Content Material
Student Directions:
Project Overview:
As you look back in time, do you notice any
patterns or trends in the weather when it comes to changes in
temperature? Use your ingenuity
to determine in which month(s) the temperature changes most rapidly for a
major city of your choice. Can
you figure out in which month(s) the temperature changes most slowly for
this city? We are going to form
small groups and make these predictions. Give it some serious thought because
a reward will be granted to those group(s) whose predictions are
accurate. Through the power of
mathematics, you will find the answer to these questions. Good luck in your quest for the
truth!
Day 1:
1.
Form groups
of three or four and choose a major city in the USA. For the city of your choice, predict
in which month the temperature:
a.
Increases
most rapidly.
b.
Decreases
most rapidly.
c.
Changes most
slowly.
Provide some sort of rationale for your predictions. You may use your ingenuity, common
sense, experience, or whatever comes to mind.
2.
Submit your
predictions and the rationale on a sheet of paper. Make sure the names of all the
participants in your group are listed.
3.
As a
homework assignment, access the National Oceanic and Atmospheric
Administration (NOAA) Website.
Find the average daily maximum temperature for the last 12 months
for the city of your choice and construct a chart containing this data. Each student is to have a copy of
the chart. To obtain this data,
follow these directions:
a.
Use the web
address: http://www.noaa.gov
b.
Scroll down
to “Today’s Weather” on the lefthand side.
c.
Type in city
and state. Click Go.
d.
Scroll down
to “Additional Forecasts & Information” on the righthand
side.
e.
Click on
“Past Weather Information”.
f.
Scroll down
to “Monthly Climatic Summaries”.
g.
Enter each
month separately and obtain “Average Daily Maximum”
temperatures.
Day 2: Within each group, use teamwork by
working collaboratively to help each other with the project, especially
with the use of calculators.
Each of you is to submit your own work individually to complete the
assignment.
4.
Use your
graphing calculator to:
a.
Enter the
data into lists (columns).
i.
Use the STAT
feature.
ii.
Let L1
contain the numbers 1 through 12, representing each month of the year.
iii.
Let L2
contain the average daily maximum temperature for each corresponding month.
b.
Plot the
data.
i.
Use the STAT
PLOT feature.
ii.
Use the
GRAPH feature.
c.
Find a regression
function of the form T(x) = a*sin(bx + c) + d where T is the temperature
and x is the time in months.
i.
Use the
STAT, CALC, and SinReg features.
ii.
Round each
constant to the nearest tenth.
d.
Graph the
regression function to observe the curve of best fit to data set.
i.
Use the Y=
feature.
ii.
Use the
GRAPH feature.
5.
Find the
derivative of the regression function by hand applying basic
differentiation rules.
6.
Use your
graphing calculator to:
a.
Graph the
derivative function.
i.
Use the Y=
feature.
ii.
Use the
GRAPH feature.
b.
Observe both
the regression function and its derivative function at the same time.
i.
Use the ZOOM
feature
ii.
Use the
ZoomFit feature.
iii.
Use the
WINDOW feature
7.
On a sheet
of graph paper, plot the points and graph the regression function and the
derivative function as seen on your calculator screen. Label the graphs accordingly.
8.
Analyze the
graph of the derivative function to find the actual real month where the
temperature:
a.
Increases
most rapidly.
b.
Decreases
most rapidly.
c.
Changes most
slowly.
9.
State the
mathematical reasoning that supports each of your answers.
10. Compare your predictions made in the beginning
with the actual real results found through mathematics. How accurate were your predictions
when using nonmathematical reasoning?
11. Each of you is to submit:
a.
A chart
containing the information obtained from the Website.
b.
An equation
for:
i.
The
regression function.
ii.
The
derivative of the regression function.
c.
A sheet of
graph paper containing:
i.
The plotted
points
ii.
The graph of
the regression function
iii.
The graph of
the derivative function.
d.
Based on the
graph of the derivative, the month where the temperature:
i.
Increases
mostly rapidly.
ii.
Decreases
most rapidly.
iii.
Changes most
slowly.
e.
The
mathematical reasoning that supports each of the three answers.
12. Receive a reward if all of your predictions were
right. Ask the instructor to
verify the correctness of your answers.
Referenced URLs:
A
backup Website address is http://www.weather.com
