![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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/1.jpg)
Developingcalcula.onandproblemsolvingskills
MarianSmallNovember,2015
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Background
• SomeofyouexpressedaninterestintalkingaboutdevelopingbeAercalcula.onskills.
• SomeofyoutalkedaboutdevelopingbeAerproblemsolvingskills.
• Todayisamix.• Wewillalsoblendintheac.vi.esyoutriedandarerepor.ngon.
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Let’sstartwith…
• Someexamplesofopenques.onsyouusedthatwentwell.
• Talktothepeopleatyourtable.• Thetablewillchoosetwotopresenttoeveryone.
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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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/5.jpg)
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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/6.jpg)
BUT
• Weneedflexibilitywhichcomeswithunderstandingandnotjustinstantaneousresponses.
• InyourMinistrydocuments,thereismen.onmadeofstrategieslikeMaking10,Usingdoubles,AddingtoSubtract,etc.
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Addi7on/subtrac7onissues
• Everysubtrac.oncanbesolvedusingaddi.on.
• Howwouldyousolve13–8thisway?
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Addi7on/subtrac7onissues
• Orderdoesn’tmaAer.
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Addi7on/subtrac7onissues
• Youcanaddorsubtractinparts.• Youcan“juggle”whenyouadd.
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Addi7on/subtrac7onissues
• Youcanuseaconstantdifferencewhenyousubtract.
• Addingorsubtrac.ng0isespeciallyeasy.• Addingorsubtrac.ng1ispreAyeasy.
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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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/12.jpg)
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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/13.jpg)
ButIwouldalsoask
• Showme10andshowme12sothat:• Eachisshownintwoparts.• Onepartfor10isthesamesizeasonepartfor12.
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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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/15.jpg)
ButIwouldalsoask
• Predicthowmuchmore8+3isthan6+2withoutgeengtheanswers.
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Addi7onandsubtrac7onprocedures
• Howwouldyouusebasetenblocksfor:• 35+48• 76+99• 81–17• 241–167
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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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/18.jpg)
Mul7plica7onanddivisionconcepts
• Orderdoesn’tmaAer
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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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/20.jpg)
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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/21.jpg)
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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/22.jpg)
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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/23.jpg)
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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/24.jpg)
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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/25.jpg)
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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/26.jpg)
Whataboutfrac7ons?
• Howdoyoumodel• 2/3+1/5• 2/3–1/5• 2/3x1/5• 2/3÷1/5
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2/3+1/5
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2/3+1/5
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2/3+1/5
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2/3–1/5
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2/3–1/5
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2/3–1/5
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2/3x1/5
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2/3x1/5
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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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/41.jpg)
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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/42.jpg)
Nowforproblemsolving
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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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/44.jpg)
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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/45.jpg)
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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/46.jpg)
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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/47.jpg)
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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/48.jpg)
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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/49.jpg)
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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/50.jpg)
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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/51.jpg)
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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/52.jpg)
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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/53.jpg)
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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/54.jpg)
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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/55.jpg)
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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/56.jpg)
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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/57.jpg)
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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/58.jpg)
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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/59.jpg)
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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/60.jpg)
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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/61.jpg)
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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/62.jpg)
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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/63.jpg)
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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/64.jpg)
Represen7ngintegers
• Youusesome+1.lesandfour.mesasmany–1.les.
• Whatintegerscanyourepresent?Whichcan’tyou?
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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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/66.jpg)
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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/67.jpg)
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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/68.jpg)
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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/69.jpg)
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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/70.jpg)
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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/71.jpg)
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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/72.jpg)
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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/73.jpg)
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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/74.jpg)
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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/75.jpg)
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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/76.jpg)
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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/77.jpg)
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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/78.jpg)
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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/79.jpg)
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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/80.jpg)
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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/81.jpg)
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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/82.jpg)
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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/83.jpg)
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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/84.jpg)
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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/85.jpg)
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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/86.jpg)
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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/87.jpg)
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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/88.jpg)
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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/89.jpg)
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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/90.jpg)
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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/91.jpg)
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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/92.jpg)
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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/93.jpg)
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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/94.jpg)
Fornext7me
• Let’sgoatitagain,butwithaslightlydifferentslant.
• 1)Useanopen-endedproblemthatyouthinkisvaluableforyourstudents.
• 2)Teachonecomputa.onlessonbasedonideas,butwhichprac.sesskills.
![Page 95: 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](https://reader034.vdocuments.mx/reader034/viewer/2022042322/5f0c07147e708231d43364f5/html5/thumbnails/95.jpg)
Download
• www.onetwoinfinity.caLouisRiel2