Friday, May 24, 2013

Our Solar System, Graphs, and Classification Schemes

Following the previous week's intro to the solar system, on Friday May 17 I visited the 3-4 grade room and used the solar system as a context for practice with graphs.  We used the graphs in turn as a tool for helping us think about how to classify solar system objects.  By establishing several clearly different classes of solar system objects, we raised questions about how the solar system might have formed these different classes, and we even began to answer those questions.  I think this worked quite well as a coherent activity while asking the students to practice a variety of skills.

The centerpiece was a graph (technically a scatterplot*) of size vs distance from Sun for various solar system objects.  My first idea was to help the kids make their own graphs from a table of data, but I discarded that idea as requiring too much time before we got to any science.  So I made this graph and handed out a copy to each student:



I still wanted students to graph some data, so I planned to make them analyze and understand this graph as a gateway to getting them to add more points and do more analysis.  I think this plan went well.  I started with the question: can you identify any of the points?  This required them to think about the meaning of the axes, and once they understood, they started saying things like "the top one must be Jupiter, because it's the biggest planet" and "the one most to the right must be Neptune because it's most distant from the Sun."  Once they grasped that, they were able to label more and more points until we eventually got them all. (The word "eventually" hides a lot of time spent one-on-one with kids, helping them with the reasoning.  Eg, Earth and Venus are almost exactly the same size, but Earth is a bit bigger, so which point is Earth?  Double-check your conclusion by looking at distance from the Sun.  Does it make sense? Etc.)

This was an excellent activity to make them think about the meaning of the graph rather than getting caught up in big numbers which wouldn't mean much to them anyway.  (Jupiter is 90,000 miles across?  How big is that?)  But now let's think about the numbers.  The graph says Earth's distance from the Sun is 1.  What is that? One foot?  One billion miles?   The only unit that makes sense is units of "Earth-Sun distance."  In other words, the graph makes it easy to read off the relative distances of the planets.  It's a scale model. Again, this makes it easy to think about what the solar system is without getting caught up in a bunch of meaningless numbers.  We repeated that exercise with the vertical axis.

Then we looked at whether the planets form any distinct groups.  The graph makes it clear that there are two groups: small and close to the Sun, vs large and far from the Sun. What other differences might these groups have? It turns out that the large ones are made of different stuff (mostly gas vs rock), so maybe we should really think of two types of planets (gas giants and rocky planets) rather than thinking that all things called "planet" are similar things.

Next, I took them back to the year 1801 when a new planet was discovered: Ceres.  I gave them the Ceres-Sun distance in units of the Earth-Sun distance (2.77) and Ceres' size in Earth-size units (0.07) and asked them to put Ceres on the graph.  For the faster students, I gave them three more planets which were discovered soon after Ceres (Pallas**, Juno, and Vesta, which have similar distances and sizes) while the teachers helped the slower students with the graphing.  After graphing these, it's clear that they form a distinct group: a group of very small things between Mars and Jupiter.  Today we call these things main-belt asteroids, but when they were discovered they were simply called new planets.  It was only after discovering many of them that people began to think that maybe we shouldn't call all new discoveries planets, and especially not these new discoveries which clearly form a separate group.  The way we think about things is highly dependent on how much information we have.

This took until the break.  After the break, we added Pluto to the graph.  When Pluto was discovered, it was immediately called a planet because it was much larger than any asteroid, and there was no other category it could have been assigned to.  But it does seem a bit out of place on the graph, being substantially smaller than any of the eight planets we started with, and also breaking the pattern of the larger planets being farther from the Sun. Well, it took 60 years, but eventually astronomers started discovering lots of other things roughly as far from the Sun and roughly the same size. I gave the kids data for these new objects: Eris, Sedna, Quaoar, and Orcus to start with.

Just as with the asteroids, it became clear that things like Pluto form a new category: the Kuiper Belt.  This is even more clear when we realize that all these things are made of ices***, which is not like the inner planets or the outer planets. Once this new category was recognized, it became silly to continue calling Pluto a planet, just as in the 1800's it became silly to continue calling Ceres, Pallas, Juno, and Vesta planets.  Perhaps Pluto should have been in a category of its own from the start, but there was no available category other than "planet," and why create a new category just for one object?  Another illustration that the way we think about things depends on how much information we have.

[A side note: astronomers created the additional category "dwarf planet" to describe a body which, regardless of its location, is large enough that its gravity pulls it into a round shape (but smaller than the eight planets).  Thus Pluto is both a Kuiper Belt object and a dwarf planet just as I am both a teacher and a father---they are not exclusive categories.  But  "Kuiper Belt object" is a much more descriptive term because it implies being made of ice, being a certain distance from the Sun,  etc, whereas  "dwarf planet" implies only that the size is neither very large nor very small.]

Next, we talked about how the solar system might have formed in order to form these different classes of objects. I showed clips from the Birth of the Earth episode of the series How the Earth Was Made.  It has some really nice visualizations, and it is constructed around evidence, which is a key feature missing from most science documentaries.  It tells science like the detective story it is.  We spent probably half an hour on this, but I won't write much here because it's already a long blog post.

To cap off this intense morning, I brought some liquid nitrogen to demonstrate how cold the outer planets are. I froze a racquetball and shattered it just by trying to bounce it off the floor; I froze a banana and showed how it can be used as a hammer (until it shattered), and I made a balloon shrink and then expand again as I warmed it up.  LN2 is always a great hit with the kids.  On Pluto summers can be just warm enough to vaporize some nitrogen, but right about now Pluto is in early fall, and it will get so cold that nitrogen will not only liquify, it will freeze.

Notes

*Notice that this graph is not a histogram, which seems to be the only type of graph elementary teachers ever work with.  I see that kids start working with graphs around second grade if not earlier, so by the time they get to college, they should be highly proficient.  But in my college classes that students are typically far from proficient.  My guess is that much of the time spent on graphs in school is wasted because students are never introduced to the idea of graphing the relationship between two different abstract quantities, which is absolutely key to data analysis and science.

**I got the idea for some of this activity when I saw that the element palladium was so named because for a long time it was fashionable to name newly discovered elements after recently discovered planets. I was long aware of uranium, neptunium, and plutonium being named this way, but I had never made the connection to cerium and palladium.  People really thought that asteroids were planets until enough asteroids were discovered.

***Ices includes ice made of materials other than water, such as methane, ammonia, etc.

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