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Performance Task:
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You are to assume the role of an apprentice who
works at an architectural firm assigned to design an
urban sports facility. Your task is to design a basketball court. You know
you can use coordinate geometry
to help you model the court, and you have decided to use the Geometer's
Sketchpad as a tool to assist you.
You have assigned the following coordinates as court corners: (-7, 0) (11,
0) (11, 10) and (-7, 10). Verify that
these coordinates actually form a rectangle. Set up the scale of 1 cm = 5
feet on the Geometer's Sketchpad. Using the Sketchpad, find the midpoints of each side of the court, connect
these midpoints and confirm
that the figure formed is a parallelogram. Construct the diagonals of this
parallelogram. Each of these lines
divides the court into two congruent parts. Construct two concentric
circles with diameters of 5 feet and 10
feet at center court.
Print out the diagram of the court. In your math
journal, write a concise explanation to
the chief architect telling what you did and justifying your work.
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Knowledge / Skills:
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Understand the properties of circles (e.g.,
radius, arc, diameter, chord, secant, tangent, etc.). (m10)
Use geometric methods (e.g., an unmarked
straightedge and compass) to complete basic geometric constructions (e.g.,
perpendicular bisector of a line segment, angle bisector, etc.). (m23)
Understand the properties and classification of
quadrilaterals by orientation (e.g., parallelogram, rectangle, rhombus,
square, and trapezoid). (m27)
Use geometric methods (e.g., an unmarked
straightedge and compass) to complete basic geometric constructions (e.g.,
perpendicular bisector of a line segment, angle bisector, etc.). (m28)
Use the technique of dimensional analysis to
convert units of measure (e.g., convert km/hr to m/min). (m33)
Use writing as a tool for learning in formats
such as learning logs, laboratory reports, note-taking, and journals. (ela40)
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Rubric:
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4 Points =
Student independently completes the task. He/she demonstrates a high
level of understanding of the basic geometric terms and principles. He/she
follows directions and easily uses necessary technology. All steps are
complete and justified. Journal entry is concise, accurate and clearly
written.
3 Points = Student needs some assistance in
completing task. He/she understands most geometric concepts. He/she is able
to follow directions, but needs some help using necessary technology. All
steps of procedure are completed; most are justified. Journal entry is
concise and accurate, but not smoothly written. Some grammatical errors are present.
2 Points = Even with assistance, student has
difficulty with the task. The difficulty appears to stem from a lack of
understanding of major geometric concepts. He/she has difficulty following
directions and/or
using necessary technology. Although all steps are completed, there is
little justification of what the
student did. Journal entry is vague, and the student has poor English
skills/many grammatical errors.
1 Point = Student does not complete the task. He/she demonstrates a
lack of understanding of the major geometric concepts. The steps of the
procedure are not completed, and no justification of what the student did
is given. The student does not make a journal entry. He/she extended little
effort to
complete the project and showed little interest in the task.
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