Hook
The student
page contains the hook only. It is intended to spark interest
in the topic and lead students to ask questions or make predictions.
We all know
that summers usually mean warmer temperatures and winters mean
cooler temperatures, but have you ever hear somebody say on a
hot summer day, "I would love to go up to the mountains
to get away from this heat."
Or maybe
you've heard somebody else say on a cold winter day, "I
would love to take a vacation down south so I could bask in the
warm sun."
When temperature
is the issue, what's the big deal about...
 going
up to the mountains?
 going
south for the winter?
Look at the
following cities on a map.
 Beijing,
China
 Cairo,
Egypt
 Vancouver,
Canada
 Quito,
Ecuador
 Melbourne,
Australia
 St. Petersburg,
Russia
 Honolulu,
Hawaii
 Mexico
City, Mexico
How would
you expect the temperatures of the following cities to vary? Why?
Go to weather.com's
averages and records and find the average yearly
temperature for each city. Then look up each cities elevation
and latitude at the Global
Gazetteer.
 Do
you notice anything about each city's average temperature and
their elevation and latitude?
Questions
Students
might ask similar but different questions than those listed here.
The more students are guided to ask specific questions, the less
inquiryoriented the activity.
Two factors,
elevation and latitude, have been briefly introduced as potentially
affecting a given city's average temperature. Students might list
other factors as well. The point to this activity is to help students
see patterns in temperatures around the world, namely that temperature
can be determined by a locations elevation and latitude. Questions
that would be pertinent to this activity are:
 How
are elevation and latitude correlated with a location's average
temperature?
 If
you were given the elevation and latitude of a location, could
you predict what that location's average temperature would be?
To predict
temperatures for different locations, developing a mathematical
equation from these relationships would be helpful, so you might
also want to lead your students to ask:
 What
is an equation(s) that would predict temperatures for different
locations?
Procedures
After
students have asked questions related to the topic, they will
need to decide a number of things, including:
 Type(s)
of data needed to answer the questions
 Defining
important terms
 Choosing
tools for data manipulation
 Defining
how data will be manipulated and presented
Type(s)
of Data
Average
temperature data, either yearly, monthly, or seasonal, for
many locations will be needed for this activity. Also, the elevation
and latitude for each location will be needed.
Defining
"Correlation"
This activity
might be a good opportunity to introduce the concept of correlationto
your students. MeriamWebster.com
defines correlation as a "relation existing between
phenomena or things or between mathematical or statistical variables
which tend to vary, be associated, or occur together in a way
not expected on the basis of chance alone."
It might
be helpful to use the word in a sentence, such as, "There
is a correlation between smoking and lung cancer."
Defining
"Regression" and "Trend Line"
This activity
might also present an opportunity to introduce or futher expose
students to regression and trend lines. It is likely
that students will complete a linear regression on collected data
(temperature vs. elevation and temperature vs. latitude). Since
these might be foreign concepts to students, they might require
some explanation.
Investigation
Tool(s)
Students
will be using numerical data. Both graphing calculators and spreadsheets
will scatter plot data and then calculate trend lines and their
equations. The example shown uses a spreadsheet.
Manipulating
Data
To caculate
trend lines, students will need to invidually scatter plot temperature
vs. elevation and temperature vs. latitude (see Data Investigation).
When selecting
locations for the elevation scatter plot, best results will be
found when all the locations are relatively near each other but
at different elevations. Countries such as Ecuador, Peru, India,
Nepal, and Switzerland have cities with varying elevations.
When selecting
locations for the latitude scatter plot, best results will be
found when all locations are at or near the same elevation but
at different latitudes.
Data
Investigation
There
is often a giant leap from defining the type(s) of data desired
and actually finding the data. Providing guidance to students
in finding the necessary data may be necessary.
To find average
temperatures, elevation, and latitude, students will need to use
web sites such as WorldClimate.com
or WeatherBase.com.
Temperature data for thousands of separate places can be found
at these sites. Latitude, longitude, and elevation of these places
are usually provided as well.
Elevation
For this
example, Ecuador was chosen as a country to seek the relationship
between elevation and temperature. The country borders the Pacific
Ocean and quickly rises into the Andes mountains, and as a result,
Ecuador has cities with widely varying elevations. The CIA
World Factbook might be a good place to find a map of
the country showing its major cities.
CIA World Factbook Map
Latitude
For
this example, several North, Central, and South American cities
were chosen. In order to eliminate elevation as a possible cause
for variation in temperature, all cities chosen are relatively
near sea level. A world map or globe might be helpful for students
as they choose cities for this part of the investigation.. A
Analysis
Raw
data/information usually has to be manipulated before it can answer
any questions. Students might be unaware of how data can best
be manipulated, so teacher guidance may be appropriate.
Elevation
 Using
a site such as WorldClimate.com
or WeatherBase.com,
monthly average temperatures and elevations are entered
into Microsoft Excel for several Ecuadoran cities. A
good sample of cities with varying elevations is needed. After
all the data has been placed in the spreadsheet it should be
sorted by elevation.
 The Elevation
and Temp columns are highlighted and then charted into a
scatter plot.
 To determine
the correlation and the regression line, right click (PC) or
CTRLclick (Mac) on any of the points on the chart. Select Add
Trendline... Choose Linear
under "Type."
 Click
on "Options" and check the Display
equation on chart and Display
Rsquared value on chart boxes.
In
this example, the equation for determining temperature based
on elevation is Temperature = 0.0026 (Elevation) + 77.177°F.
For those interested, R^2 = 0.9634 is the correlation.
Latitude
 Monthly
average temperatures and latitudes are entered
into Microsoft Excel for several locations in North,
Central, and South America. After all the data has been placed
in the spreadsheet it should be sorted by latitude.
 As in
the Elevation example, a scatter plot is created,
 Before
a trend line is added it is sometimes helfpul to take a closs
look at the scatter plot:
 It
appears that locations between 0°N and 20°N all
have average temperatures near 80°F.
 It
appears locations between 20°N and 60°N are related,
but...
 a
different relationship occurs for locations above 60°N.
 To find
the trendlines for these subsets, two new charts need to be
created:
 So we
now have three important equations for cities at or near sea
level:
 For
locations below 20 degrees north: Temperature = 80°F.
 For
locations between 20 and 60 degrees north: Temperature =
0.988 (latitude) + 96.827°F.
 For
locations above 60 degrees north: Temperature = 2.5826
(latitude) + 193.33°F
Findings
No
result is meaningful unless communicated appropriately. Discussion
of findings should be supported. There may or may not be definitive
answers to the questions students raised.
In this example
we produced four separate equations, one for elevation and three
for latitude.
Elevation
Actual results
will vary depending on cities selected, as well as a variety of
other factors.
 Temperature
= 0.0026 (Elevation in feet) + 77.177°F
Latitude
Actual results
will vary depending on cities selected, as well as a variety of
other factors.
 For
locations below 20°N: Temperature = 80°F.
 For
locations between 20°N and 60°N: Temperature = 0.988
(latitude) + 96.827°F.
 For
locations above 60°N: Temperature = 2.5826 (latitude) +
193.33°F
Combining Equations
We cannot
quite combine two equations together. For example, it will
not work to create an equation Temperature = 0.0026 (Elevation)
+ 77.177 0.988 (Latitude) + 96.827. By putting 0 in for elevation
and 30 in for latitude, we would get:
 Temperature
= 0.0025 (0) +77.177  0.988 (30) + 96.827 = 144.36 °F!
That's way to high. The problem is the adding of both 77.177
and 96.827.
We should
first use one of the latitude equations to establish what the
temperature of a city would be if it were located at sea level.
We could then adjust this temperature for the city's elevation.
Consider
the following examples.
Examples
Mexico City, Mexico
Mexico
City is located at 19.4°N and is 7,329 feet above sea level.
We'd start with the equation for locations below 20°N (the
contant 80°F) and then adjust for elevation:
WorldClimate.com
shows an that the average temperature of Mexico City is 60.8°F,
so 60.9°F is very close.
Tahoe City, CA
For example,
consider Tahoe City, California. Tahoe City is located at 39.2°N
and is 6,227 feet above sea level. We would start with the latitude
equation for locations between 20°N and 60°N Temperature
and then adjust for elevation:
WorldClimate.com
shows an that the average temperature of Tahoe City is 43.3°F,
so again we're not far off in our prediction of 41.9°F.
Possible
New Questions
Answers
often lead to new questions, starting the inquiry cycle over again.
This activity
might cause students to ask additional questions, such as:
 We
focused on locations north of the equator. Do the same rules
apply south of the equator?
 Are
there places that have average temperatures that deviate significantly
from what the equations predict? If so, why?
 What
is the role of seasons for various geographic regions in determining
average temperatures?
 How
is rainfall effected by latitude, elevation, and other factors?
The following
web sites might be helpful in helping students explore further
how elevation, latitude, and also seasons are related to temperature:
