Geometry Standard
Instructional programs from prekindergarten through grade
12
should enable all students to—
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Analyze
characteristics and properties of two- and three-dimensional geometric
shapes and develop mathematical arguments about geometric relationships
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Pre-K–2
Expectations:
In
prekindergarten through grade 2 all students should– |
| • |
recognize, name, build, draw, compare, and sort two- and
three-dimensional shapes; |
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describe attributes and parts of two- and three-dimensional
shapes; |
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investigate and predict the results of putting together and
taking apart two- and three-dimensional shapes. |
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Grades 3–5 Expectations:
In grades 3–5 all students should– |
| • |
identify, compare, and analyze attributes of two- and
three-dimensional shapes and develop vocabulary to describe the
attributes; |
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classify two- and three-dimensional shapes according to their
properties and develop definitions of classes of shapes such as
triangles and pyramids; |
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investigate, describe, and reason about the results of
subdividing, combining, and transforming shapes; |
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make and test conjectures about geometric properties and
relationships and develop logical arguments to justify
conclusions. |
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Grades 6–8 Expectations:
In grades 6–8 all students should– |
| • |
precisely describe, classify, and understand relationships among
types of two- and three-dimensional objects using their defining
properties; |
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understand relationships among the angles, side lengths,
perimeters, areas, and volumes of similar objects; |
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create and critique inductive and deductive arguments concerning
geometric ideas and relationships, such as congruence,
similarity, and the Pythagorean relationship. |
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Grades 9–12 Expectations:
In grades 9–12 all students should– |
| • |
analyze properties and determine attributes of two- and
three-dimensional objects; |
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explore relationships (including congruence and similarity)
among classes of two- and three-dimensional geometric objects,
make and test conjectures about them, and solve problems
involving them; |
| • |
establish the validity of geometric conjectures using deduction,
prove theorems, and critique arguments made by others;
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| • |
use
trigonometric relationships to determine lengths and angle
measures. |
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Specify
locations and describe spatial relationships using coordinate
geometry and other representational systems
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Pre-K–2
Expectations:
In prekindergarten through grade 2 all students should– |
| • |
describe, name, and interpret relative positions in space
and apply ideas about relative position; |
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describe, name, and interpret direction and distance in
navigating space and apply ideas about direction and
distance; |
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Grades 3–5 Expectations:
In grades 3–5 all students should– |
| • |
describe location and movement using common language and
geometric vocabulary; |
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Grades 6–8 Expectations:
In grades 6–8 all students should– |
| • |
use
coordinate geometry to represent and examine the properties
of geometric shapes; |
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use
coordinate geometry to examine special geometric shapes,
such as regular polygons or those with pairs of parallel or
perpendicular sides. |
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Grades 9–12 Expectations:
In grades 9–12 all students should– |
| • |
investigate conjectures and solve problems involving two-
and three-dimensional objects represented with Cartesian
coordinates. |
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Apply
transformations and use symmetry to analyze mathematical situations
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Pre-K–2
Expectations:
In prekindergarten through grade 2 all students should– |
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recognize and apply slides, flips, and turns; |
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recognize and create shapes that have symmetry. |
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Grades 3–5 Expectations:
In grades 3–5 all students should– |
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predict and describe the results of sliding, flipping, and
turning two-dimensional shapes; |
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describe a motion or a series of motions that will show that
two shapes are congruent; |
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identify and describe line and rotational symmetry in two-
and three-dimensional shapes and designs. |
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Grades 6–8 Expectations:
In grades 6–8 all students should– |
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describe sizes, positions, and orientations of shapes under
informal transformations such as flips, turns, slides, and
scaling; |
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examine the congruence, similarity, and line or rotational
symmetry of objects using transformations. |
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Grades 9–12 Expectations:
In grades 9–12 all students should– |
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understand and represent translations, reflections,
rotations, and dilations of objects in the plane by using
sketches, coordinates, vectors, function notation, and
matrices; |
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use
various representations to help understand the effects of
simple transformations and their compositions. |
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Use
visualization, spatial reasoning, and geometric modeling to solve
problems
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Pre-K–2
Expectations:
In prekindergarten through grade 2 all students should– |
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create mental images of geometric shapes using spatial
memory and spatial visualization; |
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recognize and represent shapes from different perspectives;
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relate ideas in geometry to ideas in number and measurement;
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recognize geometric shapes and structures in the environment
and specify their location. |
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Grades 3–5 Expectations:
In grades 3–5 all students should– |
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build and draw geometric objects; |
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create and describe mental images of objects, patterns, and
paths; |
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identify and build a three-dimensional object from
two-dimensional representations of that object; |
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identify and draw a two-dimensional representation of a
three-dimensional object; |
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use
geometric models to solve problems in other areas of
mathematics, such as number and measurement; |
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recognize geometric ideas and relationships and apply them
to other disciplines and to problems that arise in the
classroom or in everyday life. |
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Grades 6–8 Expectations:
In grades 6–8 all students should– |
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draw geometric objects with specified properties, such as
side lengths or angle measures; |
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use
two-dimensional representations of three-dimensional objects
to visualize and solve problems such as those involving
surface area and volume; |
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use
visual tools such as networks to represent and solve
problems; |
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use
geometric models to represent and explain numerical and
algebraic relationships; |
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recognize and apply geometric ideas and relationships in
areas outside the mathematics classroom, such as art,
science, and everyday life. |
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Grades 9–12 Expectations:
In grades 9–12 all students should– |
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draw and construct representations of two- and
three-dimensional geometric objects using a variety of
tools; |
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visualize three-dimensional objects and spaces from
different perspectives and analyze their cross sections;
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use
vertex-edge graphs to model and solve problems; |
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use
geometric models to gain insights into, and answer questions
in, other areas of mathematics; |
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use
geometric ideas to solve problems in, and gain insights
into, other disciplines and other areas of interest such as
art and architecture. |
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