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ICLE Standards:
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Geometry: Develop an appreciation of geometry as
a means of describing the physical world.
Statistics: Read and interpret tables, charts,
and graphs.
Measurement: Make and use measurements needed in
the solution of problems.
Computation: Use computation to solve problems.
Mathematical Connections: Value the role of mathematics in our culture and
society.
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Performance Task:
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This task consists of two parts. First, you will
need to follow the directions to determine solar noon; then, you will calculate the degrees of latitude and longitude of your location. Work
with one other class member on this task. Hand in one report showing your answers and all work required to
arrive at those answers.
Part I: Directions to Determine Solar Noon
1. Locate a level area that is exposed to the sun.
2. Place a stick in the ground to measure its shadow.
3. Mark the end of the shadow for about 30 minutes - from 15 minutes before
noon to 15 minutes after noon.
4. Using an accurate watch, mark the length of the shadow every minute and
record the time.
5. Note the exact time, to the nearest minute, that the shadow is the
shortest. This is Solar Noon.
Part II: Directions to Determine Degrees Latitude and Degrees Longitude of
Your Location
1. Construct a right triangle whose two legs are the length of the stick you
used in Part I and the length of the stick's shadow at solar noon. You may use a scale and construct a triangle
using smaller sides.
2. Your apparent latitude is the angle formed by the hypotenuse of the
triangle and the leg representing the length of the stick.
3. Locate on the Latitude Correction Graph (attached) the approximate
degrees of correction.
4. Your actual latitude is the sum of your apparent latitude and the
degrees of latitude correction.
5. Subtract standard time zone noon (12:00) from solar noon. This can be a
negative number.
6. Locate on the Longitude Correction Graph (attached) the number of
minutes correction.
7. Add the correction minutes to the time you had in step 5 and multiply
the result by 0.25 (the number of degrees that the sun moves in one minute)
8. Add the result of step 7 to the Degrees West of Greenwich for your time
zone (see attached chart). This number is your actual longitude.
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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 angle relationships in triangles
(i.e., acute, obtuse, right, interior, and exterior). (m14)
Use the Pythagorean theorem to compute side
lengths of right triangles. (m21)
Use the technique of dimensional analysis to
convert units of measure (e.g., convert km/hr to m/min). Understand and use variuos techniques
for estimating, making and converting measure; and using these to perform dimensional
analysis. (m33)
Use expository writing skills in subjects other
than English language arts. (ela58)
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Rubric:
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The following
represent the criteria upon which each pair of students will be assessed in
this task.
1. The ability to follow directions and stay on task.
2. The ability to work cooperatively with another class member.
3. The ability to work without coaching from the teacher.
4. The ability to carry out measurement activities.
5. The ability to perform calculations accurately.
6. The ability to read charts and graphs.
7. The ability to apply mathematical knowledge needed in the task
appropriately.
8. The ability to organize your work and indicate your results in a written
report.
Each pair of students will get a grade from 1 to 5 on this task as outlined
below.
5 Points = All criteria above are met at a high
level. Both students demonstrate an excellent understanding of the
mathematics needed to complete the task. The students appear highly
motivated, and a high level of independence is evident. The final report
indicates that the students have a good grasp of the task and that they put
forth sustained effort in performing the task with quality.
4 Points = Most criteria are met at a high level.
Both students demonstrate a fairly good understanding of the mathematics
needed to complete the task. The students appear adequately motivated
although they need some coaching from others to carry out all aspects of
the task. The final report indicates that the students have an adequate
grasp of the task and that they put sufficient effort into performing the
task.
3 Points = Most of the criteria are met, but only
some of them at a high level. Both students demonstrate only a minimum
level of understanding of the mathematics needed to complete the task. The
students do not appear motivated to work on the task and need considerable
help from others to complete it. The final report indicates that the
students have only a minimal grasp of the task and that they put little
sustained effort into performing the task.
2 Points = Only a few of the criteria are met and
those are not met at a very high level. Very little understanding of the
mathematics needed to complete the task is indicated. The students lack
motivation and need constant assistance to work in a sustained manner. The
final report indicates that the students have little understanding of the
task and that they put little effort into doing any kind of quality
performance.
1 Point = None of the criteria is met at a satisfactory level. The
students indicate little, if any, understanding of the mathematics needed
to complete the task. The students demonstrate no motivation to do the task
and needed constant prodding to keep working on the task. The final report
indicates that the students have no real understanding of the task and that
they were unwilling to put forth any effort in an attempt to do a
satisfactory performance.
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