Vertical Alignment
Geometry
Prince William County Public Schools
NCTM Process Standards:
 Problem Solving
 Reasoning and Proof
 Communication
 Connections
 Representation
Mathematics
K-5
Big Ideas:
 Shapes, both two and three-dimensional, exist in great variety. There are
many different ways to see and describe similarities and differences among
shapes. The more ways that one can classify and discriminate shapes, the
better one understands them.
 Shapes have properties that can be used when describing and analyzing
them. Properties can be explored and analyzed in a variety of ways.
 An analysis of geometric properties leads to deductive reasoning in a
geometric environment.
Grade 2
Kindergarten
Grade 1
K.11A Identify, describe, and trace
plane geometric figures (circle, triangle,
square, and rectangle).
1.12 Identify and trace, describe, and
sort plane geometric figures (triangle,
square, rectangle, and circle)
according to number of sides, vertices,
and right angles.
2.15A Draw a line of symmetry in a
figure.
1.13 Construct, model, and describe
objects in the environment as
geometric shapes (triangle, rectangle,
square, and circle) and explain the
reasonableness of each choice.
2.16 Identify, describe, compare, and
contrast plane and solid geometric
figures (circle/sphere, square/cube, and
rectangle/rectangular prism).
K.11B Compare the size (larger,
smaller) and shape of plane geometric
figures (circle, triangle, square, and
rectangle).
K.12 Describe the location of one object
relative to another (above, below, next
to) and identify representations of plane
geometric figures (circle, triangle,
square, and rectangle) regardless of
their positions and orientations in space.
2.15B Identify and create figures with
at least one line of symmetry.
Revised July 20, 2011
Grade 3
3.14 Identify, describe, compare, and
contrast characteristics of plane and
solid geometric figures (circle, square,
rectangle, triangle, cube, rectangular
prism, square pyramid, sphere, cone,
and cylinder) by identifying relevant
characteristics, including the number of
angles, vertices, and edges, and the
number and shape of faces, using
concrete models.
3.15 Identify and draw representations
of points, line segments, rays, angles,
and lines.
3.16 Identify and describe congruent
and noncongruent plane figures.
Grade 4
4.10A Identify and describe
representations of points, lines, line
segments, rays, and angles, including
endpoints and vertices.
4.10B Identify representations of lines
that illustrate intersection, parallelism,
and perpendicularity.
4.11A Investigate congruence of plane
figures after geometric
transformations, such as reflection,
translation, and rotation, using mirrors,
paper folding, and tracing.
4.11B Recognize the images of figures
resulting from geometric
transformations, such as translation,
reflection, and rotation.
Grade 5
5.11 Measure right, acute, obtuse, and
straight angles.
5.12A Classify angles as right, acute,
obtuse, or straight.
5.12B Classify triangles as right, acute,
obtuse, equilateral, scalene, or
isosceles.
5.13A Using plane figures (square,
rectangle, triangle, parallelogram,
rhombus, and trapezoid), develop
definitions of these plane figures.
5.13B Using plane figures (square,
rectangle, triangle, parallelogram,
rhombus, and trapezoid), investigate
and describe the results of combining
and subdividing plane figures.
4.12A Define polygon.
4.12B Identify polygons with 10 or
fewer sides.
Revised July 20, 2011
Vertical Alignment
Geometry
Prince William County Public Schools
NCTM Process Standards:
 Problem Solving
 Reasoning and Proof
 Communication
 Connections
 Representation
Mathematics
6–8
Big Ideas:
 Spatial reasoning skills are essential to formal inductive and deductive
reasoning skills required in subsequent mathematics learning.
 Geometric relationships can be determined by visualizing, comparing,
constructing, sketching, measuring, transforming, and classifying geometric
figures.
 Plane and solid figures can be described, classified, and compared according
to their attributes.
 Transformations are used in a variety of ways including: modeling, tiling,
fabric design, etc.
 The surface area and volume of prisms, cylinders, pyramids, and cones can
be developed conceptually.
 Visualization, measurement, and proportional reasoning skills are used to
understand the effect of scale change on distance, area, and volume, and in
the study of similar figures.
 The Pythagorean Theorem is applicable to life experiences.
Grade 6
Grade 7
Grade 8
6.11A Identify the coordinates of a
point in a coordinate plane a coordinate
plane.
7.6 Determine whether plane figures
(quadrilaterals and triangles) are
similar and write proportions to
express the relationships between
corresponding sides of similar figures.
8.6A Verify by measuring and describe
the relationship among vertical angles,
adjacent angles, supplementary angles,
and complementary angles.
6.11B Graph ordered pairs in a
coordinate plane.
6.12 Determine congruence of
segments, angles, and polygons.
6.13 Describe and identify properties of
quadrilaterals.
8.6B Measure angles of less than 360˚.
7.7 Compare and contrast the
following quadrilaterals based on
properties: parallelogram, rectangle,
square, rhombus, and trapezoid.
7.8 Given a polygon in the coordinate
plane, represent transformations
(reflections, dilations, rotations, and
translations) by graphing in the
coordinate plane.
8.8A Apply transformations to plane
figures.
8.8B Identify applications of
transformations.
8.9 Construct a three-dimensional
model given the top or bottom, side and
front views.
8.10A Verify the Pythagorean Theorem.
8.10B Apply the Pythagorean Theorem.
Revised July 20, 2011