| Instructional
programs from prekindergarten through grade 12 should enable
all students to— |
In grades 3–5 all students should— |
| Analyze
characteristics and properties of two- and three-dimensional
geometric shapes and develop mathematical arguments about
geometric
relationships |
| • |
identify,
compare, and analyze attributes of two- and three-dimensional
shapes and develop vocabulary to describe the attributes;
|
| • |
classify
two- and three-dimensional shapes according to their properties
and develop definitions of classes of shapes such as triangles
and pyramids; |
| • |
investigate,
describe, and reason about the results of subdividing,
combining, and transforming shapes; |
| • |
explore
congruence and similarity; |
| • |
make
and test conjectures about geometric properties and relationships
and develop logical arguments to justify conclusions.
|
|
| Specify
locations and describe spatial relationships using coordinate
geometry and other representational systems |
| • |
describe location and movement using common language and
geometric vocabulary; |
| • |
make and use coordinate systems to specify locations and
to describe paths; |
| • |
find the distance between points along horizontal and
vertical lines of a coordinate system. |
|
| Apply
transformations and use symmetry to analyze mathematical
situations |
| • |
predict and describe the results of sliding, flipping,
and turning two-dimensional shapes; |
| • |
describe a motion or a series of motions that will show
that two shapes are congruent; |
| • |
identify and describe line and rotational symmetry in
two- and three-dimensional shapes and designs. |
|
| Use
visualization, spatial reasoning, and geometric modeling
to solve problems |
| • |
build and draw geometric objects; |
| • |
create and describe mental images of objects, patterns,
and paths; |
| • |
identify and build a three-dimensional object from two-dimensional
representations of that object; |
| • |
identify and draw a two-dimensional representation of
a three-dimensional object; |
| • |
use geometric models to solve problems in other areas
of mathematics, such as number and measurement; |
| • |
recognize geometric ideas and relationships and apply
them to other disciplines and to problems that arise in
the classroom or in everyday life. |
|
