Project Overview

Student Learning Objectives

Procedure

Content Material

Assessment

Links to Course Competencies

Supplementary Resources

Recommendations

 

 

Real World Learning Objects: Mathematics

Rate of Change in Temperature

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) Web-site.  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 left-hand side.

c.      Type in city and state.  Click Go.

d.      Scroll down to “Additional Forecasts & Information” on the right-hand 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 non-mathematical reasoning?  

11. Each of you is to submit:

a.      A chart containing the information obtained from the Web-site.

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 back-up Web-site address is http://www.weather.com