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1 Name: (This only happens every four years or does it?)

2 Calendars: Then and Now Name: 1. What is a leap year? What do you already know about leap years? 2. List at least three questions about leap years or calendars that you would like to know. 3. As you watch the PowerPoint on the history of calendars, take notes on important terms, facts, numbers, and people.

3 Original = 365 Julian = Gregorian = Tropical = Use the numbers above to answer the following questions: a. How far off from the Tropical Year would the Julian calendar be after 1500 years? b. How long will it take the Gregorian calendar to be one day off from the Tropical Year? How serious is this problem? Now you will do some of your own calculations on leap years. Use the 4 types of year calculations given in the box above. 5. If each year were counted as being exactly 365 days long, how many days off would we be from the Tropical year after 100 years? Why would this be a problem? 6. After 4 years using a 365 day calendar, how many days are we off (from the Tropical year)? How does this explain Leap Years? 7. Now let s assume that the year is counted as days long, as in the Julian Calendar. Using the average Tropical year stated above, how many days are we off per year? (give as a decimal) a. For each of the number of years stated below, give a decimal that represents the number of days off the calendar will be in the Julian Calendar. (Hint: multiply the days off per year from above by the number of years.) i. 100 years ii. 400 years iii years b. Which are significant? Why?

4 8. Describe the current process for determining when a leap year will occur (should be in your notes it s called the Gregorian Calendar!) How often, which years? 9. Using your answers to question 7a, explain why the Julian calendar had to be switched to the Gregorian calendar described above. You need to use the numbers in your explanation. 10. What is the probability that you will be born on leap year day? 11. Is this current calendar system perfect now with all its modifications for leap years? How much error still remains? When will this catch up with us? Provide a recommendation for dealing with this problem. 12. In your own words, describe what calendars are for and why it is important that they are accurate.

5 Perpetual Calendar A method for determining the day of the week for any date in history! 0=Saturday 1=Sunday 2=Monday 3=Tuesday 4=Wednesday 5=Thursday 6= Friday Your final answer will be divided by 7. The remainder will give you the day of the week as shown at the left. 1. Find the code for the month of your birthday in the table below. 2. Add on the last 2 digits of the year you were born in. 3. Add on the day of the month you were born on. 4. Add on the century code from the table below for the century in which you were born. 4. Now divide the last two digits of the year you were born by 4 and keep only the whole number part. Add this whole number on. 5. Divide your answer by 7 and look at the remainder. 6. EXCEPTION If your date is in January or February of a leap year, subtract 1. Challenge: Where do the codes from the months come from???

6

7 Other Planet Challenge Now you will have the opportunity to create your own calendar for a different planet. Think back through how our calendar was created and what natural events were tied to the calendar. 13. Below is a chart of the orbits and rotations of the planets in our solar system. All of the information is given in Earth days or hours for easy comparison. Choose one planet that you want to develop a calendar for. Planet YEAR: Time for 1 orbit of the sun (in Earth days) DAY: Time for 1 rotation on axis (in Earth days/hours) Mercury 88 days 59 days Venus days 243 days Mars 687 days 24.6 hours Jupiter 4332 days 9.8 hours Saturn days 10.2 hours Uranus days 15.5 hours Neptune days 15.8 hours Pluto days 6.4 days 14. Recall that our year is based on number of our days. For your planet, how many of your days make up one year (as opposed to Earth days). To do this, divide the number of days into the number of days per year. (If your days are in hours, divide them by 24, then divide that answer into the year.) Round your answer to the nearest thousandth. 15. Given the information that you now have, come up with a calendar with whole numbers of days that uses leap years wherever they are needed (doesn t have to be every four years) The steps below will help you. a. Using your answer above, how many whole number of days will a normal year have? b. Look only at the fraction part of your decimal above. What fraction comes close to estimating this decimal? How does this turn into leap years? How often? c. Now, have you added too many or too few leap years? Out of 1000 days, how many more/less days need to be leap years?

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