A Games-based, Strategy-focused Fluency Plan

A Games-based, Strategy-focused

Fluency Plan

Jennifer Bay-Williams

University of Louisville

@JBayWilliams

To have with you for tonight’s webinar: ü Deck of Cards ü  2 dice (6-sided or 10-sided) ü Games Recording Sheet ü  This powerpoint with Game Boards

Revisiting the

5 Fundamentals

Procedural fluency is “skill in carrying out procedures flexibly, accurately, efficiently and appropriately”

(CCSSO, 2010, NCTM, 2014, NRC, 2001)

Bay-Williams, J. M. & Kling, G. G. (in press). Math Fact Fluency: 60+ Games and Assessment Tools to Support Learning and Retention. Alexandria, VA: ASCD.

AdditionFactsMasteryChartFlexibleLearningProgression

+/-0,1,2

Doubles Combosof10 10+___

NearDoubles Making10Pretend-a-10

AdditionFactsMasteryChart

FlexibleLearningProgression:FoundationalFacts

+/-0,1,2


FoundationalFactSets

DerivedFactStrategies

Bay-Williams, J. M. & Kling, G. G. (in press). Math Fact Fluency: 60+ Games and Assessment Tools to Support Learning and Retention. Alexandria, VA: ASCD.

Mastering Basic Facts

Based on Baroody, 2006

Use Quick Looks: A Progression

¡ Quick Looks

¡ Quick Looks + Equations

¡ Equation and “Imagine” a Quick Look

¡ Explicitly encourage selected strategies

ü Are engaging.

ü Provide opportunities for strategy discussion and assessment.

ü Should be sequenced developmentally (for example, playing combinations of ten games before exploring making ten strategies).

ü Can be targeted practice or general practice.

ü Lend to differentiation.

ü Are targeted toward a single strategy, fact group or set of reasoning strategy

ü Do not have time-pressure as an element of the game.

ü Have each student in the group solving different problems.

ü Lend to talking about the possible strategies.

SQUARES

Fill your game board with these squares: 0, 1, 4, 9, 16, 25, 36, 49, 64, 81 •  Yes, use a number more than once. •  One a turn, you can only cover ONE

number.

Reflecting on the Game

①  Which fact sets are supported?

②  Which strategies are supported?

③  Is it aimed at fundamental facts? Derived fact strategies? Or both?

④  How might the game be adapted?

BINGO

Free






Lucky 13 GamesforBasicFactStrategyDevelopment

GamefromBay-Williams,J.M.,&Kling,G.G.(inpress).Math Fact Fluency: 60+ Games and Assessment Tools to Support Learning and Retention. Alexandria, VA: ASCD.

Lucky13

Materials:Deckofcardswithnumbers0–10(Ace=1,Jack=0),

Players:2-4Players

HowtoPlay:1. Eachplayerturnsover5cards.

2. Eachplayerselects2cardswhich,whenaddedtogether,produceasumasclosetoLucky13aspossible.

3. PlayersfindhowfartheirtotalisfromLucky13andrecordthat

difference(e.g.,ifthetwocardsaddto11,thescoreis2because

11is2awayfrom13).

4. Playersdiscardthetwocardsthatwereusedanddrawtwonewcards.

5. Repeatfor5rounds.

6. Lowestscorewins!

PossibleAdaptations:ChangetheLuckyNumber;Use3addends(3cards

each);Finddifference(luckynumbercanbesmall,like3);Multiplication

(similarrulestothese).

Rectangle Fit (Tetris)

Rectangle Fit

You need:

q  Empty Grid

q  2 Dice

RectangleFitMaterials:Twodice;MultiplicationTetrisGameBoardorcentimetergridpaper(oneperstudent)(1or2centimeterpapercanwork).

Players:WholeClass

HowtoPlay:

1. Theteacher(orselectedstudentleader)rollstwodice.

2. Eachstudentdecideswhereontheirgameboardtoshadearectangle of the dimensions rolled. For example, if theleader rolls 4 and 6, each student decides where and inwhat orientation they can best fit a 4-by-6 rectangle ontheirgridpaper.

3. Students record the related multiplication fact inside therectangle.

4. Theleadercontinuestoroll,andstudentsfillinarectanglewiththosedimensionssomewhereontheirgameboard.

5. Whenastudentcannotfitarectanglewiththedimensionsrolled,theyareoutofthegame.

6. Thelaststudentsinthegamearethewinners.

PossibleAdaptations:Use10-sideddiceandagameboardwithmoreunitsquares.

GamefromBay-Williams,J.M.,&Kling,G.G.(inpress).Math Fact Fluency: 60+ Games and

Assessment Tools to Support Learning and Retention. Alexandria, VA: ASCD.






RectangleFitGameBoard(6-SidedDice)



Double to

Connect 4

You need:

q  Game board

q  10 Sided Die or Deck of Cards

q  Optional: 2 colors of chips

GamesforBasicFactStrategyDevelopment


DoubletoConnect4

Materials:Deckoftenframecardsorplayingcardswithnumbers1–10

(Ace=1,removefacecards);twodifferentcolored/shapedobjectsto

covergameboard(10-20perplayer);DoubletoConnect4GameBoard

(onepergroup).

Players:Partners

HowtoPlay:1. Eachpartnerhasadifferentcoloredchiptocoverboard,or

partnersdecidewhowillbeXsandwhowillbeOs.

2. Partnerstaketurns.Ontheirturn,theyflipoveranumbercardand

doublesthevalueofthecard.

3. Playerplacestheircolorchip(oranXorO)ononetheGameBoard

onthatdoublevalue(e.g.,ifplayerturnsupa6,theychoosewhich

12theywanttocover).

4. Playerstrytogetfouroftheirowncolor(mark)inarow.Foreach

Connect4(column,rowordiagonal),playersscore5points.

5. Optional:Winnerisfirstplayertoscore20.

PossibleAdaptations:Useseparategameboards;Connect3(or5)

ratherthan4;Haveplayerssaythesumand/ortheproduct.






Double to Connect 4


Fishing for 10s

You need:

q  Deck of Cards



FishingforTens

(adaptedfromInvestigationsinNumber,Data,andSpace,2008)Materials:Tenframecardsordeckofcardswithnumbers0–10(Ace=1,

Jack=0,removeotherfacecards),

Players:2-4Players

HowtoPlay:1. Thisisplayedlikethecardgame“GoFish,”onlyinsteadoflooking

formatchingcards,amatchisacombinationoften.

2. Deal5cardstoeachplayer.

3. Taketurns.Onaplayersturn,askforacardthatmakesatenfora

cardinyourhand.Forexample,ifyouhavea4,askanotherplayer

“Doyouhavea6?”

Ø Ifyes,theplayergivesyouthecardandyouhaveamatch.

Ø Ifno,theplayersays‘GoFish.’

4. Drawacardfromthedeckanditisthenextplayersturn.

5. Playuntilallcardsareused.

Optional:Playersrecordequationsforthepairstheygot.






Fishing for 10s

One More

Cover It

You need:

q  Game Board

q  Die

q  Chips to cover board.



OneMoreCoverIt

Materials:Numbercubeorstackofcards,numbered1-6;Counters(25perplayer);OneMoreCoverItBoard(oneperplayer)Players:PartnersHowtoPlay:

1. Eachpartnerhasadifferentcoloredchiptocoverboard.

2. Partnerstaketurns.Eachplayerrollsthenumbercubeandcoversasquarethatisonemorethanwhatwasrolledonthenumbercube.

3. Playerstrytocoveracompletecolumn,rowordiagonal.

4. Optional:Theplayerwhofirstgetsacolumn,rowordiagonalwins.

PossibleAdaptations:Ratherthanrows,columns,diagonals,makeasquare(2by2);Coverall;AdaptgameboardtoOneLess,TwoMore,orTwoLess.Withany/alladaptations,use10-sideddice.






One More Cover It

Crossed Wires

You need:

q  Two Dice

q  Blank Paper



CrossedWires(basedonBritt,2015)

Materials:Numeralcardsorplayingcardswithnumbers0-5(Ace=1,Jack=0,other

cardsremoved);CrossedWiresRecordingSheet.Players:PartnersHowtoPlay:

1. Shufflethecardsandplacethemfacedown.

2. Eachplayertakesonecardfromthedeck.Thistellsthemhowmany

horizontallinestodrawontheirpaper.Forexample,player1maydrawa3,

sodrawsthreelines:

3. Eachplayerdrawsasecondcardanddrawsthatmanyverticallines,Creating

crossed“wires”.Forexample,player1drawsa4ontheirseconddraw:

4. Eachplayerdetermineshowmanycrossedwirestheyhave(pointsof

intersection)andrecordstheproductonarecordingpage.[Note:A0on

eitherdrawleadsto0pointsofintersection]Player1has12crossedwires:

5. Play8rounds.Thewinneristheonewiththemosttotal

intersections.






Crossed Wires

Product

Pile-Up

You need:

q  Cards


ProductPile-Up(adaptedfromBelletal.,2016)

Materials:Playingcardswithnumbers0-10(Ace=1,Queen=0,

otherfacecardsremoved)

Players:3-4Players

HowtoPlay:

1. Eachplayerisdealt8cards.2. Theplayertotheleftofthedealerbeginsbyplayingtwo

cardsandsayingoutloudtheproductofthosetwocards.

3. Thenextplayer(totheleft)mustplaytwocardsthathave

aproducthigherthantheproductjustshared.Playcontinuesaroundthegroupinthismanner.

4. Ifaplayercannottoptheproductjustplayed,heorshedrawstwocardsfromthedeckandtriesagaintocreatea

higherproduct.Ifheorsheisstillunabletocreateahigher

product,theplayersays“pass”andplaymovestothenext

player.

5. Onceallplayershavetopass,theplayerwhoplayedthelastsetofcards(thehighestproduct)getstostartanew

round,selectinganytwocardsfromtheirhand.

6. Thefirstplayertousealltheircardsisthewinner.PossibleAdaptations:Changetolowestproduct;Usedivision.






Product Pile Up

6 2

7 2

5 4

Fixed

ADDEND WAR

You need:

q  Cards



FixedAddendWar

Materials:Playingcardswithnumbers0-10(Ace=1,Queen=0,otherfacecardsremoved)

Players:Partners

HowtoPlay:

1. Identifyanaddend(e.g.,9)andplaceacardwiththatnumberfaceupinthemiddle.

2. Dealtherestofthecardsequally,facedown.

3. Atthesametime,partnersturnuptheirtopcardandsaythesum.

4. Eachpartnertakesturnssayingtheirfulladditionequation,andhowtheyadded.Bothdecideifsumsarecorrect.

5. Theplayerwiththelarger(correct)sumgetsthecards.

6. Ifthereisatie,itisa“war”andpartnersrepeatsteps3–5.

7. Optional:Playforasettime;playerwiththemostcardswins.

PossibleAdaptations:Usenumeralcards;Havestudentskeepalogoftheirsums.






Fixed Addend War

8

Fixed

ADDEND WAR

You need:

q  Cards



FixedAddendWar

Materials:Playingcardswithnumbers0-10(Ace=1,Queen=0,otherfacecardsremoved)

Players:Partners

HowtoPlay:

1. Identifyanaddend(e.g.,9)andplaceacardwiththatnumberfaceupinthemiddle.

2. Dealtherestofthecardsequally,facedown.

3. Atthesametime,partnersturnuptheirtopcardandsaythesum.

4. Eachpartnertakesturnssayingtheirfulladditionequation,andhowtheyadded.Bothdecideifsumsarecorrect.

5. Theplayerwiththelarger(correct)sumgetsthecards.

6. Ifthereisatie,itisa“war”andpartnersrepeatsteps3–5.

7. Optional:Playforasettime;playerwiththemostcardswins.

PossibleAdaptations:Usenumeralcards;Havestudentskeepalogoftheirsums.






Fixed Addend War

8

Finding 5s

You need:

q  Cards (only 0 – 5)



FindingFive

Materials:Deckoftenframecards,usingonlycards0–5Players:PartnersHowtoPlay:

1. Spreadthecardsoutfacedown(likeconcentration)

2. Eachpartnertakesaturn.

3. Ontheirturn,apartnerturnsovertwocardsandaddsthenumberstogether,sayingtheequation(Forexample,ifa2anda5areturnedup,say“2plus5equals7.”

4. Ifthetwocardsdonotequal5,theyareturnedbackupsidedown.Ifthetwocardsdoequal5,theplayerkeepsthepair,faceup,asonecombinationthatmakes5.

5. Playuntilallcardsaregone.

6. Theplayerwiththemostcombinationsisthewinner.

PossibleAdaptations:Usenumeralcards;Usedotcards;ChangetoFindingTen(orothertotal).






Finding 5s

Subtraction

Stacks

You need:

q  Game Board

q  10 Counters

q  2 Dice

SubtractionStacks

Materials:Twodice;Counters(10perplayer);SubtractionStacksPlayCard(orsimilarsketchinanotebook)Players:2-4PlayersHowtoPlay:

1. Eachplayercountsout10counters.

2. Eachplayerplacesthe10countersontheSubtractionStacksPlayCardwherevertheywanttoplacethem,asillustratedhere.

0 1 2 3 4 5

3. Onaplayersturn,theyrollbothdice,andfindthedifferencebetweenthetwonumbers.

Ø Ifthedifferenceis2,theplayerremovesacounterfromthe2stack.

Ø Iftheplayerhasnothingintheir2stack,nocounterisremoved.

4. Theplayerwhoremovesalloftheircountersfirstisthewinner.

PossibleAdaptations:Changetosums(usecardswithhighernumbers);Use12-or10-sideddiceandadaptgameboard,andgivemorechipsperplayer.


①  Which fact sets are supported? ②  Which strategies are supported? ③  Is it aimed at fundamental facts? Derived fact

strategies? Or both? ④  How might the game be adapted?

Subtraction Stacks

Factor Game

You need:

q  Game Board

q  Optional: Counters to cover

TheFactorGame

Materials:FactorGameBoard(to30orto49);Pencilorcounterstomarkout/coverspaces.

Players:Partners

HowtoPlay:

1. Player1choosesanumberonthegameboardandmarksit/coversit.ThiswillbePartner1’sscoreforRound1.Forexample,ifPlayer1selects15,theyget15points.

2. Player2marks/coversalltheproperfactorsofPlayer1’snumber.Partner2addsallofthefactorstheyfound.ThisisPlayer2’sscoreforRound1.Forexample,ifPlayer1selects15,Player2maytake1,3,and5,scoring9points.

3. Player2goesfirstforRound2,selectingavaluethathasnotbeentaken.Player1thengetsallthefactorsoftheselectednumber(thathavenotyetbeencrossedout).

Note:Ifplayer2marks/coversanumberthathasnofactorsleftontheboard,player1gets0points.

4. Playcontinuesinthismanner,withplayerstakingturnsselectingvaluesandtheotherplaying‘collecting’availablefactors.

5. Thegameendswhenallnumbersaretaken.

6. Playerssumtheirtotalsfromeachround;theplayerwiththelargersumwins.






Factor Game – V1

Right-Price

Game

You need:

q  Cards

q  2 Dice



TheRightPriceGame

Materials:Twodice,deckofplayingcardswithfacecards

removed(ace=1)

Players:2-4Players

HowtoPlay:1. Dealsixcardstoeachplayerandplacetherestfacedown

inadrawpile.2. Thefirstplayerrollsthetwodiceandusesthetwo

numberstodecideaprice.(Forexample,a2anda5canbe$25or$52.)

3. Theotherplayersusethecardsintheirhandtoformamultiplicationfactthatcomesasclosetothepriceaspossiblewithoutgoingover.

4. Theplayerwiththeclosestproductscores12points.Ifthereisatie,theplayersdividethepointsevenly.

5. Usedcardsarediscarded,andnewcardsaredrawn.Continueplayuntilthedeckisgone.

6. Theplayerwiththehighestscorewins.PossibleAdaptations:Dealadifferentnumberofcards;Usetwo10-sideddicetodetermineprices.






Right-Price Game

TRIOS

You need:

q  Game Board

q  Optional: 2 colors of counters to cover



TRIOS

Materials:Deckofcardswithfacecardsremoved(ace=1,Q=0),one5×5gameboardwithamultipleof5ineachsquare,15countersinonecolorand15inanothercolor(ortwocolorsofmarkers,ifthegameboardislaminated)Players:PartnersHowtoPlay:

1. Giveeachplayerasetofcounters(onepersonhasonecolor,the

othertheothercolor).

2. Taketurnsrollingthedie(orchoosingacard),

3. Onyourturn,multiplyyournumberby5,andplaceoneofyour

countersonanysquarewiththatproduct.

4. Theobjectistocoverthreespacesinarow(horizontally,vertically,

ordiagonally)withthesamecolor.And,yourobjectistotryto

blockyourpartnerfromgettingthreespacesinarow!

5. Eachsuccessfultrioisfivepoints.Thepersonwiththehighestscore

wins.

PossibleAdaptations:Changethesizeofthegameboard;changethemultiplesontheboardforotherfactsets;changetoFourinaRow.






TRIOS

Salute! ¡  Form a Group of 3 and Identify a

‘Leader’

¡  The other two players, without looking at your card, place it on their forehead facing outward (so the others can see it).

¡  The leader says the product (sum) of the two cards.

¡  The other two players determine the value of the card on their forehead.

¡  Both players share how they determined their number. The player who was fastest, keeps the cards.

¡  Rotate so that one of the players is now the leader.

Strategy Games

Multiplication Games: •  Squares Bingo •  Trios •  Rectangle Fit •  Crossed Wires •  Product Pile-Up •  The Factor Game •  Right Price Game •  Salute

Addition Games: •  Lucky 13 •  Finding 5s •  One More Cover It •  Fishing for 10s •  Double to Connect 4 •  Fixed Addend War •  Subtraction Stacks •  Salute

Strategy Games

AdditionFactsMasteryChartFlexibleLearningProgression

+/-0,1,2


NearDoubles Making10Pretend-a-10

AdditionFactsMasteryChart

FlexibleLearningProgression:FoundationalFacts

+/-0,1,2


FoundationalFactSets

DerivedFactStrategies

Multiplication Games: •  Squares Bingo •  Trios •  Rectangle Fit •  Crossed Wires •  Product Pile-Up •  The Factor Game •  Right Price Game •  Salute


Strategy Games Multiplication Games: •  Squares Bingo •  Trios •  Rectangle Fit •  Crossed Wires •  Product Pile-Up •  The Factor Game •  Right Price Game •  Salute


Strategy-Focused Game Play: Aligning strategies with games Fact Set: Multiply by 4s

Strategy: Double and Double Again

Game(s): Bingo, Trios, Connect 4, and/or Fixed-Factor War

PreTeach/Number Talk: Quick Looks with double and double again combinations

Questions to Ask While Playing Basic Facts Games : How did you figure it out? Can you share how you thought about it in your head? Is there another way you could figure it out? What is another fact that could be solved with that strategy? If someone didn’t know the answer to ____, how would you tell them to figure it out?

Questioning During Game Play: Focus

on Strategies!

Name

Bowl-a-Fact

7 8 9

2 3

10 4 5

1

6

1st Roll (for Strike): _________ _________ __________

2nd Roll (for Spare): _________ _________ __________

3rd Roll (for Score): _________ _________ __________

Equations:

Scoring: Strike: 100 points Spare: 75 points Score: Sum of all ‘taken’ facts

My Score: ________________________

ACTIVITY PAGE Copyright © 2019 Pearson Education, Inc. All rights reserved.


①  How might the game be adapted?

②  How might you use this game?

Which game(s) will you use (and

for which fact sets/strategies)?

NCTM Articles

ASCD

A Games-based, Strategy-focused Fluency Plan

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