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Performance Task:
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In this task, students will work in pairs to choose
a distant object (e.g., a parked
car or a tree) such that it would be inconvenient to measure the distance
to the object with an ordinary tape measure.
Materials Needed:
Large and small protractors
Wooden stakes
50-meter measuring tape
Meter stick
Hammer
Metric ruler
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The two students stand next to each other and walk in opposite
directions a measurable distance. Put stakes in the ground as markers.
Label the stakes A and B and measure the actual distance from A to B in
meters.
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Approximate the measures of the angles formed by the base line AB and
the line of sight to the distant object, using a large instructor's
protractor or a compass. Call the distance object point C.
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Using a ruler, draw a horizontal line to scale representing the base
line AB. Call this line A'B'.
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Using a protractor, construct angles at A' and B' until they intersect.
Label the intersection point C'.
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Use triangle A'B'C' and the scale established in drawing line A'B' to
find the distances AC and BC.
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Use a 50-meter tape to measure the actual distance from each stake to
the distant object, comparing calculated distances to the actual measured
distances.
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Construct a data table and record all approximated, actual, or computed
measures.
Optional
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Have each pair use this procedure to estimate the distance of an object
across a body of water and/or to a celestial body.
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Analyze the procedure used in this task and state in a written report
how this method could be applied in other mathematics/science activities or
in real-world situations.
Note to the teacher: This activity may be used to integrate geometry and
trigonometry learning activities into physics or earth science. The
objective of this activity is to learn procedures and methods that
astronomers and engineers use to calculate great distances over bodies of
water, through line-of-sight obstructions, and through space.
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Knowledge / Skills:
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Perform operations with signed (positive and
negative) numbers, including decimals, ratios, percents, and
fractions. (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 best procedures for statistical
data collection, organization, and display. (m5)
Understand the angle relationships in triangles
(i.e., acute, obtuse, right, interior, and exterior). (m14)
Use the technique of dimensional analysis to
convert units of measure (e.g., convert km/hr to m/min). (m33)
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Rubric:
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(Material in
parentheses refers to the optional part of the task.)
3 Points = The student through performance and
analysis demonstrates an understanding of how to find unknown distances
through scale drawings of actual measurements. He/she understands fully the
concept of ratio and proportion as applied in this activity. The diagram is
drawn with an appropriate scale and is neat and accurate. The student's
calculations are correct. (He/she is able to apply this method to problems
involving given distances between the earth and celestial bodies and is
able to do the calculations between points if given the angles and
distances.)
2 Points = The student shows some lack of
understanding of the concepts involved but is able to make meaningful
conclusions about most parts of the task. With coaching, the student is
able to complete the task. (With coaching, the student is able to apply the
concepts to other problems.)
1 Point = The student shows little understanding of the concepts
involved. The diagram is incomplete and not to scale. (He/she can not apply
the concepts to any situation.)
0 Points = The student shows no understanding of
the concepts and is unable to complete the task. The diagram is unorganized
and untidy. Little effort was applied. (The student shows no ability to
apply the concepts to this or any situation.
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