes?
•Use1-to-1correspondenceskills?
•Haveawayofkeepingtrackofhis/hercount?
•Realizethelastnumbersaidindicateshowmanyshe/hehas?
•Knowwhichtrainisbiggerbypriorknowledge,estimatingorby matching?
QuestionstoGuideStudentThinking
•Doyouknowwhichonesyouhavecounted?
•Wherecouldyouputthecountedcubes?
•Tellmehowyouknowwhichtrainhasmorecubes.
Misconceptions
Studentsmaynotunderstandthatthelastnumbertheysayindicateshow manyitemsareintheset.
VocabularyConsiderations
Greaterthan,lessthan,equalto
Taskadaptedfrom:DevelopingNumberConcepts:Counting,Comparing,andPatternsBook1 byKathyRichardson,Apr16,1998
K.CC.5
ClusterHeading:Counttotellthenumberofobjects.
ContentStandard:Counttoanswer“howmany?”questionsaboutasmanyas20thingsarrangedina line,arectangulararray,oracircle,or asmanyas10thingsinascatteredconfiguration;givena numberfrom1-20,countoutthatmanyobjects.
PracticeStandard:MP2Reasonabstractlyandquantitatively.
Problem/TaskSuggestionsFormativeAssessmentSuggestions
LettersinYourName
Showstudentsashort nameanda longname.Askabout differences.
Studentswill findout howmanylettersareintheirown namesbycuttingapart
thelettersin theirnamesandcounting.Studentsgluetheirlettersonapieceof constructionpaper.Theythenglueona2"× 2"paperwith thenumberof letters in theirname.Havestudentslook attheirneighbor'sname.Ask,"Whohas the shortername,you oryourneighbor?"Theyshareresponseswith theclass, comparingeach others’names.Giveeach studentapaperstrip, which reads,“I have lettersin myname.”Studentswillcompletethesentencebywritingthe numberof lettersintheir name,andgluingthe sentenceontheirpage.Students canfinishtheirpagefortheclassbook by gluingonasnapshot of themselvesor drawingapictureof themselves.
Differentiation
Support
•Writetheirnameon1-inchgraphpaperwith aletterineach square.Don’t cut thelettersapartbuthold theirnameuptootherstocomparelengths. Putamarkoneach letterasyou saythenumberword.
Extensions
•Students’names,writtenonindividual strips,areplacedinabox.Have studentsdrawnames& count thenumberof letters.
•Students,inpairs, taketurnsrollingadie. Theylook forclassmates’names containingthesamenumberof lettersas indicatedonthedie.
•Studentswritetheirnameson1-inch grids/graphpaper,one letterper square.Theycut theirstripsandcomparewith classmates’namestrips.
•Readthestoryof Chrysanthemum,byKevinHenkes.Havestudentscount thenumberof lettersinChrysanthemum’sname& comparethe numberof lettersinhernametothe numberof lettersintheirnames.
ObservationofStudents
•Listenforaccuracyaseachstudentcountsthelettersinhisorhername.
•Usecompletednamepagestodetermineifstudentswereareableto writethenumberoflettersintheirnames.
QuestionstoGuideStudentThinking
•Lookatnamesofstudentsinourclass.Whatis differentabout
everyone'sname?
•Howdidyoufindoutwhatnumberyouneededtowriteyoursentence?
•Isyournamelongerorshorterthanyourneighbor'sname?
•Ifwearrangeourclassbookfromshortestnametothelongestname, whosenamewouldbefirst?
•Showstudentsthepagesofthebook.“Ifthisisthefirstpagewhatwould thenextpagebe?”
Misconceptions
Studentsmaynotunderstandthatwhentheyarecountingthelastnumber theysayindicateshowmanyitems(inthiscaseletters)areinthegroup
Taskcreatedby:DeeannaD.Golden Adaptedfrom:
Mathematics:OperationsandAlgebraicThinking
ClusterHeading:Understandadditionasputtingtogetherandaddingto,andunderstandsubtractionastakingapartandtakingfrom.
K.OA.3
SnapIt
ContentStandard:Decomposenumberslessthanorequalto10intopairsinmorethanoneway,e.g.,byusingobjectsordrawings,andrecord eachdecompositionbya drawingorequation(e.g.,5=2 +3 and5=4 +1).
PracticeStandards:MP1 Makesenseofproblemsandpersevereinsolvingthem,MP5Useappropriatetoolsstrategically.
Problem/TaskSuggestionFormativeAssessmentSuggestions
ObservationsofStudents
Askeachstudenttocountout10unifixcubesandsnapthemtogetherina train.Whilestandingina circle,studentsholdtheirunifixcubesbehindtheir backs.Whentheteacher/designatedstudentsays“SnapIt”,studentsbreak theirtrainsintotwoparts.Studentsbringonepartineachhandaroundtothe frontoftheirbodiesforalltosee.Eachchildreportsonthecombinationof
tenbysaying,e.g.,4 plus6 =10.
Differentiation
Support
•Havethestudentsstartwith2-9unifixcubesinsteadof10.
Extension
•Havechildrenrevealwhatisinoneoftheirhandsbutkeeptheother behindtheirback.Otherstudentstrytofigureoutwhatisinthehand behindtheback.
•Writeequationsbasedonthecombinationstheymake.
•PlayTensGoFishcardgame.Havestudentslookforpairsofnumbersthat equal10.If a childhasa7 intheirhandtheyaskapartner“Doyouhavea
3?”Thiswillworklikeatraditional“GoFish”cardgame.
Solution
•Eachchildreportsonthecombinationoften.
Isthestudentableto:
•Makecombinationpairsforagivennumber?
•Findthemissingnumberfromthepair?
•Representthepairinmaterials?
QuestionstoGuideStudentWork
•Whathappenstothetencubeswhenyousnapthem?
•Istheremorethanonewaytosnapyourtrain?
•Whatmustthetwopiecesofthetraintotal?
Misconceptions
•Believethatthereisonlyonetobreakupten.
•Believethattheymustbreakitinhalf.
•Believethatafterthebreakthereis nolongera totaloften.
Vocabulary
Sum,equal,addition,adding,subtraction
Adaptedby:JoanBarrettfromthefollowingresources:“Snap-It”activityfromKathyRichardson’sDevelopingNumberConceptsBookOne:Counting,Comparing byKathyRichardson;DaleSeymourPublicationsCompiledApr1,1998;TensGoFish–InvestigationsinNumberDataandSpacegrade1,TERC2012