Wordless Wednesday: Hoarfrost makes North Dakota winters beautiful February 8, 2012
Posted by mareserinitatis in Fargo, photography, younger son.Tags: fargo, hoarfrost, winter, younger son
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How I can tell the younger son is my child… January 28, 2012
Posted by mareserinitatis in math, younger son.Tags: math, minus, negative numbers, younger son
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The younger son is learning how to manipulate negative numbers in math. However, he was getting very irritated when listening to the ‘lectures’ yesterday. The lecture would use the term ‘minus’, as in -6 is pronounced ‘minus six’. Every time it did that, the younger boy would make some exasperated grunt and say, loudly, “Negative!”
I can only think this may be because I always call them ‘negative’. The term minus, to me, implies an operation. If so, he obviously picks up on subtleties a lot better than I thought.
Pinewood derby: What a drag! January 16, 2012
Posted by mareserinitatis in engineering, physics, science, younger son.Tags: air resistance, cub scouts, drag, energy, energy conversion, friction, gravitational energy, physics, pinewood derby
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My husband son competed yesterday in my son’s his scouting group’s pinewood derby race. For those of you who have never had a kid in cub/boy scouts, they hand out these blocks of wood that you get to make into a car. The idea isn’t to win the race: it’s supposed to be that dads and their boys spend some time bonding over manly things like woodworking.
(One year, Mike was out of town during this whole thing, so I got to be manly and help the older boy build his car. All I can say is that Dremel tools are awesome.)
If you look on the web, you’ll find a lot of advice on how to prep pinewood derby cars and make them faster. One thing that consistently bugs me is that one should pay attention to aerodynamics of the car and give it a low profile.
This makes me nuts.
To understand the following, you might want to know what a track looks like. So here you go:
Let’s start out with the specifications. Most pinewood derby tracks have a height of about 4 feet and a length of 32 feet. I also will note that the ones we’ve raced on were wood, not aluminum.
Most of the pinewood derby cars I watched made it the whole 32 feet, though not all did. So let’s say that, on average, they travel 32 feet. The *fastest* ones traveled at an average speed of 10 ft/s (or 3 m/s). The maximum they can weight 5 oz. or 140 g.
What we’re going to do here is look at how much energy the system puts into overcoming air resistance versus friction. It’s very hard to figure out exactly how much goes into friction simply using equations, so we’re going to figure out the total energy and the energy lost to drag forces. Once we have those two quantities, we can subtract the drag forces from the total energy and assume that the difference is equal to the frictional losses. Finally, we can compare the drag and frictional losses.
First things first: what is our total energy? It starts out entirely as potential energy as the cars are placed at rest on the top of the ramp. Potential energy is, fortunately, very easy to calculate. It is simply the product of the height of the object, its mass, and the gravitational acceleration. In other words,
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We know the mass of the car (0.14 kg), the height is approximately 1.22 m, and the graviational acceleration is 9.8 m/s2. This results in a total potential energy of approximately 1.67 J.
The potential energy is equal to the total energy in the system since the cars start with no other kind of energy. In a frictionless and drag-free system, all of this energy would be converted to kinetic energy and the cars would drive forever at the same speed once they reached the bottom of the ramp. Obviously, however, that’s not what happens. Eventually, all of the energy is converted to friction and drag, and the cars stop.
Now we need to determine the drag on the cars. The drag equation is:
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The drag force is proportional, therefore, to the density of the fluid (ρ), velocity (v), drag coefficient (CD), and cross-sectional area (A).
The density of the fluid (air) is approximately 1.2754 kg/m3, and the velocity is 3 m/s. The cross-sectional area of the car, at maximum, is 2.75 x 3 in. In real *ahem* units, this is 0.00532257 m2.
The drag coefficient for a long cylinder, according to Wikipedia, is 0.82. Given the cars are all sorts of different shapes, I think this would probably be the closest approximation, although for some cars, this will be high.
All of this put together gives us a force of 0.025 N. Over a distance of 32 feet (or 9.75 m), this gives an energy of 0.24 J.
If we assume that all of the potential energy is converted to either drag or friction, that means 0.24 J is converted to drag while 1.43 J goes into friction. This means that roughly 14% of your energy losses are due to drag while the other 86% are due to friction.
My advice, therefore, is to not worry so much about drag and the aerodynamics of the car and to worry far more about the ways to reduce friction.
What should you do to help your pinewood derby car to be fast? There are three things:
1) You want to maximize your potential energy, so being as close to the 140 gram maximum weight is good. You can get all sorts of weights commercially to assist with this. Some people have argued that putting the weights near the back of the vehicle helps even more. I wouldn’t doubt this as you’re putting the weight at greater height, giving the car more initial energy to start with.
2) The biggest issue is reducing the friction between the wheel and the axle, and there are a few easy ways to do that: sanding and polishing the axles as well as using graphite or teflon as a lubricant. (Our troupe doesn’t allow graphite because it marks the floors, but teflon is allowed.)
3) Reduce the friction between the car and track. The best way to do this is to make sure your wheel alignment is as straight as possible as this will keep it from rubbing against the center of the track.
The winner of our pinewood derby actually had a very blocky car designed to look like a platypus. I’m guessing the winner didn’t spend much time focusing on aerodynamics and instead chose to minimize their frictional losses.
Outnumbered January 5, 2012
Posted by mareserinitatis in gifted, math, teaching, younger son.Tags: math, teaching, younger son
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Today I’m going to be working with the elementary students again. This will be interesting as I completely switched gears from what we were doing before. The stuff we were doing before was fun, but as we move through the book, it looks like they need a lot of multiplication and division…which most second graders don’t have.
Today, we’re going to learn about other number systems. In particular, I’m going to have them pick a number using Indo-Arabic numerals and ‘translate’ into other numbering systems – Egyptian, Roman, Babylonian, Mayan, and Chinese. This will give us an opportunity to talk about different bases, positional numbers (i.e. the concept of place value), and how many systems don’t have a zero. (Although, there’s debate in some cases.)
After doing the prep, I’m SO glad that we don’t use the Babylonian system. Base 60?! No wonder my math professor got annoyed when we used degrees.
Thanks to the MacTutor History of Mathematics Archive for the picture!
Wordless Wednesday December 28, 2011
Posted by mareserinitatis in family, Fargo, food/cooking, pets, photography, younger son.add a comment
Wordless Wednesday December 21, 2011
Posted by mareserinitatis in family, food/cooking, math, older son, personal, pets, photography, religion, younger son.Tags: cooking, food, Gigadog, hannukah, older son, younger son
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Happy Hanukkah! December 20, 2011
Posted by mareserinitatis in religion, younger son.Tags: hannukah, health, illness, menorah, younger son
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I think running myself ragged finally caught up with me the past couple days. I was starting to get a cold a couple days ago and woke up this morning in bad shape. Fortunately, it’s not an infection…just my immune system overreacting to everything and telling me that today was a day off, whether or not I wanted it. I guess this is the up side to having the teenager home during the day now: his younger brother has this week off from school, so they kept each other entertained while I lay there in a cold- and cold medicine-induced stupor.
I thought this only happened as a student, but I guess not. Teaching is just as tiring as learning.
Despite feeling cruddy, we managed to celebrate the first night of Hanukkah. A couple weeks ago, the younger boy came to us and said he wanted to celebrate. I wasn’t sure what to do, but a friend sent me some information and I spent a bit of time researching how to properly observe it.
I have to admit that I feel a little funny observing a holiday from a religion with which I have extremely limited familiarity. I’m not sure why this is. I would never feel funny if my non-Christian friends participated in Christmas (and I have a lot that do). I’ve also been invited to participate in a Hillel meeting once. (I had no idea what was going on, unfortunately…but I was still welcome!) So I don’t think anyone would get annoyed…but it’s still an odd feeling.
We lit the first candle of the Menorah in our front window. I don’t know if any of the neighbors saw it, but if they did, I suspect they’re going to think this explains why we never hang up Christmas lights. Actually, we did hang them up one year, but we didn’t take them down until August. So now we just never bother with hanging them up.
Overall, it was fun. My friend sent us a card game that’s about Hanukkah, so we played that after lighting the Menorah. I guess I thought we had to wait until indulging in fried foods, but I guess not. Donuts, anyone?
Lexile ranges December 19, 2011
Posted by mareserinitatis in education, gifted, homeschooling, older son, science fiction, societal commentary, teaching, younger son.Tags: books, gifted, gifted education, lexile range, older son, reading, younger son
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The younger boy’s school sent home a bunch of information on lexile range. I’d never heard of this before, but it’s a way to rate books so that kids are reading at an appropriate level. On the surface, it seems like a good idea: it’s very hard, as a parent, to provide reading material for your kids that’s appropriate. Aside from the basic issues of whether they’ll understand the language and sentence structures of a book, there are the themes and situations: are they too complex or adult-oriented for a child to read?
A lot of this, of course, depends not only on cognitive ability but emotional maturity, as well. I remember how my older boy started reading Harry Potter very early. Sometime in third grade, he read the fifth book. I began to wonder about him reading the fourth and fifth books at such a young age because of the adult themes. We were fortunate, however. Reading books about such emotional and adult themes started giving him words to explain a lot of his thoughts and feelings with minimal emotional fallout.
After receiving these results, I dutifully trucked my troops down to the library (no complaints from said troops) where they had a program to help us find books in the appropriate range. However, I forgot the letter with the lexile range and so had to guess where he was at. The younger boy had already been reading Magic Tree House books, so I figured some of the Dragon Slayer Academy books might be up his alley. We got those and some Bionicle books and headed home. He really seemed to like the Dragon Slayer Academy books and has been reading bits at a time. Language-wise, they seemed perfect, although their length is a bit intimidating for him.
It turned out, I had remembered the incorrect values. The books we picked were near the top of his range. And yet, I was confused. If these were supposed to be too difficult, why was he having no difficulty reading them?
Mike, unbeknownst to me, had also started looking at lexile information on specific books. He was curious where he would’ve been placed when he was in various stages of school. After we returned from the library, he started telling me about this and that he didn’t buy the results. He’d been comparing some of his favorite sci-fi books, and he was puzzled at the results. I threw out some books I read as a kid and made some comparisons. Books that I thought were very difficult showed up as supposedly easier to read than ones I’d zipped through.
We looked up the criteria for determining lexile range:
A Lexile measure does not address the content or quality of the book. Lexile measures are based on two well-established predictors of how difficult a text is to comprehend: word frequency and sentence length. Many other factors affect the relationship between a reader and a book, including its content, the age and interests of the reader, and the design of the actual book. The Lexile measure is a good starting point in your book-selection process, but you should always consider these other factors when making a decision about which book to choose.
Both Mike and I read this and shook our heads. We both had different takes on it. I found that one thing that made a book challenging for me was dealing with vocabulary. It’s not clear to me whether or not this is reflected in the “word frequency” measure. (Do they mean word frequency in the book or relative to the English language?) Mike felt he struggled most with books that had very adult themes, something not reflected in the range.
Our take on this is that this is only a very rough guideline, and probably not a good one to use. We both felt that interest in a book or topic was probably going to be a far better predictor of readability than using the lexile range. I suppose that’s what they’re saying about considering other factors.
My concern in this is that some schools go a bit overboard with these things. When the older boy was in fifth grade, he was going to public school part time. I got a couple calls from the school librarian because he wanted to check out books that were designated for 7th-9th graders. I felt this was silly because he’d been reading at above that level already, and probably had come across themes in his reading that were more adult than what was in those books. I told her it alright for him to check the books out, but she seemed to be very opposed to it. I finally gave up and told older son that he should just probably check most of his books out from the public library.
I’m hoping I don’t see something similar happen with the younger son, i.e., that he not be allowed to check books out from the library if they’re outside of his lexile range. On the other hand, I’m glad that they seem to be promoting reading at the upper end of the scale so that kids will stretch their mental muscles a bit as well as that they make the point that within any grade level, you’ll have a wide variety of reading levels. In other words, it seems like they’re trying to get rid of the fantasy that kids all read at the same level and thus require the same reading level. Therefore, while I may disagree with assessments of individual books, I think they’re definitely taking a huge step in the right direction.
















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When you think of a scientist… January 26, 2012
Posted by mareserinitatis in science, societal commentary, younger son.Tags: science, women in science, younger son
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On the way to school yesterday, the younger boy started telling me that Dr. Frankenstein wasn’t a real scientist. I asked him what he thought of when he heard the word scientist. He was very quiet, and I started feeling anxious that this was going to end up in a “dude in a lab coat with beaker”.
I interjected, “You think of your mom, right?”
“No,” he paused for a few moments more. ”I think of someone who is already dead.”
Oh great. So to be a scientist, you can only be recognized post-mortem, right? I wondered if it was someone crazy like Tesla.
“Already dead?”
“Yeah, she discovered radium, I think.”
I was kind of stunned. He wasn’t thinking of guys in lab coats – he was thinking of Marie Curie. Upon conversing further, it turned out that he knew quite a bit about her. There was a Magic School Bus book on science fairs at his classroom, and he had read about her in there.
I had to admit that I was hugely relieved that not only did he suffer from a common misconception about what a scientist is but that his first thought of a scientist was actually a very accomplished female scientist.
Although I’m still a tiny bit sad he didn’t think of me.