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Developing calcula.on and problem solving skills Marian Small November, 2015

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Page 1: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Developingcalcula.onandproblemsolvingskills

MarianSmallNovember,2015

Page 2: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Background

•  SomeofyouexpressedaninterestintalkingaboutdevelopingbeAercalcula.onskills.

•  SomeofyoutalkedaboutdevelopingbeAerproblemsolvingskills.

•  Todayisamix.•  Wewillalsoblendintheac.vi.esyoutriedandarerepor.ngon.

Page 3: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Let’sstartwith…

•  Someexamplesofopenques.onsyouusedthatwentwell.

•  Talktothepeopleatyourtable.•  Thetablewillchoosetwotopresenttoeveryone.

Page 4: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Calcula7onskills

•  Myfocuswillbeondevelopingtheimportantideasthatunderliecalcula.ons,ratherthanthemechanics.Iwillalwaysbereferringtomeaning.

•  Butwewilllookatvarie.esofstrategiesforperformingcalcula.on.

Page 5: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Facts(SmallNumbers)

•  Yourcurriculumspeaksclearlytotheimportanceofdevelopingfluencywithsmallfacts.

•  TheseareESSENTIALfores.ma.on,workwithpropor.onalthinking,workwithfrac.ons,etc.etc.

Page 6: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

BUT

•  Weneedflexibilitywhichcomeswithunderstandingandnotjustinstantaneousresponses.

•  InyourMinistrydocuments,thereismen.onmadeofstrategieslikeMaking10,Usingdoubles,AddingtoSubtract,etc.

Page 7: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Addi7on/subtrac7onissues

•  Everysubtrac.oncanbesolvedusingaddi.on.

•  Howwouldyousolve13–8thisway?

Page 8: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Addi7on/subtrac7onissues

•  Orderdoesn’tmaAer.

Page 9: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Addi7on/subtrac7onissues

•  Youcanaddorsubtractinparts.•  Youcan“juggle”whenyouadd.

Page 10: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Addi7on/subtrac7onissues

•  Youcanuseaconstantdifferencewhenyousubtract.

•  Addingorsubtrac.ng0isespeciallyeasy.•  Addingorsubtrac.ng1ispreAyeasy.

Page 11: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Sohowwouldyouencourage

•  8+3•  6+7•  9–4•  12–9

Page 12: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

ButIwouldalsoask

•  Showme6sothat:•  Therearemorethan2parts.•  Thereare2parts-oneliAleandonebig.•  Thereare2parts-similarinsize.

•  Repeatabovewith25.

Page 13: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

ButIwouldalsoask

•  Showme10andshowme12sothat:•  Eachisshownintwoparts.•  Onepartfor10isthesamesizeasonepartfor12.

Page 14: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

ButIwouldalsoask

•  Whatnumberscouldyoudecomposeintoanumberandtwiceasmuch?

•  Whatnumberscouldyoudecomposeintothreenext-to-each-othernumbers?

Page 15: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

ButIwouldalsoask

•  Predicthowmuchmore8+3isthan6+2withoutgeengtheanswers.

Page 16: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Addi7onandsubtrac7onprocedures

•  Howwouldyouusebasetenblocksfor:•  35+48•  76+99•  81–17•  241–167

Page 17: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Mul7plica7onanddivisionconcepts

•  Everydivisioncanbesolvedbymul.plying

•  Howwouldyouusemul.plyingtosolve36÷4?

•  Tosolve546÷6?

Page 18: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Mul7plica7onanddivisionconcepts

•  Orderdoesn’tmaAer

Page 19: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Mul7plica7onanddivisionconcepts

•  Youcanmul.plyinparts(distribu.veandassocia.ve).

Page 20: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Mul7plica7onanddivisionconcepts

•  Youcan“juggle”factors(e.g.half/double)•  Youcandouble/triplebothdivisoranddividend.

Page 21: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Mul7plica7onanddivisionconcepts

•  Youcandivideinparts•  It’seasytodivide0.•  It’seasytodivideby1.

Page 22: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

ButIwouldalsoask

•  Buildarectangularprismthatis2x2x3cubes.

•  Howdoesthishelpyouseethat4x3=2x6?

Page 23: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

ButIwouldalsoask

•  Makeabigarrayofcounters.•  CanyoualwaysbreakitupintoliAlearrays?

Page 24: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Models

•  Howwouldyouusebasetenblockstomodel•  8x49?•  21x21?•  512÷4•  312÷4

Page 25: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Whataboutintegers?

•  Howdoyoumodel5–(–3)?•  5x(–3)?•  (–15)÷(–3)?

Page 26: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Whataboutfrac7ons?

•  Howdoyoumodel•  2/3+1/5•  2/3–1/5•  2/3x1/5•  2/3÷1/5

Page 27: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of
Page 28: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of
Page 29: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of
Page 30: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of
Page 31: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of
Page 32: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

2/3+1/5

Page 33: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

2/3+1/5

Page 34: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

2/3+1/5

Page 35: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

2/3–1/5

Page 36: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

2/3–1/5

Page 37: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

2/3–1/5

Page 38: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

2/3x1/5

Page 39: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

2/3x1/5

Page 40: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

2/3÷1/5

Page 41: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Now

•  Let’stalkaboutexamplesofques.onsyouusedtopushthinking.

•  Shareatyourtable.•  Yourtablewillchoosetwotopresenttoeveryone.

Page 42: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Nowforproblemsolving

Page 43: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Characteris7csofgoodproblems

•  Thereissomeelementofdecisionmaking.•  Thereissomereasoning.•  Communica.ngaboutprocesswillworkformoststudents.

•  It’sniceifyoucandrawavisual.

Page 44: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Characteris7csofgoodproblems

•  It’sniceifthereismorethanoneapproachorevenmorethanoneanswer.

•  It’sniceifyoucaneasilyextend.

Page 45: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Forexample…

•  KaylahadjustafewmorepencilsthanLevi.•  Togethertheyhad20pencils.•  Howmanydoyouthinkeachonehad?

Page 46: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

So…

•  Decisionmaking?•  Reasoning?•  Communica.ng?•  Whatsortofvisual?•  Morethanoneapproach?•  Extendable?

Page 47: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Forexample

•  Wemightask:Amyis4.Sindyis6yearsolder.HowoldisSindy?

OR•  WemightaskwhetherSindycanbeboth6yearsolderthanAmyandalsotwiceasold.

Page 48: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Possiblevisual

Page 49: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

So…

•  Decisionmaking?•  Reasoning?•  Communica.ng?•  Whatsortofvisual?•  Morethanoneapproach?•  Extendable?

Page 50: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Or…

•  Whatnumberscanyoumakebyusingonly2s,5s,+sand–s?

•  e.g.3=5–2•  10=5+5•  9=5+2+2•  Arethereanycoun.ngnumbersyoucannotmake?

Page 51: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

So…

•  Decisionmaking?•  Reasoning?•  Communica.ng?•  Whatsortofvisual?•  Morethanoneapproach?•  Extendable?

Page 52: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Maybe

•  Es.matethenumberofsquarecen.metresofpizzathatallofthekidsinWinnipegeatinoneweek.

Page 53: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

So…

•  Decisionmaking?•  Reasoning?•  Communica.ng?•  Whatsortofvisual?•  Morethanoneapproach?•  Extendable?

Page 54: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Maybe

•  Onerectanglehashalftheareaofanother.•  Wouldtheperimeteralsobehalf?•  Isitever?Usually?Omen?

Page 55: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Maybe

•  Createrectangleswherethenumberofcen.metresintheperimeterisveryclosetothenumberofcm2inthearea.

Page 56: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Maybe

•  Yourepresentanumberwithbasetenblocks.

•  Youusethreemorerodsthanflats.•  Youusetwofeweronesthanrods.•  Whatcouldyournumberbe?

Page 57: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Maybe

•  UsepaAernblocks.•  Createadesignthatis1/5blueand1/2green.

Page 58: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Maybe

Page 59: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Maybe

•  AngelaandBenbothhavecoins.•  Benhas2½.mesasmanycoins,butAngela’samountisworth8.mesasmuch.

•  Whatcoinsdoeachhave?

Page 60: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Maybe

•  Elizabethcanrun200min2[].[]seconds.Youcanchoosethenumbersintheblanks.

•  Howlongwouldittakeher,atthatrate,torun1000m?

Page 61: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Maybe

•  AgrowingnumberpaAernincludesthenumbers25and40somewhereinthepaAern.

•  HowlongwillittakeyourpaAerntoreach1000?

Page 62: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Meanandmedian

•  Themeanofasetof10numbersisdoublethemedian.

•  Whatmightthenumbersbe?

Page 63: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Visual

__________44____________Ifthemeanif8,thenthesumofthemissingnumbers=72

Page 64: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Represen7ngintegers

•  Youusesome+1.lesandfour.mesasmany–1.les.

•  Whatintegerscanyourepresent?Whichcan’tyou?

Page 65: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Visual

Page 66: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Horseproblem

•  Amanbuysahorsefor$50.•  Hedecideshewantstosellhishorselaterandgets$60.

•  Hethendecidestobuyitbackagainandpaid$70.

•  However,hecouldnolongerkeepitandhesolditfor$80.

•  Isheahead,behind,oreven?

Page 67: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Times

•  Howmany.mesina12hourperioddoesthesumofthedigitsonadigitalclockequal6?Trytothinkofawaytosolvethiswithoutgoingthrougheverysingle.me.Describewhatyoudid.

Page 68: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Legs

•  Alexbuildsstoolsandtables.•  Heused72legs.•  Hebuilt3morestoolsthantables.•  Howmanyofeach?

Page 69: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Somevideoproblems

•  hAp://threeacts.mrmeyer.com/sugarpackets/

•  hAp://mrmeyer.com/threeacts/cokevsprite/

Page 70: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Mathalicious

•  Anothersource•  Whatdoyouthink?

Page 71: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Wealwaysstartwithcurriculum

•  Let’slookatsomeoutcomesandseeifwecandevelopsomegoodproblems.

Page 72: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Gr1outcome

•..compareandordersetscontainingupto20elementstosolveproblems….

Page 73: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Problem

•  Youpar..onanumberintothreeparts.•  Onepartissmall.•  Onepartisabouttwiceasmuchasanotherpart.

•  Whatnumbercoulditbeandhowisitpar..oned?

Page 74: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Possibili7es

•  15as1,2and12•  13as1,4and8•  18as3,5,and10

Page 75: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Let’sconsolidate

•  Whatdowewanttobringout?•  Thatsmallisrela.ve•  Thattwiceasmuchisanumberaddedtoitself

•  Thatthesmallonecouldbethetwiceornot•  Thatthe3rdnumbercouldbetwicethesmalloneortwicethe2ndnumber.

•  HowtoaAacktheproblem

Page 76: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Grade2outcome

•  Demonstrateanunderstandingofaddi.onandthecorrespondingsubtrac.onby…

•  Crea.ngandsolvingproblemsthatinvolveaddi.onandsubtrac.on

Page 77: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Firsttrythis

•  Chooseanumber.•  Add20.•  Subtract4.•  Subtractthenumberyoustartedwith.•  Subtract8.•  Subtract3.

Page 78: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Whatshouldtheyno7ce?

•  Totalamountofsubtrac.onvsaddi.on•  Howsubtrac.ngtheoriginalnumbermadeitirrelevant

Page 79: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Anotheridea

•  Makeupatrickinvolvingatleast5stepssothatamerfollowingyoursteps,theresultisalways10.

Page 80: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Agrade3outcome

•  Demonstrateanunderstandingofmul.plica.onto5x5by…

•  Crea.ngandsolvingproblemsincontextthatinvolvemul.plica.on

Page 81: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Maybe

•  Inoneclassroom,therewas1morebookinthelibrarythaninanother.

•  Eachshelfineachlibraryheldthesamenumberofbooks.

•  Howmanyshelvesandhowmanybooksmighthavebeenineachclassroomlibrary?

Page 82: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Agrade4outcome

•  Demonstrateanunderstandingofareaofregularandirregular2-Dshapesby..

construc.ngdifferentrectanglesforagivenareainordertodemonstratethatmanyrectanglesmayhavethesamearea

Page 83: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Maybe

•  Tworectangleshadanareaof20cm2butonewastwiceaslongastheother.

•  Howisthatpossible?

Page 84: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Agrade5outcome

•  Demonstrateanunderstandingoffrac.onsbyusingconcreteandpictorialrepresenta.onsto

•  Comparefrac.onswithlikeandunlikedenominators.

Page 85: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Maybe

•  5/[]isalotmorethan12/[].•  Whatnumberscouldgointheblanks?

Page 86: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Agrade6outcome

•  Demonstrateanunderstandingofpercentconcretely,pictoriallyandsymbolically.

Page 87: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Maybe

•  Chooseanumberthanisabout25%ofonenumberbutabout75%ofadifferentnumber.

•  Whatisyournumber?•  Whatarethenumbersitis25%and75%of?•  Showthatyou’reright.

Page 88: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Agrade7outcome

•  Demonstrateanunderstandingofaddingandsubtrac.ngposi.vefrac.onsandmixednumbers,withlikeandunlikedenominators,concretely,pictoriallyandsymbolically

Page 89: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Maybe

•  Youaddtwofrac.onswithdifferentdenominators.

•  Thedenominatorofthesumwas5morethanthenumerator.

•  Whatfrac.onsmightyouhaveadded?

Page 90: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Agrade8outcome

•  solveproblemsthatinvolverates,ra.os,andpropor.onalreasoning.

Page 91: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Maybe

•  Aboxofcookiescosts1½.mesasmuchasapackageofmuffins.

•  Youboughtsomecookiesandsomemuffinsandpaid$43.

•  Howmanyofeachmightyouhaveboughtandatwhatprice?

Page 92: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Doyouwanttotry?

•  Createaproblemthatmeetsanoutcomeofyourchoice.

Page 93: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Now

•  Shareatyourtablethelessonyoureorganizedtofocusmoreonbigideasthanskills.

•  Yourtablewillchoose1or2lessonstosharewitheveryone.

Page 94: Developing calculaon and problem solving skills · 2015-11-25 · Background • Some of you expressed an interest in talking about developing beAer calcula.on skills. • Some of

Fornext7me

•  Let’sgoatitagain,butwithaslightlydifferentslant.

•  1)Useanopen-endedproblemthatyouthinkisvaluableforyourstudents.

•  2)Teachonecomputa.onlessonbasedonideas,butwhichprac.sesskills.

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