Geometry Standard for Grades 35
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
threedimensional geometric shapes and develop mathematical arguments about
geometric relationships 
 identify, compare, and analyze attributes of two and threedimensional
shapes and develop vocabulary to describe the attributes;
 classify two and threedimensional 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
twodimensional 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
threedimensional 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 threedimensional object from twodimensional
representations of that object;
 identify and draw a twodimensional representation of a threedimensional
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.


Having trouble running our Java apps in eExamples? Get help here.
Page Feedback
Your feedback is important! Comments or concerns regarding the content of this page may be sent to nctm@nctm.org. Thank you.