From Maura:
We began by reviewing some of the carbon footprint calculations from Tuesday’s class. In particular, I wanted to go through the movie download estimate. The two estimates we had were different (hundreds of thousands vs. tens of millions). We talked it through and to my surprise, I began to agree with the tens of millions estimate! The group that made that estimate was pleased.
We talked through the large metric prefixes (kilo, mega, tera, etc) and did exercise 1.25: how many 200 Gb computers would we need to store all of the books from the Library of Congress? I gave out one starting piece of information: there are about 32 million books in the Library of Congress’ collection. The class worked in groups on getting to the answer. All of the groups realized that they needed to estimate the size of the average book. Some did a real Fermi approach to this estimation, others realized the book has an estimation. I pointed out to them that this estimate is in fact footnoted, referring the reader to the exercises, and that in fact this exercise is where they can make this estimate. At least people are reading the book! We used the metric prefixes for the calculation and it was a good transition to unit conversions.
We started chapter 2: the main idea I wanted to get across is that numbers aren’t that interesting or useful to us unless we know the units. We talked through a few examples, including the miles-per-gallon versus gallons-per-mile. The class was surprised to see that their instinct was incorrect for this situation. I’m not quite sure they saw how the units were a part of that, but there is a follow-up problem for homework so we’ll see.
Postscript: A few observations from grading the first homework. Woody Allen allegedly said, “90% of life is just showing up.” I would argue that a good percentage (not quite 90%) of your homework life is just reading the directions. I had several students who only did one part of a problem, or who didn’t finish the problem. Some didn’t show their work, others estimated but then used the Google calculator (does that make sense? the point of estimating is to not rely on the calculator!). And I saw a number of people who wrote an answer but clearly didn’t think about it. We’ll talk about it tomorrow in class and I’ll be curious to see how this feedback affects the next work I receive.
From Ethan:
For me this was just the second class of the semester – two snow days since last week. I was afraid that we’d have lost all momentum after a good start. In the event, my worry was unfounded. Class today was quite exciting.
We started with each row of three students estimating the number of Google searches in a day in the United States. Instructions were to do this with no technology – no searches, no calculator. All six groups came up with the same answer – about 2 billion, which I wrote as 2 * 109. When we tried to verify this estimate using the net, we found one claim of 91 million. Since that was off by an order of magnitude, we had a problem. Reading the not-so-fine-print told us it was a statistic from about 2006. So we had a good lesson in using the internet wisely.
Then I handed out the carbon footprint graphic.
That prompted a digression into thousand/million/billion/trillion and the corresponding metric prefixes. When I asked who knew other words with “mega” one student volunteered “megaton” so we got to talk about nuclear bombs. Yields of today’s are measured in megatons, yields of the ones used in 1945 (everyone knew that there were two, each of which destroyed a city) were measured in kilotons. That brought home the meaning of three orders of magnitude.
I’d intended to use the task counts together with the carbon footprint per task to start on units (Chapter 2). Ran out of time. I assigned homework 2.
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