FocusingLens(es) / RelationshipsVisualization / StandardsandGradeLevelExpectationsAddressedinthisUnit / MA10-GR.7-S.4-GLE.1
MA10-GR.7-S.4-GLE.2
InquiryQuestions(Engaging-Debatable): /
- Whyispianimportantnumber?(MA10-GR.7-S.4-GLE.2-IQ.8)
- Howmanytwo-dimensionalshapescanyoumakebyslicingathree-dimensionalobject?
UnitStrands / Geometry
Concepts / Circumference,area,circle,diameter,π,ratio,radius,slice,three-dimensionalfigures,two-dimensionalfigures,scalefactor, magnification,zoomlevel,scaledrawings,characteristics,drawing,tools(rulers,protractors,compasses),complementary,supplementary,adjacent,vertical,angles,indirectmeasurement,additiveproperty,area,volume,decomposition,composition
Generalizations
MystudentswillUnderstandthat…
GuidingQuestions
FactualConceptual
Mathematiciansrecognizethespecialrelationshipbetweenthediameterandcircumferenceofacircleas
theratiocalledπ,andutilizethisrelationshiptocalculate
thearea,circumference,diameterorradiusofacircle. (MA10-GR.7-S.4-GLE.2-EO.a,b) / Whatistheradius?
Whatistheformulaforfindingthecircumferenceofacircle?
Whatistheformulaforfindingtheareaofacircle?Whatisπ? / Howarethecircumferenceanddiameterofacirclerelated?
Howdoesthederivationoftheformulafortheareaofa
circlerelyonboththecircumferenceandradiusofthecircle?
Slicingthree-dimensionalfiguresresultsintwo-dimensionalfigures (MA10-GR.7-S.4-GLE.1-EO.a.iv) / Whattypesoftwo-dimensionalfigurescanbecreatedwhenslicingacone? / Howdoesslicinga3-Dshapeparalleltothebasedifferfromslicingthesame3-Dshapediagonaltothebase?
Mathematiciansrepresentscalefactorintermsofmagnificationorzoomlevel.(MA10-GR.7-S.4-GLE.1-EO.a.i) / Howdoesscalefactoraffectlength,perimeter,anglemeasure,area,andvolume?(MA10-GR.7-S.4-GLE.1-IQ.3) / Whyisthescalefactorforsidelengthsandperimetersdifferentfrom theoneforareas?
Mathematiciansdrawgeometricfigureusingrulers,protractors,andcompasseswithprecision(MA10-GR.7-S.4-GLE.1-EO.a.ii, a.iii) / Howissketchingdifferentfromdrawing?
Whendrawingtriangles,whendoprovidedcharacteristicsleadtonotriangle,exactlyoneormorethanonepossibletriangle?
Isthereageometricfigureforanygivensetofattributes? (MA10-GR.7-S.4-GLE.1-IQ.1) / Whyarerulers,protractorsandcompassesnecessarywhendrawingshapes?
Anglerelationshipssuchascomplementary,supplementary,adjacentandverticalanglesprovidemathematiciansanindirectmeanstosolveforunknownanglesinafigure(MA10-GR.7-S.4-GLE.2-EO.c) / Whatarecomplementaryangles?Whataresupplementaryangles?Whatareadjacentangles?
Whatareverticalangles?
Howdolinerelationshipsaffectanglerelationships? / Howcanyouindirectlydeterminethemeasurementofanunknownangleformedbytwointersectinglines?
Howcangeometricrelationshipsamonglinesandangles begeneralized,described,andquantified?(MA10-GR.7-S.4-GLE.2-IQ.1)
Theadditivepropertyofareaandvolumeprovidesameansforderivingequationstofindthesurfaceareaandvolumeoftwo-andthree-dimensionalobjects (MA10-GR.7-S.4-GLE.2-EO.d) / Whatareexamplesoffamiliarshapesthatarehelpfultorecognizewithinlargerobjectswhentryingtofindvolumesorsurfaceareas?
Whatdosurfaceareaandvolumetellaboutanobject?
(MA10-GR.7-S.4-GLE.2-IQ.6) / Whyareaandvolumebothhaveadditivepropertiesofcompositionanddecomposition?
Howcantwoshapeshavethesamevolumebutdifferentsurfaceareasandviceversa?(MA10-GR.7-S.4-GLE.2-IQ.2,3)
KeyKnowledgeandSkills:
Mystudentswill…
Whatstudentswillknowandbeabletodoaresocloselylinkedintheconcept-baseddisciplineofmathematics.Therefore,inthemathematics
sampleswhatstudentsshouldknowanddoarecombined.
- Solveproblemsinvolvingscaledrawingsofgeometricfigures,includingcomputingactuallengthsandareasfromascaledrawingandreproducingascaledrawingatadifferentscale.(MA10-GR.7-S.4-GLE.1-EO.a.i)
Find the area and perimeter of geometric figures–rectangles, triangles, circles
- Compute actual lengths and areasfrom a scale drawingofgeometric figures (square,rectangle, triangle,circle)
- Reproduceascale drawingofageometric figureat adifferent scale
- Draw(freehand,withrulerandprotractor,andwithtechnology)geometricshapeswithgivencondition,withfocusontrianglesfromthreemeasuresofanglesorsides,notingwhentheconditionsdetermineauniquetriangle,morethanonetriangle,ornotriangle.(MA10-GR.7-S.4-GLE.1-EO.a.ii,a.iii)
Given threemeasures ofangles or sides foratriangle, determinewhen theconditions would createauniquetriangle, morethan onetriangle, or no
triangle
- Describethetwo-dimensional figuresthatresultfromslicingthree-dimensionalfigures,asin planesectionsofrightrectangularprismsandrightrectangularpyramids.(MA10-GR.7-S.4-GLE.1-EO.a.iv)
Describethetwo-dimensional figures that result from slicingthree-dimensional figures, as in planesections of right rectangular prisms and right
rectangular pyramids
- Know the formulasforthe areaandcircumferenceof acircle anduse them tosolve problems(MA10-GR.7-S.4-GLE.2-EO.a)
Learn the formula for the areaand circumferenceofa circle
- Usethe formulasfortheareaand circumferenceof acircle to solveproblems
- Givean informal derivation oftherelationship between thecircumferenceand area ofacircle. (MA10-GR.7-S.4-GLE.2-EO.b)
Describethe relationshipbetween thecircumference andareaof a circle
- Usefactsaboutsupplementary,complementary,vertical,andadjacentanglesinamulti-stepproblemtowriteandsolvesimpleequationsforanunknownangleinafigure. (MA10-GR.7-S.4-GLE.2-EO.c)
Applyproperties of angle relationships
- Useproperties ofcomplementaryangles to solveproblems oUseproperties ofsupplementaryangles to solveproblems oUseproperties ofverticalangles to solve problems
- Applyproperties ofparallel lines
- Useproperties ofcorrespondingangles to solveproblems
- Useproperties ofalternateinterior angles to solveproblems
- Solvereal-worldandmathematicalproblemsinvolvingarea,volumeandsurfaceareaoftwo-andthree-dimensionalobjectscomposedoftriangles,quadrilaterals,polygons,
cubes,andrightprisms.(MA10-GR.7-S.4-GLE.2-EO.d)
Calculate thesurfacearea and volume,given formulas for:
ocubes, right prisms, pyramids, cylinders, sphere
- Solve real-world and mathematical problems involvingsurfacearea and volume
Critical Language:includestheAcademicandTechnicalvocabulary,semantics,anddiscoursewhichareparticulartoandnecessaryforaccessingagivendiscipline.
EXAMPLE:AstudentinLanguageArtscandemonstratetheabilitytoapplyandcomprehendcriticallanguagethroughthefollowing statement:“MarkTwainexposesthehypocrisyofslaverythroughtheuseofsatire.”
Astudent incandemonstratetheabilitytoapplyandcomprehendcriticallanguagethroughthefollowingstatement(s): / Theareaofacircleisderivedbycuttingthecirclelikeapizzaintosuccessivelysmallerslicesandrearrangingtoformaparallelogramwithabasethatishalfthecircumferenceandaheightoftheradius.AcademicVocabulary: / Solve,draw,freehand,ruler,protractor,triangle,area,circle,angles,polygonscubes,slice,three-dimensionalfigures,two-dimensionalfigures,scalefactor,magnification,zoomlevel,scaledrawings,characteristics,volume,derive,parallelogram
TechnicalVocabulary: / Circumference,diameter,π,ratio,radius,drawing,tools(rulers,protractors,compasses),complementaryangles,supplementaryangles,adjacentangles,verticalangles,indirectmeasurement,additiveproperty,decomposition,composition,congruentquadrilateral,rightprisms