Friday, September 30, 2016

Science: The Earth-Moon-Sun System (Days 32-33)

This upcoming Monday is Rosh Hashanah, the Jewish new year. For decades, the LAUSD has observed both Rosh Hashanah and Yom Kippur as holidays. Thus my charter school, which mostly follows the LAUSD calendar, is closed both Monday, October 3rd and Wednesday, October 12th.

I've decided that this is a great time to teach a science lesson about the earth, moon, and sun. I told my students about the earth's revolution around the sun, which leads to the seasons of winter, spring, summer, and fall. Then I moved on to the moon's revolution around the earth, which leads to the phases of new moon, waxing crescent, first quarter, waxing gibbous, full moon, waning gibbous, last quarter, and waning crescent.

Then I told my students about the calendar used by the ancient Hebrews. On this calendar, which is still used today by the Jews, the new month begins at the new moon and the new year begins near the fall equinox. I said that calculating the date of Rosh Hashanah is quite complicated, but I did show them the following link:

(I've mentioned this link in previous blog spots when trying to explain the Easter date.)

A simplified formula for the date of Rosh Hashanah on the Gregorian calendar for 1900-2099 is gotten by calculating
N + fraction = 6.057778996 + 1.554241797*Remainder(12G|19) + 0.25*Remainder(y|4) - 0.003177794*y,

where y=Y-1900. Use the same postponement rules (note that 23269/25920=0.898, and 1367/2160=0.633). This method is easier to calculate using a pocket calculator.

I showed them the calculation for this year. Here y = 116 and the Golden Number G is 3, since 114 is a multiple of 19. The first division is 36 (12 times 3) divided by 19, which has remainder 17, and the second is 116 divided by 4, which has remainder 0. So the calculation is:

6.057778996 + 1.554241797*17 + 0.25*0 - 0.003177794*116 = 32.57204557

This gives the date as September 32nd, which really means October 2nd. But October 2nd is a Sunday, and the rules given above state that Rosh Hashanah can't fall on Sunday. (The reason for this is indirectly related to the fact that Saturday is the Jewish Sabbath. Neither Rosh Hashanah nor Yom Kippur can fall on the day before or after the Sabbath.) Thus  the holiday is on Monday, October 3rd.

Then I showed the students the calculation for next year. Some students guessed that Rosh Hashanah will fall on a Tuesday next year, since October 3rd next year will be a Tuesday (that is, in analogy with their birthdays). But let's see -- the Golden Number will be 4, and the first division is 48 (12 times 4) divided by 19, which has remainder 10, and the second is 117 divided by 4, which has remainder 1. So the calculation is:

6.057778996 + 1.554241797*10 + 0.25*0 - 0.003177794*117 = 21.69314744

September 21st, 2017 is a Thursday, and so no postponement is required. Next year, Rosh Hashanah will indeed be on that Thursday, not Tuesday. (Notice that Yom Kippur will fall on a Saturday. When either high holiday falls on the Sabbath, the LAUSD does not take an extra day off.)

But how do we know that September 21st next year will be a Thursday? According to the link, the simplified Rosh Hashanah formula shown above is attributable to the British mathematician John Conway, whom I've mentioned on the blog before. And so that means Conway Doomsday.

I told my students the Conway Doomsday formula. I figured they'd get a kick out of finding out what day of the week they were born. Interestingly enough, the first birthdays I randomly selected ended up being in either June or October, where 6/6 and 10/10 are easily identified as Doomsday. But one sixth grader gave me a January birthday, which is the hardest month in the Doomsday formula.

The earth-moon-sun system is included in the Next Generation standards for eighth grade. And so after this lesson, I give my eighth graders the online science assignment for this system.

This is a Calendar-labeled blog post due to the mention of a religious holiday. I didn't tell my students the following, but it may be instructive to blog readers to figure out where all the magic numbers in the Conway formula come from:

N + fraction = 6.057778996 + 1.554241797*Remainder(12G|19) + 0.25*Remainder(y|4) - 0.003177794*y

Here are my best guesses:

-- 6.05777... means that the earliest Rosh Hashanah is September 6th. Actually, it could be on the 5th due to the minus term later in the formula (and it did fall on September 5th, 2013 -- the early Rosh Hashanah that led to "Thanksgivukkah").

-- 19 refers to the 19 years of the Metonic cycle. The significance of the 19-year cycle is that new moons link up with solar years approximately 19 years apart. For example, I was born under a new moon, and there was a new moon on my 19th birthday as well.

-- 1.55424... doesn't mean anything on its own, but 1.55424...*19 = 29.53059..., which is about the length of a lunar month.

-- Likewise, 12 doesn't mean anything on its own, but 1.55424... * 12 = 18.65090... If there is a new moon one year on September 1st, there will be a new moon the following year about 18.65 days later, which is September 19th or 20th.

-- The numbers 0.25 and 4 obviously refer to Leap Days.

-- 0.003177794 is a slight adjustment to the Metonic cycle. The author at the above link writes that the 19-year Metonic cycle isn't exact, and so this term gives a slight adjustment (though it's still not as accurate as the Gregorian calendar).

Originally, I wanted to give this lesson today, since it's the last day before the three-day weekend caused by the Rosh Hashanah holiday. But there were continued problems with the mousetrap cars, and in fact I actually gave this lesson yesterday (even though I waited until today to post it here on the blog). This gave me an extra chance to figure out how to make the cars work before having my students complete the cars today.

The problem is that the launching string is so hard to wrap around the axle (a bit like wrapping spaghetti around a fork). It is just like setting up dominoes, where placing them too close risks making them fall before you're ready, and placing them too far apart risks having them remain standing when you are ready to let them fall. If the string is loaded improperly, the mousetrap is released too early or too late for the car to move.

I don't like how difficult it is to launch the cars. The reason for the project title "What's the Best Advantage?" is that students are supposed to make changes such as adjusting the size of the wheels and seeing what effect this has on the distance the car travels. But it is so hard to make the car go even once that neither the students nor I really want to perform that experiment. If Illinois State, who provided us with the cars, really wanted students to make this investigation, then the effort required to load the string should have been trivial.

But I am able to salvage some science out of this project. I have the students consider whether the cars will travel farther on the indoor carpet or on a smoother surface, such as the tiles located near the sink or the corridor outside the room. The students figure out that the car travels a shorter distance on the carpet due to greater friction.

The seventh graders are the most successful in launching the cars. The sixth graders are too confused, and some of the eighth graders are just lazy. We take videos of some of the seventh and eighth graders who race their mousetrap cars, but again I don't post the videos on the blog in order to maintain student privacy.

Thinking about the "Day in the Life" project, there technically is a participant whose monthly posting day is the 30th -- Kevin Cormier, who is apparently a Massachusetts middle school teacher. But unfortunately, the list of participating teachers provides only Cormier's email address, not his blog. It is a shame, though, since I enjoy reading the blogs of fellow middle school teachers. (Naturally, there is no participant for the 31st, since not every month has a 31st day.)

I wish everyone who celebrates it a happy Rosh Hashanah! There will be no blog post on Monday due to the holiday, and there is no post on Tuesday as this will be my scheduled day off (since the remainder of 33 divided by 3 is zero). So the next post will be Wednesday, October 5th.

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