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Supportingyourchildinlearningmath

Marian Small

September,2017

Tonight I will talk about

• Howtheteachingofmathhasandhasnotchanged• Thingsyoucandotosupportyourchildʼsmathlearning

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Howdoyourememberlearningmath?

• Doyouhavegoodmemorieswhenyourememberlearningmathorlesshappyones?

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Whatmathskillsareimportantin2017andbeyond?

• Theworldhaschanged.• Wenowhaveeasyaccesstotoolsthatcandocalculations.• Whatweneedarepeoplewhoknowwhatcalculationstodoandpeoplewhocansolveproblems- bothgeometriconesandnumberones.

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Forexample…

• Imightwantayoungchildtofigureouthowmanycookiestomaketoshareeasilyamong4peoplecomparedtohowmanyfor5people.

• ThatmeansIneedmorethanbeingabletocompute15÷ 5or12÷ 4oncommand.

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There are 5 strands in K – 8

• Number• Geometry• Measurement• Patternsandalgebra• DataandProbability

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Most of you…

• are likely to be most concerned about number, so I will start there.

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Working with numbers

• Thewayweapproachthelearningofcomputationhaschangedinsomeways,butnototherways.

• Wewilldiscussboththehowandthewhy.

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Little number work

• Factsarethingslike4+8=12or7x4=28or12– 3=9or40÷ 5=8.

• Theyinvolvesmallnumbers.• Factsremainimportantbecausetheyarefundamentalbothtoestimationandanyothercalculations.

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We used to believe…

• Thebestwaytolearnfactsistositdownandmemorizethembysayingthemoverandover.

• Andthatbeingsuperfastwiththemisreallyimportant.

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Now we realize…

• thatachildisbetteroffifheorshehastoolstorecallsomethingheorshemayhavememorizedbutmayforget.

• Wecallthesestrategies.

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Forexample…

• Wheneveryouaddsomethingto9,whydon’tyou,instead,add1lessto10.

• e.g.9+8=10+7

• Later299+215=300+214.

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There is now research that shows…

• Thateventhoughsomekidsmemorizewell..• forkidswhoareanxiousaboutmathorgetnervoushavingtobequick,oldstrategiesdoomthemtofailure.

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There is now research that shows…

• Brainresearchshowsthatwhenyouareanxious,itisshorttermmemorythatisimpactedandthatiswherefactsarestored.(SianBellock)

• Weneedtoapproachfactlearningindifferentwaysfordifferentkids.

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So we teach principles and strategies

• Forexample,since8combinedwith5isthesameas5combinedwith8,weonlyhavetolearnhalftheadditionfacts.

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So we teach principles and strategies

• Forexample,since8combinedwith5isthesame8+2+3,itʼsreally10+3

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O O O O O

O O O X X

X X X

So we teach principles and strategies

• Forsomereason,welearndoublesquickly,sokidscanrelate3+4to(3+3)+1or(4+4)– 1.

• Or7+8to(7+7)+1or(8+8)– 1.

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So we teach principles and strategies

�Forexample,since4groupsof5canbeseenas5groupsof4,weonlyneedtomemorizehalfthemultiplicationfacts.

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So we teach principles and strategies

• Forexample,since4groupsof7canbeviewedas4groupsof5with4groupsof2,weknowthe7xtableifwecanlearnthe5xand2xtables.

o o o o o x xo o o o o x xo o o o o x xo o o o o x x

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Many of these principles can be..

• Seenonadditionandmultiplicationtables• visualizedusingmanipulatives

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Math tools

• 10-frames

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It’s easy to see why 9 + 9 = 10 + 8 (18).Just move one counter up.

InGrade7,

• Instead of learning a rule that to figure out 8 – (–3), you just add 8 and 3 because I told you to….

• Kids learn that 8 – (–3) is actually asking how many steps and in what direction you move if a temperature of –3 changes to a temperature of +8.

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8– (–3)

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–3 –2 –1 0 1 2 3 4 5 6 7 8

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Orinsteadoflearning

• The reason that ½ ÷ 1/5 = 5/2 is not because of a “flip and multiply” rule, but because when you try to fit 1/5 into ½, it fits 2 ½ (5/2) times.

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Accessing virtual manipulatives

• There are tools for materials your children use in class freely available on line.

• Many are also available as apps.

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Pattern Blocks

• http://oame.on.ca/CLIPS/swfPlayer.html?swfURL=tools/ubPatternBlocksToolCreator.swf

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Pattern Blocks

• APP: Pattern shapes

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Rekenrek

• http://oame.on.ca/CLIPS/swfPlayer.html?swfURL=tools/Rekenrek1.swf

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App

• NumberRack

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Hundreds chart

• http://nlvm.usu.edu/en/nav/category_g_2_t_1.html

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App

• InteractiveHundredchart

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Base ten blocks• https://www-

k6.thinkcentral.com/content/hsp/math/hspmath/na/gr3-5/itools_intermediate_9780547274058_/basetenblocks.html

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App

• Basetenblocksmath

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Relationalrods

• http://oame.on.ca/CLIPS/swfPlayer.html?swfURL=tools/ubRelationalRodsCreator.swf

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App

• Numberrods

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Fractionbars

• http://nlvm.usu.edu/en/nav/category_g_2_t_1.html

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OrApp:FractionTiles

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Colourchipsforintegers

• http://nlvm.usu.edu/en/nav/category_g_2_t_1.html

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Or

App:InteractiveIntegers

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Geometric shapes

• http://illuminations.nctm.org/Activity.aspx?id=3521

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What about computing with 2-digit or larger numbers• Thereisincreasinglymorefocusonestimationandmorefocusoncalculationusingstrategies,oftenmentally

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Adding on a 100 chart

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44 + 32

Subtracting on a 100 chart

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Alternative strategies that might seem new

• Howwouldyoucalculate342– 121?• Wouldyoudo200– 2thesameway?

• ChildrenarelearningdifferentstrategiessincedifferentonesaremoreefficientormoremeaningfulindifferentsituationsAND

• Differentonesmakemoresensetodifferentkids.

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For example

• Itisreasonableandcorrecttoaddlikethis:38

+4770

+1585

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For example

• Itisreasonableandcorrecttoaddlikethis:38+47

=38+50– 3=88– 3=85

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Or subtract like this...

• 100=99+1- 79- 79

20+1=21

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Orinintermediate

• How can you figure out 2/3 + 1/5?

• One way is to do what you learned about renaming this as 10/15 + 3/15 to get 13/15.

• But there are other ways

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Maybe

• You use a grid to show 2/3.

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Then

• Add1/5

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Thenrearrange

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Attention to estimation

• Intheworldtowardwhichwearemoving,technologywillberegularlyusedtocalculate,butwestillneedtoestimatetoseeifthoseanswersmakesense.

• Estimationmayactuallybemoreimportantthancalculation.

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Teaching through problem solving

• We show kids we have faith that they can figure things out.

• What happens is that as we solve a problem, we clarify a lot of ideas.

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I might ask…

• I bought something and gave the clerk $20.

• She gave me back one bill and 4 coins.

• How much might the item have cost?

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Imightask

• The volume of a cylinder is 100 cm3.

• What could the dimensions be?

• (It could be taller and narrower or shorter and wider or…)

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Youmightbewondering

• Is it good for kids to work together in math or should I worry about that?

• It is important for you to realize that most people learn better with an opportunity to talk to others, so itʼs good.

• There will always still be opportunities for individual accountability.

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Sometimes

• We might offer two tasks for students to choose from.

• The tasks will be similar in nature, although one might be slightly less complicated than the other.

• This allows students to build success but still learn about the “more complicated” problem as both are discussed together.

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Whatwillcomehome?

• Inthissortofenvironment,whatyouwillseecominghomeorshowingyouhowyourkidsaredoingwillbedifferent.

• Itmightbephotosofworkwithmanipulatives,recordingsoftheirsolutions,notworksheets.

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What can you do?

• Ourbigquestionasparentsiswhatwecandotohelpourchild.

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Number Play

Lots of children respond well to “magic”.For example:

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Number Play

} Choose a number.} Add it to itself.} Add 5 } Add 6.} Subtract 1} Divide by 2

Tell me your answer and I will tell you your number.

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How many….?

• Spoonsinthedrawer?• Stepstogetdownstairs?• Treesonthestreet?• Sectionsinanorange?• Windowsinthehouse?

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Interesting Questions

• Howlongislonghair?

• Howlongwouldittaketocountto100?

• Howfarcouldyougoin100steps?

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Support involves…

• Notshowing,butprobing.• Askingwhythisorwhythat…• Buildingconnections

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Youmight

• Encouragekidsto“teachyou”whattheylearnedorexplaintheirthinkingtoyou.

• Notworryaboutyourkidʼs“rank” butmoreabouttheirownsuccesswiththemaththeyarelearning

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Games

• Youcouldplaygameswhereyoumakeuptherulesoruseexistinggamestopractiseskills.

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Games to Play

• 2players• Eachrollstwodice.Thescoreisthesum.• Thefirstplayertogetto100wins.

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Games to Play

• 2players• Eachrollstwodice.Thescoreis2xonevalue+theother.• Thefirstplayertogetto100wins.

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Board games

like Equate

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Box cars and one eyed jacks

• http://www.boxcarsandoneeyedjacks.com/

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You could solve interesting problems

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How much is your name worth?

A B C D E F G H I1 2 3 4 5 6 7 8 9

J K L M N O P Q R10 11 12 13 14 15 16 17 18

S T U V W X Y Z19 20 21 22 23 24 25 26

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What words are worth 40 – 50?

A B C D E F G H I1 2 3 4 5 6 7 8 9

J K L M N O P Q R10 11 12 13 14 15 16 17 18

S T U V W X Y Z19 20 21 22 23 24 25 26

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Figure this

• http://www.figurethis.org

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Figure this

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Useful web sites

• http://www.dreambox.com/parent-resources

• http://www.cbc.ca/news/health/back-to-school-2015-parents-math-anxiety-can-pass-to-kids-psychologists-say-1.3207956

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Useful web sites

• https://www.edu.gov.on.ca/eng/literacynumeracy/parentGuideNumEn.pdf

•http://www.ocdsb.ca/med/pub/OCDSB_Publications/Numeracy%20Parent%20Guide.pdf

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What is success?

• Notjustamark• Enjoyingthemath• Makingsenseoftheworldusingmath• Buildingconnections

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You need to…

• Encouragekidsto“teachyou”whattheylearnedorexplaintheirthinkingtoyou.

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You need to…

• Showthatyouenjoymathtoo.• Showconfidence- believethattheycanifyougivethemthetim.• Emphasizegoodthinking,notspeed.• Emphasizethegoodthinking,notthemistakes.

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