Symmetry and Mathematical Elements of Design
Lesson Plan
Grade level(s): 9-10, (Can be used and adapted for 8th grade
level.)
Time frame: 1-2 days in class, may need out-of-class time
Subject matter: Symmetry,
geometric shapes and scale models
Teacher information:
Julie
Caluwe Ladwig
Southern
Lesson Plan Description and Rationale:
Through
the analysis of several plans for the Washington Memorial grounds, students
will see how mathematical elements of symmetry, patterns and geometric shapes
are used for visual effect as well as the importance and use of scale diagrams. Symmetry is a main concept in the basic geometry
unit in my Integrated Algebra course. Scale
factors and the use of scale models/diagrams are also a concept in most introductory
algebra courses. Basic geometric figures
are also a component of any geometry course. These concepts, merged together in one unit/project,
show students that geometry and algebra are not independent of one another,
but interrelated, as this course, too, is designed.
State Standards:
STATE
GOAL 7: Estimate, make and use measurements of objects, quantities and relationships
and determine acceptable levels of accuracy.
7.A.3b
Apply the concepts and attributes of length, capacity, weight/mass, perimeter,
area, volume, time, temperature and angle measures in practical situations.
7.A.4a Apply units and scales to describe and compare numerical data and physical
objects.
7.C.3a Construct a simple scale drawing for a given situation.
STATE
GOAL 9: Use geometric methods to analyze, categorize and draw conclusions
about points, lines, planes and space.
9.A.3c Use concepts of symmetry, congruency, similarity, scale, perspective,
and angles to describe and analyze two- and three-dimensional shapes found
in practical applications (e.g., geodesic domes, A-frame houses, basketball
courts, inclined planes, art forms, blueprints).
9.A.4b Make perspective drawings, tessellations and scale drawings, with and
without the use of technology.
9.A.5
Use geometric figures and their properties to solve problems
in the arts, the physical and life sciences and the building trades, with
and without the use of technology.
9.B.5
Construct and use two- and three-dimensional models of
objects that have practical applications (e.g., blueprints, topographical
maps, scale models).
Objectives:
After
a class discussion/analysis of one plan for the Washington Memorial Grounds,
students will work in small groups (partners) to do an analysis of four other
scale plans for the Washington Memorial grounds and identify elements of symmetry
and geometric shapes (including conic sections) used in the design. Students will compare and contrast the four
plans with a modified Venn
Diagram/Frayer Model. Students
will create a scale plan for the Washington Memorial grounds or for the Gateway
Arch grounds incorporating elements of symmetry and geometric shapes for design.
Resources:
 |
“The
Future Washington, proposed treatment of monument and gardens.” 1949.
Library
of Congress, Prints and Photographs Division, |
 |
Horydczak,
Theodor. “Proposed drawing for Library
of Congress, Prints and Photographs Division, |
 |
Horydczak,
Theodor. “Proposed drawing for Library
of Congress, Prints and Photographs Division, |
 |
Horydczak,
Theodor. “Proposed drawing for Library
of Congress, Prints and Photographs Division, |
 |
Horydczak,
Theodor. “Proposed drawing for Library
of Congress, Prints and Photographs Division, |
Methods:
1. As a class, study plan E for the Washington
Memorial grounds and monument. This
may be done as a whole class activity or in small groups with the attached
worksheet to guide discussion. This
discussion will include review of types of symmetry, basic geometric shapes,
and an introduction to the four conic sections (circles, parabolas, ellipses,
hyperbolas).
STUDENT ACTIVITIES for ASSESSMENT (click
here for printable word document)
2. Students will be put into small groups and given
copies of the four additional plans (A-D) for the Washington Memorial grounds
and monument.
3. Students will fill out the modified Venn Diagram/Frayer Model
to identify similarities and differences in the four plans.
4. Students will write (at a minimum) one paragraph
discussing why they believe different designers all had certain similar ideas
when planning the grounds for the Washington Memorial. In other words, why do they believe the similarities
they noted in their Venn diagrams exist?
5. Students will identify all types of symmetry
found in each plan as well as all mathematical elements (such as conic sections
and other geometric shapes or patterns) that are key to the overall look and
design of the plan. Students will draw
lines of symmetry on each plan and label all geometric elements.
6A) Using the actual dimensions of the grounds,
and the location/size of the monument itself, students will create a plan/design
for the Washington Memorial grounds. They will use grid paper and provide a legend
that tells the scale. They are to identify
water, types of plants, and walkways clearly, either by differing colors or
by shading (all defined in the legend). The design must have at least one conic section
and one other geometric shape incorporated in it. All symmetry and geometric figures will be identified
on the plan.
-or for a local flavor-
6B) Using the actual dimensions of the Gateway Arch
grounds and the location/size of the Arch itself, students will create a plan/design
for the grounds. They will use grid paper and provide a legend that tells
the scale. They will identify water,
types of plants, and walkways clearly, either by differing colors or shading
(all defined in the legend). The design
must have at least one conic section and one other geometric shape incorporated
in it. All symmetry and geometric figures
will be identified on the plan.
Evaluation:
I
would suggest a break down as follows on a 100 point project:
A grade will be given for the completion of the Venn Diagram/Frayer
Model based on inclusion of types of symmetry and geometric figures in appropriate
places (25 points). Students will be
graded on the paragraph discussing the similarities and differences in all
the designs (25 points). They should
have complete sentences, good grammar, and should show evidence of having
used their graphic organizer as an outline for the content of the paragraph. Finally, students will receive a grade for their
plan for the grounds of a monument (50 points). The grader should consider the following:
Is the plan neat and to scale? Is
there a complete legend? Does the plan include symmetry and several geometric
figures (including at least one conic section)? Are the elements of the ground plan clearly
identified by color or shading? Are
all elements of symmetry and geometric figures identified on the plan?
Keywords for this lesson: symmetry, scale
diagram, scale model, geometry, geometric shapes