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
ÒStudents
should come to the study of geometry in the middle grades with informal
knowledge about points, lines, planes, and a variety of two- and three-dimensional
shapes; with experience in visualizing and drawing lines, angles, triangles,
and other polygons; and with intuitive notions about shapes built from years of
interacting with objects in their daily lives . . .
Middle-grades
students should explore a variety of geometric shapes and examine their
characteristics . . .
Students
must carefully examine the features of shapes in order to precisely define and
describe fundamental shapes, such as special types of quadrilaterals, and to
identify relationships among the types of shapes.Ó NCTM p. 233
ÒStudentsÕ
skills in visualizing and reasoning about spatial relationships are fundamental
in geometry. Some students may have difficulty finding the surface area of
three-dimensional shapes using two dimensional representations because they
cannot visualize the unseen faces of the shapes. Experience with models of
three-dimensional shapes and their two dimensional ÒnetsÓ is useful in such
visualization. Students also need to examine, build, compose, and decompose
complex two- and three-dimensional objects, which they can do with a variety of
media, including paper-and-pencil sketches, geometric models, and dynamic
geometry software. Interpreting or drawing different views of buildings, such
as the base floor plane and front and back views, using dot paper can be useful
in developing visualization. Students should build three-dimensional objects
from two-dimensional representations; draw objects from a geometric
description; and write a description, including its geometric properties, for a
given object.Ó NCTM p. 237
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9 – 12