Grade Bands
NCTM Principles and Standards for School Mathematics
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Pre-K – 2
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3 – 5
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6 – 8
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9 – 12
ÒIn
programs that adopt the recommendations in Principles and Standards,
middle-grades students will have explored and discovered relationships among
geometric shapes, often using dynamic geometry software. Using features of
polygons and polyhedra, they will have had experience in comparing and
classifying shapes. High school students should conduct increasingly
independent explorations, which will allow them to develop a deeper
understanding of important geometric ideas such as transformation and symmetry
. . .
High
school students should develop facility with a broad range of ways of
representing geometric ideas – including coordinates, networks,
transformations, vectors, and matrices – that allow multiple approaches
to geometric problems and that connect geometric interpretations to other
contexts.Ó NCTM p. 309
Ò[High
school students] should have some familiarity with spherical and simple polar
coordinate systems, as well as with systems used in navigation.Ó NCTM p. 314
ÒCreating
and analyzing perspective drawings, thinking about how lines or angles are
formed on a spherical surface, and working to understand orientation and
drawings in a three-dimensional rectangular coordinate system all afford
opportunities for students to think and reason spatially . . .
Visualizing
a building represented in architectural planes, the shape of a cross section
formed when a plane slices through the cone (a conic section) or another solid
object, or the shape of the solid swept or when a plane figure is rotated about
an axis become easier when students work with physical models, drawings, and
software capable of manipulating three-dimensional representations.Ó NCTM p. 315