NVACS: Geometry
Concept Overview for 4th Graders
4.G.1.2.3
Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
Students describe, analyze, compare, and classify two-dimensional shapes. Through building, drawing,
and analyzing two-dimensional shapes, students deepen their understanding of properties of twodimensional objects and the use of them to solve problems involving symmetry.
See the Visual Dictionary on www.RPDP.net for definitions of these geometry terms listed below.
Students will participate in discussions about their reasoning by using mathematically appropriate
language. The terms the students are expected to know are:
Fourth Grade Vocabulary:
Right Triangle
Triangle
Classify Shapes/Figures
Isosceles Triangle
Quadrilateral
*Properties-Rules about how numbers work.
Equilateral Triangle
Pentagon
Point
Line of Symmetry
Hexagon
Line
Symmetric Figures
Cube
Line Segment
Two Dimensional
Trapezoid
Ray
Regular
Half/Quarter Circle
Angle
Irregular
Circle
Vertex/Vertices
vertex
Cone
Right Angle
From Previous Grades:
Cylinder
Acute
Polygon
Sphere
Obtuse
Rhombus/Rhombi
Kite
Perpendicular
Rectangle
Examples
Parallel
Square
Non-Examples
Some references adapted from North Carolina and Arizona K-5 instructional documents
RPDP.net
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NVACS: Geometry
Concept Overview for 4th Graders
*The term “Property” in these standards is reserved for those attributes that indicate a relationship
between components of shapes. Thus “having parallel sides” or “having all sides of equal length” are
properties. “Attributes” and “features” are used interchangeably to indicate any characteristic of a
shape including properties, and other defining characteristics (e.g. straight sides) and nondefining
characteristics (e.g. “right side up”). Progressions for the NVACS, Geometry Writing Team
Developing Geometric Thinking
All learners in your classroom are capable of growing and developing in the ability to think and reason in
geometric contexts. “Geometry is a “network of concepts, ways of reasoning and representation
systems” used to explore and analyze shape and space. (Battista, 2007, p.843)
Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel
lines. Identify these in two-dimensional figures.
Some references adapted from North Carolina and Arizona K-5 instructional documents
RPDP.net
Page 2
NVACS: Geometry
Concept Overview for 4th Graders
Classify Two Dimensional Figures by these attributes:
Parallel lines-Two lines on a plane that never meet.
Perpendicular lines- Lines going straight up or to the side at the 90 degree angle from
another line or surface.
Absence of Angles -(See Measurement Data (4.MD) for Instruction on Angles)
Presence of Angles- (See Measurement Data(4.MD) for Instruction on Angles)
Right Triangles – A triangle having a right angle.
Students should also have opportunities to reason about statements that could be true or false.
Students need experiences with figures which are symmetrical and non-symmetrical. Figures
include both regular and non-regular polygons. Folding cut-out figures will help students
determine whether a figure has one or more lines of symmetry.
This standard only includes line symmetry not rotational symmetry.
Some references adapted from North Carolina and Arizona K-5 instructional documents
RPDP.net
Page 3
NVACS: Geometry
Concept Overview for 4th Graders
Example:
For each figure, draw all of the lines of symmetry. What pattern do you notice? How many lines
of symmetry do you think there would be for regular polygons with 9 and 11 sides. Sketch each
figure and check your predictions. Polygons with an odd number of sides have lines of
symmetry that go from a midpoint of a side through a vertex.
Some references adapted from North Carolina and Arizona K-5 instructional documents
RPDP.net
Page 4