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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– |
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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– |
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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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explore
congruence and similarity; |
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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– |
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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– |
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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; |
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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– |
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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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find and name locations with simple relationships such as "near
to" and in coordinate systems such as maps. |
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Grades
3–5 Expectations:
In
grades 3–5 all students should– |
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describe location and movement using common language and geometric
vocabulary; |
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make and use coordinate systems to specify locations and to
describe paths; |
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find the distance between points along horizontal and vertical
lines of a coordinate system. |
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Grades
6–8 Expectations:
In
grades 6–8 all students should– |
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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– |
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use
Cartesian coordinates and other coordinate systems, such as
navigational, polar, or spherical systems, to analyze geometric
situations; |
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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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