**Earth
and Moon Viewer**

Where's the Math?

**Instructors'
Notes **

Click
here for a printable document (requires Adobe
Acrobat Reader)

Back
to Earth and Moon Viewer Introduction

**The Earth and
Moon Viewer:** http://www.fourmilab.ch/earthview/

**Topics: **coordinate
geometry, measurement, number operations.

**Purpose: **Learners
will use the Earth and Moon Viewer to investigate a variety
of questions having to do with coordinate geometry and number
operations. The learner activity sheet leads them through activities
dealing with latitude/longitude coordinates, world time zones,
the 24-hour clock, and charts of sunrise/sunset data. These
investigations are done in the context of the learner’s
location and time zone.

**Materials: **Computers
with Internet access, learner activity sheet, globe or map.

**Prior Knowledge:**
This activity is most successful if learners recognize the continents
of the world and the general location of their home city. It
is helpful if learners already understand latitude and longitude,
but they can learn this concept through this activity. (See
Related Links)

**Description: **The
Earth’s latitude and longitude grid is an excellent example
of the coordinate plane. The Earth and Moon Viewer website can
be used to introduce the concept of coordinate geometry or to
provide practical applications once the concept has been learned.
When used in conjunction with the U.S. Naval Observatory website,
the Earth and Moon Viewer provides practice using basic mathematical
operations in dealing with time and daylight.

**Assessment:**
The concepts in these activities can be quickly tested in interesting
ways. After completing the activities suggested in the
learner activity sheet, learners can provide each other with
questions, such as "What is the latitude/longitude of Tokyo,
Japan?", or "What major world city will you find at approximately
34° S, 151° E?" (Learners must also know the
answers to the questions they are asking each other).
Similarly, learners can construct questions about time zones:
"Fifi is leaving New York at 6 pm local time Friday to fly to
Paris. If the flight time is approximately 7 hours, what
time and day will it be in Paris when she arrives?"

**Notes:**

- Time zones west
of the Prime Meridian (Greenwich Mean Time; Universal Time
Coordinated) are often indicated by negative numbers, while
eastward zones are indicated by positive numbers. This can
serve as a visual representation of the number line and positive/negative
numbers.

- The latitude/longitude
measurements are give in decimal form at the Naval Observatory
and the Tiger Gazetteer websites, rather than in the more
traditional degrees/minutes/seconds. The decimal form can
be entered into the Earth and Moon Viewer website, where it
will be automatically converted into degrees/minutes/. The
degree/minutes form will be displayed at the top of the webpage.
Learners may be confused about this apparent difference in
numbers. For example, Corvallis, Oregon, is described and
located either way:
44.6N, 123.3
W (decimal notation)

44°
36’N, 123° 18’ W (degrees/minutes notation)

- These explorations
of latitude, longitude, time, and the seasons can be connected
to a real-time investigation of Eratosthenes’ experiment
to estimate the Earth’s circumference. Participate in
the worldwide science and math experiment to recreate what
Eratosthenes measured. For more information about this event,
look under the Events and Celebrations section of the Science
& Numeracy Special Collection. /eventscelebs.html

**Websites used
in learner activity:**

The Earth and Moon
Viewer: http://www.fourmilab.ch/earthview/

Time Flies: http://www.planemath.com/activities/timeflies/time1.html
This website takes one through the workings of 24-hour clock
time.

Tiger Gazetteer from
US Census: http://www.census.gov/cgi-bin/gazetteer

U.S. Naval Observatory
World Time Zone Map:

http://aa.usno.navy.mil/AA/faq/docs/world_tzones.html

U.S. Naval Observatory,
Complete Sun and Moon Data for One Day:

http://aa.usno.navy.mil/AA/data/docs/RS_OneDay.html

World Cities on the
Earth and Moon Viewer: http://www.fourmilab.ch/earthview/cities.html

How Far Is It–the
Distance Calculator: http://www.indo.com/distance/

World Map of Live
Web Cams: http://members.ozemail.com.au/~worldmap/World.html

**Related Links:**

1. Maps:

National Geographic
Map Machine: http://www.nationalgeographic.com/maps/index.html

2. Coordinate geometry:

Project Interactive:

Graphing and
the Coordinate Plane: http://www.shodor.org/interactivate/lessons/fm1a.html

Cartesian Coordinate
System: http://www.shodor.org/interactivate/lessons/cartesian.html

Score Mathematics:
Coordinate Graphing

http://score.kings.k12.ca.us/lessons/graphing.html

This website
uses the activities from Project Interactive (see above)
while providing a quiz and a coordinate grid in pdf files.
The student page gives step-by-step instructions for independent
work.

Chameleon Graphing–An
Introduction to the Coordinate Plane: http://forum.swarthmore.edu/cgraph/cplane/

This is an excellent
site from the Math Forum, but some of the language and graphics
are not age neutral. There are references to "your
parents" and "notes to grownups", and there
is a cartoon-cute chameleon. The glossary of terms is excellent.

3.Time, time zones,
astronomical data:

Definitions of
Rise, Set, and Twilight: http://aa.usno.navy.mil/AA/faq/docs/RST_defs.html#top

The World Clock–Time
Zones: http://www.timeanddate.com/worldclock
Click on the name of a city and find out more information
about it.

U.S. Naval Observatory
Astronomical Applications: http://aa.usno.navy.mil/AA/faq/

This provides
an index of the answers to frequently asked questions, such
as

The International
Date Line: http://aa.usno.navy.mil/AA/faq/docs/international_date.html

The Phases of
the Moon: http://aa.usno.navy.mil/AA/faq/docs/moon_phases.html

Time Exhibits: http://www.time.gov/exhibits.html

This is an index
of exhibits recommended by the National Institute of Standards
and Technology and the U.S. Naval Observatory. Here are
two good samples:

Calendars from
the Sky: http://webexhibits.org/calendars/
This exhibit gives the history of various calendars used
by world cultures and religions.

Daylight Savings
Time: http://webexhibits.org/daylightsaving/
This exhibit gives the history of daylight savings time
as well as other interesting information.