Burning Daylight Desmos Application Activity

Transcription

1 Burning Daylight Desmos Application Activity 1. Start by going to students.desmos.com and entering the code on the board. I suggest you copy the code so you can work from home as needed. 2. There are some diagrams and videos on the last page of this packet to help you with the science part of the lab. 3. On slide #1, you are being asked: Fairbanks is a city in Alaska. It's one of the northernmost cities in the United States. Miami is a city in Florida. It's one of the southernmost cities in the United States. Which city do you think has more total hours of daylight during an entire year? Why? (Note: Daylight is the time between sunrise and sunset, regardless of that day's weather.) 4. On slide #2, you are shown two graphs (one purple and one orange). Which graph represents Miami, FL? Explain your reasoning below. 5. On slide #3, you are being asked to write an equation for the graph. Remember, we used the general form: y = A sin B x C + D. Write the equation in the box, and copy your equation below. 6. On slide #4, you are being asked to do the same for the purple graph. 7. On slide #5: You are asked to compare and contrast the functions.

2 8. On slide #6, you are being asked to calculate the TOTAL number of hours of daylight in each city for the entire year (only one year). Make sure you read the graph carefully. Write your estimates for each city below and then explain your process. Which city do you think receives more daylight per year? Explain. (Even if you can t figure out how to get the total hours of daylight, do you best to explain any educated thoughts your group has on this question). Fairbanks Graph Miami Graph

3 9. Barrow, Alaska is the northernmost city in the United States. Sketch what you think the graph of daylight hours would look like for this city. Explain. 10. On the final slide, answer the presented question. 11. Go to the website: This is the website for the United States Naval Observatory (USNO) located in Washington, DC. The department collects data on hours of sunlight and darkness for every day of the year. In Form A, change the year to Leave the type of table as daylight. Change the state to Pennsylvania and type Pittsburgh for the city. Press compute table. 12. Go to desmos.com or open the desmos app.

4 13. In the top left corner you should see a + sign. Click on it and select table from the drop down menu. The screen should look like this now. 14. In the x column, enter the days. In the y column, enter the approximate number of hours of daylight for each month. You will need to change the minutes to a decimal of an hour. For example, you would enter 10:30 (10 hours and 30 minutes) as 10.5 hrs. Make sure you are careful when converting minutes to decimal hours. 15. Don t pick all of your data points from one month. The more data points you use, the more precise your model will be. I suggest using no less than 30 data points. 16. Once all of your data is entered, click the + sign again and add an expression. 17. Type y m ~ asin b(x m c ) + d. To get y sub 1, just type y1. The ~ sign is in the ABC section of the keyboard. 18. Desmos will automatically run a regression to give you a formula that fits your data. It gives you an equation that will allow you to calculate the number of hours of daylight in a given month. You will notice that once the calculator runs the regression, it gives you the parameters (or values) for a, b, c, and d that best fit the data. Write your equation below. 19. There is another value that you get when you run a regression. That is the R t value. This is also called the coefficient of determination. This is a number between 0 and 1 and it tells you how well your equation fits the data. A value of 0 means the data does not fit the regression line. Your data points would be very spread out and in no apparent pattern. A value of 1 means that the regression line (or curve in this case) fits your data perfectly. In fact, every data point would lie directly on the curve. What is your R t value? What does it mean?

5 20. Use the regression function to estimate the number of hours of daylight in Pittsburgh, PA for each of your group member s birthdays in 2017 (be careful this is a year later than what you have data for, so your x value will be greater than 365). Group Member Birthdate (month and day) x value Predicted hours of daylight Actual hours of daylight 21. To get the data for the final column in the table above, go back to the USNO site and run the data for 2017 in Pittsburgh. How well did your model predict the actual hours of daylight? 22. On what day can we expect to have 13.5 hours of daylight? Use your equation and show your work. 23. If we wanted to know how many hours of daylight there were in Ushuaia, Argentina (southernmost city in the world) on your birthday, how well do you think your model would work? Why? 24. The latitude and longitude for Ushuaia: S, W. Use what we learned in class to change these coordinates to DMS. Write your calculations below. 25. Go back to the USNO site and use Form B Locations Worldwide. Enter the coordinates from above for Ushuaia. Click compute table. 26. Check the table for the numbers of hours of daylight in Ushuaia on each group member s birthdays. Does this match what you predicted above?

6 Helpful Videos: (made for kids easiest to understand) (TED Talk for Education) Turning in your report: The lab is due no later than Monday, November 13 in your class period. Late labs will lose 10% of the total points available per day. You do NOT have to type anything as long as I can easily read your handwriting.