Author: Lensyl Urbano

Analyzing the 20th Century Carbon Dioxide Rise: A pre-calculus assignment

Carbon dioxide concentration (ppm) measured at the Mona Loa observatory in Hawaii shows exponential growth and a periodic annual variation.

The carbon dioxide concentration record from Mona Loa in Hawaii is an excellent data set to work with in high-school mathematics classes for two key reasons.

The first has to do with the spark-the-imagination excitement that comes from being able to work with a live, real, scientific record (updated every month) that is so easy to grab (from Scrippts), and is extremely relavant given all the issues we’re dealing with regarding global climate change.

The second is that the data is very clearly the sum of two different types of functions. The exponential growth of CO2 concentration in the atmosphere over the last 60 years dominates, but does not swamp, the annual sinusoidal variability as local plants respond to the seasons.

Assignment

So here’s the assignment using the dataset (mona-loa-2012.xls or plain text mona-loa-2012.csv):

1. Identify the exponential growth function:

Add an exponential curve trendline in a spreadsheet program or manual regression. If using the regression (which I’ve found gives the best match) your equation should have the form:

y = a b^{cx} + d

while the built-in exponential trendline will usually give something simpler like:

y = a e^{bx}

2. Subtract the exponential function.

Put the exponential function (model) into your spreadsheet program and subtract it from data set. The result should be just the annual sinusoidal function.

Dataset with the exponential curve subtracted.

If you look carefully you might also see what looks like a longer wavelength periodicity overlain on top of the annual cycle. You can attempt to extract if you wish.

3. Decipher the annual sinusoidal function

Try to match the stripped dataset with a sinusoidal function of the form:

y = a \sin (bx+c) + d

A good place to start at finding the best-fit coefficients is by recognizing that:

  • a = amplitude;
  • b = frequency (which is the inverse of the wavelength;
  • c = phase (to shift the curve left or right); and
  • d = vertical offset (this sets the baseline of the curve.

Wrap up

Now you have a model for carbon dioxide concentration, so you should be able to predict, for example, what the concentration will be for each month in the years 2020, 2050 and 2100 if the trends continue as they have for the last 60 years. This is the first step in predicting annual temperatures based on increasing CO2 concentrations.

DNA Extraction Labs

My middle school class tried DNA extractions from dried split peas and cheek cells for a lab this week, and the experiments went rather well.

Strands of DNA rising from the interface between crushed split pea “sludge” and rubbing alcohol. Bubbles trapped beneath the strands make for interesting convective-like patterns.

Split Pea DNA

For the split peas, we followed the Learn.Genetics lab. I blended the peas in some salty water at the front of the class (“Don’t you need a lid for that blender?”), and filtered it. This gave about 120 ml of filtrate. Then I added in 3 tablespoons of dish soap to the filtrate. The soap to breaks down the cell membranes and nuclear membranes because they are made of lipids (fats).

Split pea residue left behind after filtering.

I shared out the resulting green liquid to the four groups. Each student was able to get a fair amount into a test tube so they could complete the lab as individuals.

Disintegrating the cell and nuclear membranes with soap exposed the DNA, but the long DNA molecules tend to be coiled up around proteins. Each student added a pinch (highly quantified I know) of meat tenderizer to their test tube to break down the protein and allow the DNA to uncoil. Enzymes are biological catalysts, large complex molecules that accelerate chemical reactions, the breakdown of proteins in this case, without breaking down themselves, so only a little is needed.

Finally, each student carefully poured rubbing alcohol into the test tube. I had to demonstrate how to tilt the test tube while alcohol was being poured into it so that the alcohol would not mix in with the pea soup but, instead, form a layer at the top, since the alcohol is less dense than the suspension of split peas in salty water.

When the DNA is mixed in with the split pea filtrate (right) it becomes a little harder to distinguish. On the left you can see that the clear rubbing alcohol floats on top of the denser split pea/water/salt mixture.

If it was done carefully enough, the DNA would precipitate at the boundary between the two liquids. If not, the DNA would still precipitate, but it would be mixed in together with the green soup and be harder to distinguish.

Either way, however, students could see the long strands of DNA, and fish them out with glass rods.

Strands of DNA on a glass rod.

Human DNA

The human DNA extraction procedure is well demonstrated by the NOVA video. One student who missed the split pea lab did this experiment instead because it’s faster. It does not require blending to crush the cells, nor does it need the meat tenderizer enzyme.

Although this procedure produces a lot less DNA — after all, you’re only getting a few loose cells from the insides of your cheeks — the strands are still visible. And it’s YOUR DNA.

A few strands of human DNA (belonging to an individual who asked to be referred to as “Suzanne”) in a test tube. The rubbing alcohol is dyed blue for visual contrast.

Since I instructed the class on how to use the microscopes last month, one student wanted to see what his DNA looked like under the microscope. An individual DNA molecule is too small to see, but the strands we have are bunches molecules that are visible. They just don’t look like very much.

DNA strands under the microscope.

Drought on the Mississippi

Last summer’s drought, and more weather extremes probably due to large-scale global climate change, is having dire effects on shipping on the Mississippi River. Suzanne Goldenberg has an excellent article in the Guardian.

Students look upstream at the Missouri River from the Melvin Price lock and dam, just north of St. Louis, and close to its confluence with the Mississippi River. The dam is tasked with maintaining about 9ft of water in the river for shipping.

Shipping companies say the economic consequences of a shutdown on the Mississippi would be devastating. About $7bn (£4.3bn) in vital commodities – typically grain, coal, heating oil, and cement – moves on the river at this time of year. Cutting off the transport route would have an impact across the mid-west and beyond.

…

Farmers in the area lost up to three-quarters of their corn and soya bean crops to this year’s drought. … Now, however, [they] are facing the prospect of not being able to sell their grain at all because they can’t get it to market. The farmers may also struggle to find other bulk items, such as fertiliser, that are typically shipped by barge.

— Goldenberg (2012): Mississippi river faces shipping freeze as water levels drop in The Guardian.

The proposed solution is to release more water from the Missouri, however there would be a steep price to pay.

The shipping industry in St Louis wants the White House to order the release of more water from the Missouri river, which flows into the Mississippi, to keep waters high enough for the long barges to float down the river to New Orleans.

…

Sending out more water from the Missouri would doom states upstream, such as Montana, Nebraska, and South Dakota, which depend on water from the Missouri and are also caught in the drought.

“There are farmers and ranchers up there with livestock that don’t have water to stay alive. They don’t have enough fodder. They don’t have enough irrigation water,” said Robert Criss, a hydrologist at Washington University in St Louis, who has spent his career studying the Mississippi. “What a dumb way to use water during a drought.”

Assessment with the Toilet Paper Timeline of Earth History

With a larger class, and quite a bit of space in the gym, I had more flexibility working on the toilet paper timeline compared to the last time.

Labeling the timeline in the gym.

I built in a friendly race to see which group could find a set of events first, and allowed me to highlight nine different, important, series of events along the timeline.

The adapted spreadsheet, racing sequences, and a short summative quiz are on this Toilet Paper Timeline spreadsheet.

I broke the class up into 4 groups of 4, and each group created their own timeline based on a handout.

Groups of students lay out their toilet paper timelines. Post-it notes were used to label the events.

Then, I gave each group a slip of paper with four events on it (one event per student), and they had to race to see which group would be first to get one person to each event on the list. Once each group got themselves sorted out, I took a few minutes to talk about why the events were important and how they were related.

Table 1: The series of events.

1) We’ll be talking about plate tectonics soon, so it’s good for them to start thinking about the timing of the formation and breakup of the supercontinents.
Event 1 Event 2 Event 3 Event 4
Formation of Rodinia (supercontinent) Breakup of Rodina Formation of Pangea Breakup of Pangea
2) This sequence emphasizes the fact that most free oxygen in the atmosphere comes from ocean plants (plankton especially), and that a lot of free atmospheric oxygen was needed to to form the ozone layer which protected the Earth’s surface from uv radiation, which made the land much more amenable to life. Also, trees came way after first plants and oxygen in the atmosphere.
Event 1 Event 2 Event 3 Event 4
First life (stromatolites) Oxygen buildup in atmosphere First land plants First Trees
3) Pointing out that flowering plants came after trees.
Event 1 Event 2 Event 3 Event 4
First life First land plants First trees First flowering plants
4) The Cambrian explosion, where multicellular life really took off, happened pretty late in timeline. Longer after the first life and first single-celled animals.
Event 1 Event 2 Event 3 Event 4
First life (stromatolites) First animals First multicelled organisms Rise of multicelled organisms
5) Moving down the phylogenetic tree from mammals to humans shows the relationship between the tree and evolution over time.
Event 1 Event 2 Event 3 Event 4
First mammals First Primates Homo erectus Homo sapiens
6) More tectonic events we’ll be talking about later.
Event 1 Event 2 Event 3 Event 4
Opening of the Atlantic Ocean Linking of North and South America India collides with Asia Opening of the Red Sea
7) Pointing out that life on land probably needed the magnetic field to protect from the solar wind (in addition to the ozone layer).
Event 1 Event 2 Event 3 Event 4
Formation of the Earth First life Formation of the Magnetic Field First land plants
8) Fish came before insect. This one seemed to stick in students’ minds.
Event 1 Event 2 Event 3 Event 4
First Fish First Insects First Dinosaurs First Mammals
9) Mammals came before the dinosaurs went extinct. This allowed a discussion of theories of why the dinosaurs went extinct (disease, asteroid, mammals eating the eggs, volcanic eruption in Deccan) and how paleontologists might test the theories.
Event 1 Event 2 Event 3 Event 4
First Dinosaurs First Mammals Dinosaur Extinction First Primates

The whole exercise took a few hours but I think it worked out very well. The following day I gave the quiz, posted in the excel file, where they had to figure out which of two events came first, and the students did a decent job at that as well.

Why Diversity is Important

Diversity has been a recurring theme this semester. It started with the diversity conference our middle schoolers attended earlier this year, which, unfortunately, I’m not sure they got a lot out of. As a result, I’ve been making a little bit of a point to bring up the subject when it intersects with our work. This week were were talking about evolution and natural selection, as was able to talk about the practical advantages of both genetic and social diversity.

When the environment changes, species don’t usually have time to adapt. Instead, individuals who already have the genes for beneficial existing traits — traits that work well under the new conditions, like the ability to survive warming climates — will tend to breed more, and over the generations, more and more of the population will have the advantageous trait.

Therefore, to ensure the continuation of the species, we’ll want to have the maximum amount of genetic diversity.

Then I tacked. I asked if anyone was not interested in seeing the continuity of humanity, and the usual wags piped up to say that they could take homo sapiens or leave it. So I showed them the Voluntary Human Extinction Movement website. VHEMT advocates that people voluntarily stop having kids so that humanity eventually will become extinct, restoring the Earth’s environment to a healthy state. Their motto is, “May we live long and die out.”

The class was pretty uniformly aghast.

I particularly like the VHEMT website because it’s really hard to tell if they’re serious or not; which drove my students a little bit crazy. And I eventually got the key question I was angling for, “How could anyone want humans to go extinct?”

My response was, for them at least, quite unsatisfactory, because I chose to answer with a different question: “Do you think that diversity of thought is good?”

For some, their answer was no. However, I then reminded them of that first amendment to the U.S. constitution has to do with freedom of expression, which does seem to suggest that the founders thought diversity of ideas was a good thing. Just like species, countries with greater diversity of ideas are more likely to be able to adapt to changing conditions and succeed.

The application of evolutionary theory to social situations has, historically, been fraught with abuse (see the eugenics movement in particular). I also did not have time to bring the conversation back to why we might want to protect biodiversity. However, this particular lesson gets the point across that diversity has some important practical benefits that might not always be obvious.

Notes

An interview with VHMET on the Discovery Channel:

Semi-artificial Selection?

Just like drug resistant germs (we’ve discussed earlier), the rats are evolving.

“They’ve also mutated genetically and are bred to be immune to standard poisons.

“We have had to start using different methods such as trapping and gassing, which can be less effective and more costly.”

–Graham Chappell, from Rapid Pest Control in Newbury in Rowley (2012): Home counties demand stronger poison to deal with mutant ‘super rats’ in The Telegraph.