7.G.3
2012
Domain: Geometry
Cluster: Draw, construct, and describe geometrical figures and describe the relationships between them
Standard: 7.G.3. Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane
sections of right rectangular prisms and right rectangular pyramids.
Essential Questions
Enduring Understandings
Activities, Investigation, and Student Experiences

How can objects be
represented and
compared using
geometric attributes?


How do geometric
relationships help to
solve problems and/or
make sense of
phenomena?
 Geometry is the study of two
and three dimensional shapes
and their relationships.
Activities:
 Have students choose a photograph of a famous threedimensional structure, such as the entrance to the Louvre
in Paris, from the Internet. Have them determine,
describe, and draw the two-dimensional figure that
would result from slicing the structure. Encourage
students to slice the structure in several different ways.
Students will share their photographs with the class and
explain their findings.

In what ways can one
match solid geometric
figures to real-life
objects?
Content Statements


Recognize two
dimensional figures that
result from slicing
three-dimensional
figures.
Sketch cross sections of
three-dimensional
figures.
Each three-dimensional
geometric figure can be sliced
to show two-dimensional
figures
 Geometry and spatial sense
offer ways to interpret and
reflect on our physical
environment.
 Analyzing geometric
relationships develops
reasoning and justification
skills.
 One can draw, construct, and
describe geometrical figures
and explain the relationships
between them.

Have students construct three-dimensional figures out of
clay. Then, have them slice the figure using a plastic
knife. Students will then describe the two-dimensional
figure they created.
Example:
 Which of the following could NOT be a cross section of
a rectangular prism?
A. rectangle
B. parallelogram
C. circle
D. triangle
7.G.3
Assessments

2012
Investigation:
If the pyramid is cut with a plane (green) parallel to the base, the
intersection of the pyramid and the plane is a square cross
section (red).
A square pyramid is shown.
The base of the pyramid has an area of 25 square inches.
a.) A plane slices through the pyramid. It forms a cross
section that is a square with an area of 9 square inches.
Describe how the plane cut through the pyramid.
b.) A plane that is perpendicular to the pyramid’s base slices
through the pyramid. It passes through the pyramid’s vertex.
What shape is the cross section?

If the pyramid is cut with a plane (green) passing through the
top vertex and perpendicular to the base, the intersection of the
pyramid and the plane is a triangular cross section (red).
Name the following cross sections formed.
a.) The top of a rectangular pyramid is sliced through.
b.) A right rectangular
to the base.
If the pyramid is cut with a plane (green) perpendicular to the
base, but not through the top vertex, the intersection of the
pyramid is sliced from the apex pyramid and the plane is a trapezoidal cross section (red).
7.G.3
2012
c.) A right rectangular prism is sliced resulting in the formation
of two congruent right rectangular prisms.
http://intermath.coe.uga.edu/dictnary/descript.asp?termID=95
Equipment Needed:
Teacher Resources:
Pen/Pencil

http://nlvm.usu.edu
Paper

http://Illuminations.nctm.org
Ruler

http://www.ncpublicschools.org/docs/acre/standards/c
ommon-core-tools/unpacking/math/7th.pdf
Internet

http://insidemathematics.org/index.php/7th-grade
Overhead

http://www.illustrativemathematics.org/standards/k8

http://www.khanacademy.org/search?page_search_q
uery=geometry

http://www.schools.utah.gov/CURR/mathsec/Core/7th
-Grade-Core/7G1.aspx
Reference books
Graphing calculator
Interactive whiteboard
Online Activities
Worksheets
Clay
Graph Paper