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ICLE Standards:
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Geometry: Identify, describe, compare and
classify geometric figures; develop an appreciation of geometry
as a means of describing the physical world.
Measurement: Develop an understanding of angle
measure.
Mathematical Connections: Value the role of
mathematics in our culture and society.
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Performance Task:
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Geometric figures and patterns have been a central
part of architecture over the centuries. For example, a
mosaic niche built in AD 135 in Isfahan, Iran, features designs of
geometric patterns and scriptures. Similar
pieces can be found in Egyptian, Greek, Roman, Renaissance Italy, modern
day architecture, etc.
Your task
is to locate a piece of architecture from history that contains polygons as
an intricate part of the design. You
will find many books containing such pieces in the media center. The art
library is also a good resource for
you to locate a design. After you choose your design, identify the polygons
in the design and find the sum
of the measures of the interior angles of each kind of polygon. State any
conclusions that you can make.
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Knowledge / Skills:
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Perform operations with signed (positive and
negative) numbers, including decimals, ratios, percents, and fraction. (m1)
Understand the characteristics and terminology
of angles, e.g., degree measure, classification of angles by measure (acute,
right, obtuse, and straight), supplementary and complementary angles, and
vertical angles. (m4)
Understand the properties and classification of
polygons of more than four sides (e.g., pentagon, hexagon, octagon,
decagon, etc.). (m26)
Use the technique of dimensional analysis to
convert units of measure (e.g., convert km/hr to m/min). (m33)
Gather information from a variety of sources,
including electronic sources, and summarize, analyze, and evaluate its use
for a report. (ela3)
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Rubric:
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The student
independently completes the task. He/she demonstrates an understanding of
polygons. He/she is able to reach the conclusion that the sum of the interior angles
of a polygon is (s - 2) x 180 , where s = the number of sides or angles in the polygon.
The student states
his/her conclusion in a clear manner.
The student needs some assistance to complete the task. He/she demonstrates
a partial understanding of polygons. The student recognizes that a pattern exists, but is able to
reach the conclusion that the sum of the interior angles of a polygon is (s - 2) x 180 only with assistance from the teacher or
another student. The student has difficulty stating his/her conclusion in a
clear manner.
The student does not fully complete the task. He/she has little
understanding of different polygons and has difficulty finding the sum of the interior angles of the polygons.
He/she finds only some of these sums. The student does not see a pattern and cannot reach any
conclusion about the angle sum. He/she does not understand the angle sum concept.
The student makes no attempt to do the task.
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