Fractal Cutout Card - fractalfoundation.org · Students will make a 3-dimensional fractal cutout...
5
Fractal Cutout Card Fractals are SMART: Science, Math & Art! www.FractalFoundation.org Copyright 2015 Fractal Foundation, all rights reserved 1 Overview Students will make a 3-dimensional fractal cutout card by repeating a simple process of cutting and folding. They can turn their cutout into a fractal popup greeting card, decorate it artistically, and share the lessons of fractals with others. Although it is formed by a very different process, the resulting fractal shares much in common with the Sierpinski triangle fractal. Appropriate for: grades K – 12, college and adults Objectives • To gain skills in measuring, cutting and precision • To gain experience in understanding that repeating a simple processes over and over can create a complex object • To draw and identify lines and angles and classify shapes by properties of their lines and angles • To experience ratio and portion in action • To create and understand complex patterns in math • To express creativity in connection with math • To model with math and classify shapes by properties of their lines and angles • To look for and make use of structure Materials • 8.5” x 11” white paper • 8.5” x 11” card stock in contrasting color • Scissors • Glue stick • Rulers in centimeters (cm) • Cutout Card worksheet
Transcript of Fractal Cutout Card - fractalfoundation.org · Students will make a 3-dimensional fractal cutout...
FractalCutoutCard
FractalsareSMART:Science,Math&Art!www.FractalFoundation.org
Copyright2015FractalFoundation,allrightsreserved
1
OverviewStudentswillmakea3-dimensionalfractalcutoutcardbyrepeatingasimpleprocessofcuttingandfolding.Theycanturntheircutoutintoafractalpopupgreetingcard,decorateitartistically,andsharethelessonsoffractalswithothers.Althoughitisformedbyaverydifferentprocess,theresultingfractalsharesmuchincommonwiththeSierpinskitrianglefractal.Appropriatefor:gradesK–12,collegeandadultsObjectives
• Togainskillsinmeasuring,cuttingandprecision• Togainexperienceinunderstandingthatrepeating
asimpleprocessesoverandovercancreateacomplexobject
• Todrawandidentifylinesandanglesandclassifyshapesbypropertiesoftheirlinesandangles
• Toexperienceratioandportioninaction• Tocreateandunderstandcomplexpatternsinmath• Toexpresscreativityinconnectionwithmath• Tomodelwithmathandclassifyshapesbypropertiesoftheirlinesandangles• Tolookforandmakeuseofstructure
Materials • 8.5”x11”whitepaper• 8.5”x11”cardstockincontrastingcolor• Scissors• Gluestick• Rulersincentimeters(cm)• CutoutCardworksheet
FractalCutoutCard
FractalsareSMART:Science,Math&Art!www.FractalFoundation.org
Copyright2015FractalFoundation,allrightsreserved
2
CommonCoreStandardsforMathematics
CommonCoreStandardsforEnglishLanguageArts
Code Standard Grade Code Standard GradeCC CountingandCardinality K NF NumberandOperations
–Fractions4
NBT NumberandOperationsinBaseTen
K,1 NS NumberSystem 6
OA OperationsandAlgebraicThinking
K–5 RP RatiosandProportionalRelationships
6,7
MD MeasurementandData K–5 SP StatisticsandProbability 6–8G Geometry K–8
Code Standard GradesK–5 Grades6–8 Grades9–12RL Reading:Literature 1,4,7,10 1,4,7,10 1,4,10RI Reading:
InformationalText1,3,4,7,10 1,3,4,7,10 1,3,4,10
FS FoundationalSkills 1,2,3forgradesK–1;3and4forgrades2–5
Noneavailable Noneavailable
W Writing 2,3,8;4forgrades3–5 2,3,4 2,3,4,9SL Speakingand
Listening1,2,3,4,5,6 1,2,3,4,5,6 1,2,3,4,5,6
L Language 1,4,6;3forgrades2–5 1,3,4,6 1,3,4,6RST Scienceand
TechnicalSubjectsNoneavailable 1,3,4,6,7,10 2,3,4,6,7,10
FractalCutoutCard
FractalsareSMART:Science,Math&Art!www.FractalFoundation.org
Copyright2015FractalFoundation,allrightsreserved
3
InstructionsTherearethreeelementstomakingthefractalcutout.Theyarerepeatedoverandoverusingasmallerscale.Thesethreeelementsare1)cutting,2)foldingand3)inverting.
Takeonepieceofpaper,holdithorizontalandthenfolditinhalf,soitlookslikeabook.
1) Cutthroughthefoldededgealongthedottedlineabove.Thecutshouldstarthalfwayupanddownthefoldandgohalfwaytotherightalongthefoldedpaper.
2) Nowfoldoveronehalfandcrease,asshownabove.3) Openupthefolded-overcreasedflap,andfolditinsideitself.Invertingisalittle
tricky,butcritical.Youhavenowcompletedthebasicsteptocreatethefractalcutout,andnowallyouhavetodoiskeeprepeatingthisprocessoverandover.Note:Youdonotneedtobeexact,butestimatethehalfwaypointsascloselyasyoucan.Olderstudentswillgenerallybemoreaccurate,andtheresultingfractalstheymakewillendupmoreuniform.
4) Next,maketwocutshalfwaythrougheachofthefoldededges,atthedottedlines.Thecutswillbehalfaslong,andagainthecutsshouldbehalfwayupanddowneachedgeandgoonlyhalfwaythroughthepiece.Becarefulnottocuttoofar!
1 32
FractalCutoutCard
FractalsareSMART:Science,Math&Art!www.FractalFoundation.org
Copyright2015FractalFoundation,allrightsreserved
4
5) Onceyou’vemadethetwocuts,foldoverandcreasetheflaps.Howcanyoutell
whichonestofoldover?Youwanttoendupwithsomethinglookinglikeastaircase.
6) Next,youunfoldtheflaps,andinvertthem.Whenyouopenupthepaper,itshouldlooklike6.
7) Repeatthesamecutting,foldingandinverting,butthistimeyouneedtomakefour
cutsinsteadoftwo.Foldandfliptheflapsinsidethemselveslikebelow.
8) Repeatthisagain,makingeightcutstotaltohaveyourfinalproduct.
4 65
7 8
FractalCutoutCard
FractalsareSMART:Science,Math&Art!www.FractalFoundation.org
Copyright2015FractalFoundation,allrightsreserved
5
Chooseapieceofheavierpaperinadifferentcolor,andfolditinhalf.Placethefractalcutoutinsideit,likethepagesofabook.Openitgently,andapplygluetothesolidareasofthefractalcutout,andthenglueitinplaceinsidethefoldedouterpaper.
Trydifferentcuttingpatterns,suchastheonesbelow.
