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Linear data sets (for your enjoyment)

Kicking off the year in my modeling physics course means practicing working with and interpreting linear data. Some students quickly pick up the modeling method of describing slope and intercept, while other students just need more practice for the data to speak to them in the same way.

I use the spaghetti bridge lab to introduce graphing linear relationships and have a pretty good handout1 with a few more linear data sets as practice.

However, my experience has taught me two things:

  1. There will be students that just need a bit more practice to really nail down the skill.
  2. It's deceptively hard coming up with linear data sets.

So, I sat down earlier and surfed the internet, found some real data sets, cleaned them up a bit, and imported them into Excel & Google Sheets (from whence they are easily copyable and paste-able). I might as well share them, because I know you'd prefer to avoid converting .txt data files to .xlsx. In fact, I'll make the Google Sheets version editable, so you can add your own awesome data sets).

Download the data sets

The Excel version includes graphs with the equation for best fit lines. Google Sheets doesn't do best-fit lines yet, so those have the graphs (as interpreted by the Google Sheets converter), but no equations.

Enjoy!

 

  1. from the AMTA Modeling Physics curricular materials, which is why I'm not sharing them here. But, seriously, you should just join the AMTA so you can access the huge wealth of resources they provide. Here's the link. Do it. [↩]
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Sand, salt, and iron

Sand. Salt. Iron.

Sand. Salt. Iron.

Mix the three together. Make the students separate them. Even better, make them figure out how to separate them before beginning. This is how I spice up an otherwise quite boring section on types of mixtures.

The content covered

  1. Compounds and elements (Which substances are elements? Which are compounds? How can you tell?)
  2. Physical properties (What are each substances' properties? How does knowing that allow you to separate them?)
  3. Types of mixtures (Are they mixed heterogenously? Homogenously? How can you tell?)
  4. Good lab practices (How can you work to recover as much of each substance as possible?)
  5. Calculating percent composition

Pre-lab

Once students write out a brief procedure of how they might separate the sand, salt, and iron from each other¹, I give them the lab procedures, go over proper filtration, boiling, and scale techniques, then have them complete a short pre-lab activity. The goal of the pre-lab is to go over proper laboratory techniques and how to calculate the percent composition of a mixture.

During the lab

Students receive a sample of the mixture, mass it, and then use a magnet wrapped in clear plastic wrap to take out the iron filings. They mass the iron filings then toss them. The students then add water to the remaining sand and salt mixture in order to dissolve the salt. Then using a funnel and filter paper, they filter out the sand. At this point they have wet sand in the filter and salt water in a beaker. They break out the hot plates in order to boil off the salt water (leaving the salt residue) and heat the sand to dryness. Once they mass the dried sand and salt, they're essentially done save for calculating the percent of the mixture recovered and the percent composition of the mixture.

Post-lab

We break out the laptops, put our data into a spreadsheet and go over how to make charts using Excel. For most freshman, this seems to be the first time they've officially been taught how to do this. We go over their findings, and they turn it in.

Take away

  1. It's not an overly difficult lab. It is complex. There are a lot of steps. Most freshmen students haven't had much lab experience, and as such their lab skills aren't too advanced. Many students this year didn't get very close to the actual composition of the mixture. A few ended up with more mass at the end than at the beginning (probably didn't drive off all the water in the sand or salt). Given their inexperience in the lab, these results aren't surprising, but I want them to improve their lab techniques as the year goes on. I have to keep reminding myself to be patient with them when they make bone-head moves².
  2. This. lab. takes. for. ever. It took my freshmen about 150 minutes to complete it. It can take 40 minutes simply to boil off the water to extract the salt. That comes down to a lot of time watching water boil. I used 150 mL beakers this time around, but perhaps if I used a larger beaker (400 mL, perhaps) the water would vaporize more quickly.
  3. For all my attempts to spice up the mixture section, students complained sitting and watching water boil wasn't that interesting (big surprise). Next time I'll give them less of the mixture to separate and use larger beakers.
  4. Is it worth my time to teach them how to graph in Excel? This first time through, students were all over the place. Some had never touched a spreadsheet before. Others were decently experienced. Some were done in 5 minutes, others took 40. I'm torn on whether I should spend the time teaching them this, yet I always seem to come out and do it. As we use Excel more, the difference between novices and the experienced gets smaller, which is one of my arguments for keeping it in.

The Schtuff

  • Lab sheet (WORD) (PDF)
  • Pre-lab (WORD) (PDF)
  • Post-lab (WORD) (PDF)
  • Graphs (PDF)
    • I used the third graph as an example to take students through the Excel graphing procedure before they made their own graph.

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¹ I require students to write a procedure on how they might separate all three and then weigh the recovered mass of all three dry solids. The dry part throws them a bit sometimes.

² Exception: If they're compromising safety rules, it's a slightly different story. Learning how to properly filter a mixture is something that understandably takes some practice. Learning to not touch the hot plate while it's on doesn't.

________________________________________________________________

Image Credits:

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Tropical Storm and Hurricane Frequency

September, 2005: The school year has just begun. The country is still reeling from Hurricane Katrina.

Instead of beginning the year covering plate tectonics (my original plan), I decide to start with hurricanes. As we learn more about Katrina and hurricanes in general, the question keeps coming up in class (and in the media): "Are we getting more hurricanes because of global warming?"

I struggled with how to answer that question. Reports from scientists were mixed. The most reliable sources (IMHO) never made a direct connection between global warming and the trend of more active hurricane seasons. They'd only go as far as something similar to, "hurricanes get their power from warm oceans. In theory, if oceans get warmer, it would make sense we'd see more hurricanes."

That didn't cut it for my students. 15-year olds don't have great appreciation for the subtleties and complexities of meteorological research. They wanted answers.

I stumbled across a website containing records of every reported hurricane and tropical storm from 1851 on. Aha! Oho! Forget the experts, let's track the trends ourselves!

I split the class into groups. Each group took a decade and recorded the number of hurricanes and tropical storms each year in their decade. Back in the pre-Google Docs era, we were forced to spend 30 minutes or so sharing data and entering into their individual spreadsheets. Today, just create a Google Doc spreadsheet (like this one!) and have each group enter their data (an example of collaborative online documents saving a huge amount of time & boredom).

Then comes the graphing! . I've found Google Docs graphs aren't too great at this now (they might get there soon), but exporting the data to Excel is easy enough.

We added moving average trendlines to see the trends. You can play with how long the moving average should be. We decided that 5-10 years seemed to give a good picture of the trends. The graphs below have trendlines with a moving average of 10 years.

The graphs:

Hurricanes by Year

Tropical Storms + Hurricanes per Year

Fun fact: The first time I saw these graphs was in class (and my students knew that). I didn't know what trends would emerge. My students and I were learning together, and they seemed to like participating in the discovery of something that wasn't pre-determined.

Good discussions that fit well with this activity

  • How valid are the counts and intensities for tropical storms before reliable weather satellites and radar were in use? Most storm reports back in the day simply came from ships at sea. How would the data be affected if several storms went unreported each year?
  • Does this information prove causality? (It doesn't) As much as it looks like it, there's no way we can say with any certainty that global warming has caused the uptick in tropical storms recently.
  • Would coastal development have occurred at the same rate the last 50 years if hurricanes were as frequent as they have been the last few years? Lots of good discussion can be had as to the wisdom of living on the coast, students seem to have strong opinions one way (you'd be stupid to do this) or another (It's way worth the risk to live on the ocean).

Whew. I'm feeling a bit like this guy. What can I say? I'm a fan. Comment it up!

Image credit: NOAA via GISUser.com on Flickr

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