Dr. E and Jessica Edens
7/9/03
Earth Algebra Temperature Activity
1. What kind of function would most accurately describe temperature during
the months from April through September?
The function would be a quadratic because the temperature increases and
then decreases over this period of time.
2. Would the function be different for different parts of the world?
Yes, because there are parts of the world whose temperature does not
change the same rate as other parts (i.e. equator). For example, at the
equator the function would be flatter because the temperature remains about
the same. In contrast, in Australia the temperatures alter between cold and
hot; therefore, the function would go up and down. Comparing US to
Australia, it would be a reflection of Australia’s quadratic.
3. What function would accurately describe temperature over only one day?
Here in the US, over one day, the function would look quadratic because our
day changes temperature through the course of 24 hours. Early in the
morning the temperature is low (about 70 degrees in the summer), then
increases throughout the day, peaks, then decreases throughout the evening.
4. Why is it important to know about the average temperatures over a period
of time?
It is important to know for agricultural purposes, habitat, decisions on where
to live, kinds of houses including air conditioning needs, etc. Also, to observe
any changes over a period of time is critical in order to measure impacts on
the environment, such as global warming.
5. How does temperature affect precipitation?
The colder the temperature the more frozen the precipitation. As
temperatures increase, precipitation increases. However, if the temperature is
too hot, precipitation decreases.
1. Make points from the average temperature data provided; the first
coordinate will be the mid-point of the month and the second coordinate will
be the average temperature for that month. Plot these points on the applet
screen.
2. Use regression to fit the given data with a quadratic function A(t). Graph
the function showing an appropriate domain and range. Use this function to
answer the remaining questions.
The function reads as follows: f(t) = -3.456t2 + 46.871t - 99.938
3. What will the average temperature be on May 15? On August 15? On April 6?
On September 21?
May 15: 41
f(4.5) = 40.9975
August 15: 57
f(7.5) = 57.19
April 6: 15
f(3.2) = 14.6
September 21: 46
f(8.7) = 46.255
4. When will the daily average temperature be 50 degrees? When will it be
freezing?
Daily average temperature of 50 degrees: June 7
September 11
Daily average temperature of 32 degrees: April 30
October 15
f(5.23) = 50
f(8.4) = 50
f(4.0) = 32
f(9.55) = 32
5. On what day will the average temperature be the warmest?
The average temperature would be the warmest on July 26 according to the
function graph. It would be 59 degrees. However, according to the data, it was
actually higher in July and August.
Reflection
Examination of the model
1. Do you think that this model would work for long periods of time, i.e.
decades or centuries? Why or why not?
We think this model would work for small periods of time, such as decades.
However, not for longer periods of time, such as centuries. The impact of
global warming will either change the function or shift it up over longer periods
of time.
2. Could this function be used to predict the temperature at a specific time on
a given day?
This function does not allow for precision per day. It gives average
temperatures over several months.
3. Could we use this function to predict average daily temperatures during
the other months (January, February, March, October, November or
December)?
We could not use this function to predict the other months because we only
used a small period of time to create this function and cannot be extended
beyond April to September. We would have to create a new function.
4. What do you see as advantages to the use of this function?
Disadvantages?
Advantages: allows for predictions on specific days of the month within the range
of April to September; finding the day when certain temperatures
occur
Disadvantages: limited to certain months of the year rather than the whole year;
precision of function might be improved with more data points
Using Earth Studies Materials in Your Classroom
1. What module did you choose? We chose the Streamflow Temperature
module.
2. What course do I teach? Sixth Grade Pre-Algebra
Where does this fit into your course? This particular module does not fit
into pre-algebra because it is not a linear module.
Does the level need to be modified? Yes, if used in sixth grade.
3. Do you need any additional applets? I have not had enough experience
with earth algebra to know at this time.
4. Do you need any additional review topics? N/A
Supplementary materials? I’d be interested in more materials pertinent to
a pre-algebra skill level.
5. How will you evaluate the students? N/A
6. Is there a meaningful local connection that you and your students could
discuss? I would relate the information to how it pertains to the region they
live in and what this has to do with climate and agriculture. For example,
the temperatures in Georgia are different than the temperatures in this
example.