Measurement

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Project Overview

Geocaching is a relatively new activity spawned by the now widely available and
affordable technology of GPS, global positioning system. Essentially, the activity
involves someone hiding a geocache. They then provide the latitude and longitude
coordinates of the cache to others. With a handheld GPS device and the coordinates of
the cache, geocachers attempt their own personal treasure hunt. Their reward of finding
the cache is a small trinket (a keychain, a lapel pin, etc…) placed by a previous
geocacher. All that is asked is that the finder replaces what they have taken with another
trinket. More information may be found at the Geocaching FAQ page at

Considering that students often begin their college education deficient in basic
knowledge areas, this RWLO attempts to assist instructors with remedial classes. The
RWLO provides instructors with the necessary materials and instructions to assist
students in completing a lesson that reviews and addresses the Measurement Standard of
the Measurement Standard of the National Council of Teachers of Mathematics’
Standards for School Mathematics: Pre-Kindergarten through Grade 12.

Note: This RWLO has two possible strands, one where students create a data set,
and one where students use a previously created data set.

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Student Learning Objectives
*Note: If students use the provided data set, they will not complete objectives 1, 2, 7, 8
and 9.

At the completion of this lesson, the student will be able to:

1. Use a GPS unit.

2. Access the web site http://www.geocaching.com to find a geocache that has been
hidden in or near their zip code.
a. Optional: Students access the web site and create a free account. An
account allows site users to log caches they have found.

3. Plot the beginning and ending latitude and longitude coordinates of the geocache
using a map of the area.

4. Estimate the distance they will travel to find the geocache.

5. Compare their estimated travel distance with their actual travel distance.

6. Discuss why there is a difference between their estimated travel distance and their
actual travel distance.

7. Compare how far they actually traveled using U.S. customary units and metric
units.

8. Calculate their average speed by using the actual distance traveled and the time
spent on the excursion.

9. Use formulas to convert their actual average speed from one measurement system
to another; e.g., miles per hour to kilometers per second.

10. Convert rates within the same measurement system; e.g., miles per hour to feet
per second.

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Procedure
Time Frame:
Depending on the structure of this lesson, it could take from 45 minutes to one school
day.

Implementation:
This activity involves two parts. One part is to gather data while completing the
geocaching excursion. If it is not feasible to complete a geocaching excursion to gather
data, a data set has been compiled from an actual geocache. This data set can be found in
the Content Materials folder in the left frame of this web site. The second part is to
analyze the data and compare predicted results with actual results.

Steps of the Geocaching Excursion (Data Gathering):

11. Students access the web site http://www.geocaching.com to find a geocache that
has been hidden in or near their zip code. This link can also be found in the
Content Materials folder in the left frame of this web site.
a. Optional: Students access the web site and create a free account. An
account allows site users to log caches they have found.

12. Students log their beginning and ending latitude and longitude coordinates of the
geocache excursion and of the geocache using the Measurement Student
Worksheet in the Content Materials folder in the left frame of this web site.

13. Students log the start time and end time of their geocaching excursion.

14. Students plot the beginning and ending latitude and longitude coordinates of the
geocache using a map of the area. This can be downloaded using
http://www.mapquest.com. Since Mapquest does not print latitude and longitude
coordinates on the map, students will need to estimate the positions of the points.
This link can also be found in the Content Materials folder in the left frame of this
web site.

15. Students estimate the distance they will travel to find the geocache.

16. Students estimate their rate of speed in finding the geocache.

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17. Students reset the GPS unit trip meter to measure the actual distance traveled in
the search for the geocache.

8. Using a GPS unit and the latitude and longitude coordinates provided by the site,
students attempt to find the geocache.

9. Students log the end time of their geocaching excursion.

Steps of the Data Analysis:

1. Students complete the Measurement Student Worksheet found in the Content
Materials folder in the left frame of this web site.

online converter. This can be useful when students complete the worksheet. This
link can also be found in the Content Materials folder in the left frame of this web
site.

2. Once students have completed the worksheet, conduct a whole class discussion on
the results.

Alternative Activity:
If it is not possible for an actual geocaching excursion to be attempted, the instructor can
create one the grounds of the school.

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Content Material
Steps of the Geocaching Excursion (Data Gathering):

18. Access the web site http://www.geocaching.com to find a geocache that has been
hidden in or near their zip code. This link can also be found in the Content
Materials folder in the left frame of this web site.
a. Optional: Students access the web site and create a free account. An
account allows site users to log caches they have found.

19. Log your beginning and ending latitude and longitude coordinates of the geocache
excursion and of the geocache using the Measurement Student Worksheet in the
Content Materials folder in the left frame of this web site.

20. Log the start time and end time of your geocaching excursion.

21. Plot the beginning and ending latitude and longitude coordinates of the geocache
http://www.mapquest.com. Since Mapquest does not print latitude and longitude
coordinates on the map, you will need to estimate the positions of the points. This
link can also be found in the Content Materials folder in the left frame of this web
site.

22. Estimate the distance you will travel to find the geocache.

23. Estimate your rate of speed in finding the geocache.

24. Reset the GPS unit trip meter to measure the actual distance traveled in the search
for the geocache.

8. Using a GPS unit and the latitude and longitude coordinates provided by the site,
attempt to find the geocache.

9. Log the end time of your geocaching excursion.

Steps of the Data Analysis:

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1. Complete the Measurement Student Worksheet found in the Content
Materials folder in the left frame of this web site.

online converter. This can be useful when you complete the worksheet. This link can
also be found in the Content Materials folder in the left frame of this web site.

2. Once you have completed the worksheet, you will participate in a discussion with

Alternative Activity:
If it is not possible for an actual geocaching excursion to be attempted, the instructor can
create one the grounds of the school.

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Assessment
Student work will be assessed by the instructor and the students as part of the whole class
discussion and review of their completed worksheet. Each student is expected to
participate in the discussion. Five points should be awarded to each student that
contributes to the class discussion. As the student worksheets are reviewed, students
should make their work as correct or incorrect. The instructor should collect the
worksheets and assign one point for each correct answer.

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The activities in this RWLO would be appropriate for a freshman level geometry or
trigonometry class. The activities would also be appropriate for a remedial math course
as required by entrance examinations. It provides an excellent review of standards that
should have been attained at the high school level.

The following course competencies are standards, benchmarks and indicators found in
the Ohio K-12 Mathematics Academic Content Standards and the National Council of
Teachers of Mathematics’ Standards for School Mathematics: Pre-Kindergarten through

I. Measurement Standard (from NCTM):
 Understand measurable attributes of objects and the units, systems, and
processes of measurement; and
 Apply appropriate techniques, tools and formulas to determine
measurements.

II. Measurement Standard, Benchmarks and Indicators (from Ohio):
 Students estimate and measure to a required degree of accuracy and
precision by selecting and using appropriate units, tools and technologies.
A. Benchmarks:
o Use proportional reasoning and apply indirect measurement
techniques, including right triangle trigonometry and properties of
similar triangles, to solve problems involving measurements and
rates.
o Explain differences among accuracy, precision and error, and
describe how each of those can affect solutions in measurement
situations.
B. Indicators:
o Measurement Units:
1. Compare and order the relative size of common U.S. customary
units and metric units; e.g., mile and kilometer, gallon and liter,
pound and kilogram.
2. Use proportional relationships and formulas to convert units
from one measurement system to another; e.g., degrees Farenheit
to degrees Celsius.
3. Convert rates within the same measurement system; e.g., miles
per hour to feet per second; kilometers per hour to meters per
second.
o Use Measurement Techniques and Tools:
1. Use appropriate levels of precision when calculating with
measurements.

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2. Use scale drawings and right triangle trigonometry to solve
problems that include unknown distances and angle measures.
3. Solve problems involving unit conversion for situations
involving distances, areas, volumes and rates within the same
measurement system
4. Explain how a small error in measurement may lead to a large
error in calculated results.

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Supplementary Resources

   Ohio’s K-12 Mathematics Academic Content Standards
   Geocaching FAQ
   The History of GPS
   Magellan GPS Units
   Garmin GPS Units

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Recommendations

Recommendations for Integration:
The activities in this RWLO would be appropriate for a freshman level geometry
or trigonometry class. The activities would also be appropriate for a remedial math
course as required by entrance examinations. It provides an excellent review of standards
that should have been attained at the high school level.

Back Up Instructions:
In the event that the Internet becomes unavailable, the following materials found
in the Content Materials folder should be printed and made available to each student.
 Map of Area of Provided Data Set
 Geocache Data Set
 Measurement Student Worksheet

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