Exploringgeometricsolids-Teachernotes

ExploringGeometricSolids-TeacherNotes

Mathematical Goals:Inthis inquiry-basedgeometryinvestigation,students create and exploregeometricsolids and their properties.Specifically,thestudentsfindnames that makesense foreachoftheshapes. Theteacher canguidethisnamingbymakingsuggestionsregardingwhentousetheterm prismorpyramid.Also,theteacher mightsuggestthese figuresbenamedaccordingtotheshapeoftheirbases.

Next,thestudentscountthenumber offaces,edges,andvertices (corners)inthevarious solids.Thestudentswillcompare thenumber offaces,edges,andvertices ineachsolidandlookforany

patterns,hopefullydiscovering "Euler's Formula."(F+V-2=EorF+V =E+2orsomeother

variation ofthesame formula couldbeused.) Studentsare NOTrequired towrite thisformula

algebraically; theycouldinstead explain the relationshipinwords. Forexample,"Ifyouaddthe

number offacesandvertices andsubtract2youwillalwaysgetthenumber ofedgesinanyoftheshapes." Theimportanceofaninquiry-basedlesson isthat thelearning ishappening during theinvestigation!Itwillbeimportantforthe teacher tobeaguidetothelearning without directlygivingthestudentsanswers.

Thinking About YourStudents: Bybuilding the geometricsolids, studentswillhave abetterunderstandingofthepropertiesofthesolids.Bylookingforthepatternsinthenumber ofvertices,facesand edges,the studentswillbeengaged inSMP7,Lookforandmake useofstructure andSMP8,Lookforandexpressregularityinrepeatedreasoning.

MaterialsandPre aration:ExploringGeometricSolidshandouts,stirstickstraws (cutinhalf)andchenillestems. Buildasetoftheshapes before thelessonfordemonstrationpurposes.Createahandleforeachoftheshapeswiththechenillestems.

Vocabulary:Geometric solid, polyhedron,face,edge, vertex (vertices-plural),prism, pyramid,triangularprism, triangularpyramid, tetrahedron,square prism, rectangularprism, rectangularpyramid, hexahedron,cube,square pyramid, pentagonal prism,pentagonal pyramid,octahedron,dodecahedron,andicosahedron.

Engage: Holduponegeometric shapeandaskthestudentsiftheycannamesomethingintherealworld that isshaped likeit.Askthestudentstofindanamefortheshape, thinking individuallyfirst,thenwithapartnerandthendiscusswholeclass.Thisiswhere youcanclarifythedifferencebetweenaprism andapyramid. Dothisforeachoftheshapes orhavethem explore thenamestogetherintheirgroupsastheybuildeachone.

Explore:Explainthat each group willneed oneofeachoftheshapes inthechart tohelpthemcomplete theproject.Theyaretousethestirstickstraws(cutinhalf)andchenillestemstocreateeachshape. Nowaskthestudentstodeterminethenumber offaces,edges,andvertices (corners)foreachshapeandrecordtheirresults inthechart.Next,theyshouldfindthesumofthefacesandvertices foreachshapeandrecord their results inthechart.Finally,theywilllookforapatternorrelationshipbetween thefaces,edges,andverticesofashape.

Extend: Anextensiontopart1ofthisinvestigationistohavethestudentscomeupwithageneralruleeither writteninwords orwritten asanalgebraic expressionfortherelationshiptheyfound.

Explore: Inpart 2the studentsare asked todetermineifthe relationship/ruleholdsforothergeometricsolidsthatarenotprismsorpyramids. Todothisthestudentsshould buildtheshapesfromthenetsgivenandbuildtheirregularpolyhedronfromthestrawsandchenillestems.

Explore: For the final explorationto this activity the studentsare going to predict what willhappen whentheirstrawpolyhedronsaredippedintobubblesolution andthentakenout.Willtheshapelookdifferent?Willthebubblesolution beontheshape?Howwillitlook?Askthemtothinktothemselvesfirst,thenshare their thoughtswithapartnerandfinallydiscussasawholegrouptheir prediction.Demonstratethis process with one ofthe shapes such as the tetrahedronortriangularpyramid.Letthemseeiftheir predictionswerecorrect.Askthemwhatmighthappen ifyoudoublediptheshape,butonlygoinpartway.Again,havethemthinktothemselvesfirst,thenshare their thoughtswith apartnerandfinallydiscuss asawhole group. Nowdemonstratethedouble dipping process. Create several stationswith buckets of the bubble solution for thestudentstodiptheir shapes into.Thebuckets fordipping must bedeep enough forthelargestshape tobecompletelysubmerged.

BubbleSolutionRecipe:4gallonsofsoftordistilledwater (hardwater doesnotmakethegreatestbubbles),4cups Dawndishwashingliquid (Dawnworks best,butJoywilldoinapinch),1cupGlycerin(availableatmostpharmacies).Fillthe5-gallonbucketwiththe4gallonsofwater FIRSTtoavoidcreating foam.Slowlypourinthesoapandglycerinandmixverygently.Forbestresultsmakethesolution atleast24hours beforeusing.Pourthissolution intosmaller bucketstodivideupthesolution tocreate 3or4stations.

Cautions:Thisactivityisbestdoneoutdoorsoroncarpet.Thesolution willnothurtthecarpet,butmightcreate cleaner spots inthecarpet.Tileflooringisnotadvised duetothefactthatwhentheflooringgetswetfromthebubblesolution itbecomesveryslippery.