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Let the Sun Shine

Student Worksheet 1




Name __________________________      Period_______      Date_______________



If you think about the time that the sun rises and sets each day, there are various changes that occur during a year. These changes vary depending on the latitude of that location. If you have been in Seattle or Canada in the summer you might notice that the sun does not set until after 10:00 PM. On the other hand, if you have spent time in Mexico City, the daylight hours do not vary much during the year.

This activity will have you explore daylight hours for various locations around the world. You will record hours of daylight for 12 different times during a year and fit these data points to a cosine curve.

Each member of your group will be recording and graphing the daylight hours for a different location. You will compare certain aspects of each graph and make some conjectures about the amount of daylight in different locations around the world.

There are many websites that have the times of sunrise and sunset. The site below is one to try. After you link to it, select the "Table of Sunrise/Sunset Times for an Entire Year". There will be 2 forms to choose from, Form A for US locations and Form B for International locations. You only need to enter the city and state (if in the US) or the city and country if international. A daylight table will appear for each day of the current year. You can print out the entire table by following the directions at the site. An alternative is to record only the days needed on this worksheet. You can use your calculator to calculate the daylight hours.

http://aa.usno.navy.mil/AA/data/docs/RS_OneYear.html#forma

Each group member needs to select one of the city choices below. Make sure that each member of the group has one city from group A, one from group B, and so on.

Group A Group B Group C Group D
Anchorage, Alaska Portland, Oregon Atlanta, Georgia Hilo, Hawaii
Helsinki, Finland Portland, Maine San Diego, California Bogota, Colombia
Reykjavik, Iceland Madrid, Spain Fukuoka, Japan Jakarta, Indonesia
Oslo, Norway Istanbul, Turkey Casablanca, Morocco Lagos, Nigeria

You will need to refer to the following website to gain the sunrise/sunset times for international cities. For the international cities, the degrees and minutes for latitude and longitude, hours from Greenwich Mean Time must be entered along with the city name. This site will give you all that information for the international city that you select; then go back to the previous site and obtain the sunrise/sunset time. There is a Time Zone table at this site for you to find the hours east/west of Greenwich time.

http://www.bcca.org/misc/qiblih/latlong_oc.html

  1. Complete the table below with the information from your city. You will enter this data into the calculator or the interactive software, graph the data, and find the algebraic model.

    You will have to calculate the hours of daylight (see shortcut method below) using the sunrise/sunset information on the table you find at the website.

    The sunrise/sunset times will be listed as 24 hour time (military time). In other words, 1:00 P.M. will be shown as 13:00. An easy and quick method to obtain the daylight time is to type in the values in terms of min/60 as shown on the screens below.

    The keystrokes represent the daylight time for sunset at 16:55 P.M. and sunrise at 6:59 A.M.

    (16+55/60)-(6+59/60)

    Your City __________________________

    Latitude __________ Longitude _________

    Day #

    Hours of Daylight

    Day #

    Hours of Daylight

    1

    		  

    172

    		  

    30

    		  

    210

    		  

    60

    		  

    240

    		  

    90

    		  

    270

    		  

    120

    		  

    300

    		  

    150

    		  

    356

    		  

  2. Enter the data into two lists, L1 and L2.

  3. Check to make sure that you do not have any functions turned on in the Y= editor. To plot the points, turn on the Statplots for the two lists and use ZoomStat to view the graph. If you entered the data correctly, you should see one cycle of the daylight time for your city. An example of the steps is shown below.

  4. TRACE along your plot. What do the x-values represent? ______________________

  5. What do the y-values represent? ___________________________________________

  6. What is the maximum daylight time for your city? ____________

  7. What are the other maximum times for the other members in your group? __________________________

  8. Which location in your group has the longest day (largest amount of daylight time)?___________________

  9. Which location in your group has the shortest day? _________________________

  10. Which day number is the longest? _____________ Is the is the same for all locations? Why or why not? _______________________________________________________________________________________

  11. Explain the relationship between a location's latitude and the amount of daylight hours it has?

  12. The locations that were given to you as choices are in the Northern Hemisphere. Can you find a location in the Southern Hemisphere with the same latitude as your city? Go back to the website and locate it. Write the name of the city and its latitude and longitude below.

    _________________________ ___________ ___________
    Name of city in Southern Hemisphere Latitude Longitude

  13. Compare the daylight hours on a given day for both places. Day # ____

    Northern Hemisphere location ________Southern Hemisphere location _______

  14. What is the sum of the daylight hours of the two locations on the same day of the year? ______

    Explain. ______________________________________________________________________

  15. If a location has approximately 12 hours of daylight each day, every day, where would it be located? ______________________________________.

  16. Can a location have 24 hours of daylight? Explain. _____________________________________________

  17. Can you find such a location and explain if and when it would have about 24 hours of daylight? _________

    __________________________________.

  18. Does this location ever have 0 hours of daylight? Explain if and when that would happen. ________________________________________________.
It would be a good idea to save the daylight data in a program so you can use it again without going back to the website. This can be done very easily.

You want to save L1 and L2 which contain the data. All you need is a 2-line program. Follow the simple steps below to create this program. You can then delete or overwrite the lists since the data will be saved somewhere else. The screenshots below will take you through each step.

Press PRGM Choose NEW and type in the name of the program. You will already be in ALPHA mode. Press ENTER when finished with the name of the program. Press 2nd STO will bring up the RCL (recall) command, then type L1.

Press ENTER and the data from L1 will be displayed.

Immediately store to list 1 by pressing the STO key and choosing L1. Press ENTER when finished.

Repeat the process for the next list.

When you are finished with both lists, press 2nd QUIT and you have now created a program with the two data lists.

To have these lists appear in the List Editor, simply run the program.


The Integrating Technology into Math Instruction webpages project is partially funded by a grant from The Boeing Company. Integrating Technology into Math Instruction is a project of +PLUS+ and is displayed on the Los Angeles Educational Partnership Learning Exchange. +PLUS+ is an initiative of the Los Angeles Educational Partnership.
Updated June 2000