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Kenora K-3

Marian SmallNOVEMBER 2018

agenda

• TeachingwithIntention• ConsolidatingwithIntention• Automaticity

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A problem

• Use20counters.• Createthreegroupsasequalasyoucan.• Tryagainwith24counters.

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The idea

• Somenumberscanbemadeintoequalgroupsofagivensizeandsomecannot.

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Another problem

• Use24counterstomaketwogroups,butonegroupisdoubletheother.

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The idea

• x+x+xcanberegroupedinto2x+x..OR• Aratioof2:1canbeshowninmanyways.

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Now

• Use20counterstocreatethreegroups.• OneisSUPERBIGandtheothertwohavetobelittle.

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The idea

• Youcanalwaysdecomposeanumberintopartswhereonepartismostofthenumber.

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OTHER EXAMPLES

• Gr1:skipcounting

These are ideas I care about

• Youskipnumberswhenyoudon’tcountby1s,andthereisapatterntohowyouskip.

These are ideas I care about

• Ifyouskipcountbyabiggernumber,yougethigherfaster.

Grade 2

• Representinghalvesandfourths

Ideas I care about

• Afourthisalwayshalfofahalf.• Ifyouhaveahalf,it’seasytoshowafourth.• Ifyouhaveafourth,it’seasytoshowahalf.

Ideas I care about

• Ahalforafourthcanbealotoralittle.• Afourthofonethingcanbemoreorlessthanhalfofanother.

Another topic

• Measuringlengthusingnon-standardunits

Ideas I care about

• Ifyouusealittlerunit,youneedmoreofthem.• Whatunitmakesmostsensedependsonsizeofobject,sizeofunit,andpurpose.

Positional vocabulary

• Oftenthesewordscomeinpairs,e.g ifAisaboveB,thenBisbelowA.• IfAisinfrontofB,thenBisbehindA.

SUBTRACTING

• Studentsrealizethatsubtractionmeansdifferentthings,e.g.whenmightyouthink12– 5.

More ideas

• Everysubtractionisa“secret”addition.• Theanswerwhenyousubtractcanbemoreorlessthanwhatyousubtracted.

More ideas

• Ifyousubtractalittle,thenumberdoesnotchangealot.

Now you try

• Chooseanexpectation.• Whatideasdoyouwanttocomeoutofit?

consolidating

• Afterkidsdoanactivity,teachersneedtopullittogetherandaskquestionsthatfocusonbringingoutideas.

algebra

• Theactivity:• Use2differentcolours ofcubesononesideofthebalance.• Use2othercolours ofcubesontheothersideofthebalance.• Makesurethereisabalance.

algebra

• Writeanadditionequationthatdescribesthebalance.

• Repeatwithotheramountsofcubes.

To consolidate

• Ipostsomeoftheequationsstudentshavecreatedandaskkidstonoticethings.

I ask

• Ifyoulinedupallthecubesontheleftandthenallthecubesontheright,whatwouldhappen?

I ask

• Supposeonesidehad6redandsomeyellow.• Theothersidehad8blueandsomegreen.• Weretheremoreyelloworgreen?Howdoyouknow?

I ask

• Supposeonesidehad3redandsomeyellow.• Theothersidehad1blueandsomegreen.• Weretheremoreyelloworgreen?Howdoyouknow?

I ask

• Whywereyourequationsadditionequations?

It might be about place value with tens and onesMyactivitymightbetoprovidebasetenrodsandones.

Iaskthemtoaccomplishthesetasks:

It might be about place value with tens and ones- Represent23with5blocks.- Represent23with23blocks.- Represent23withadifferentnumberofblocks.

I might ask

Yourepresented23with5blocks.What2-digitnumbercouldyouhaverepresentedwith6blocks?

I might ask

Whatifyouhadrepresented65?Wouldtherebemoreorlesswaystodothatthantodo23?Why?Howcouldyoudo65with20blocks?With29blocks?

I might ask

Whatisthemostnumberofblocksyoucouldusetoshow65?Theleastnumber?Why?

money

• Iwantkidstorealizethatyoucanrepresentamountsofmoneyindifferentwaysandthatyouneedmorepiecesofmoneyiftheirvaluesarelower.

Task might be

Chooseanamountofmoneybetween$20and$30.RepresentitusingaLOTofbillsorcoins.ThenrepresentitusingNOTMANYbillsorcoins

Task might be

Repeatwithoneotheramountofmoney.

To consolidate

Whothinkstheyrepresentedtheiramountusingfewerpiecesofmoneythananyoneelseintheroom?Whydoyouthinkitcouldbeyou?

To consolidate

Whothinkstheyrepresentedtheiramountusingoneofthemostpiecesofmoneyintheroom?Whydoyouthinkitcouldbeyou?

To consolidate

Supposeyouhadusedonlydimes.Wouldyouusealotofcoinsornotmany?

•Supposeyouhaduseda$20bill.Couldyoustillhaveusedalotofpiecesofmoney?

I would ask

Whendoyouusealotofpiecesofmoney?Whendon’tyou?

geometry

Makeapatternblockdesignthatfollowstheserules.•Thereissymmetry.•Thereare4moreyellowblocksthanblueones.•Thereareasmanyblueasredblocks.

What would you ask?

• Howdoyouknowthereissymmetry?•Istheredareabiggerortheblue?Theyellowortheblue?•Couldtherebeanevennumberofblueblocks?Anoddnumber?

What would you ask?

• Ifthereareonlytwoblueblocksinthedesign,couldonebeclosetothelineofsymmetryandonefarfromit?

Your turn

• Thinkofanactivitythatfocusesononeoftheseideas:

Idea choices

• Lotsofstrategiesyoucanusetoadd• Lotsofpatternsmightincludesomeofthesamenumbersorshapes• Centimetres vsmetres

now

• Thinkofanactivity,butfocusonhowtoconsolidate.

automaticity

• Whatcomputationsdoyouthinkkidsshouldbefastat?• Howfast?Thesameforall?

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