Category Archives: Precalculus

The EarthCalc book is now on Amazon, too! Amazon is a touch inconvenient because I couldn't include the worksheets and solutions as an automatic download, but it's a big platform that reaches a lot of people. At Leanpub you get the worksheets and solutions as well as epub/pdf/mobi formats for the book...

Raccoon River: A while ago I wrote some posts about the Raccoon River in Iowa, and the flow of nitrates into the river. The posts talked about how fertilizing our big corn and soybean fields can lead to problems with nitrate runoff, especially in spring when the snow melts and washes leftover fertilizer into rivers and lakes. The associated worksheets were about increasing/decreasing functions, average rate of change, interpretation of graphs, etc.

It's spring again! Nitrates are a topic with continuing relevance even though the worksheet data is from 2013. Recently, the city of Des Moines voted to sue three Iowa counties for not managing nitrate and nitrite runoff: according to the linked National Public Radio report, removing the nitrates in 2013 cost the city $900,000! The New York Times (coincidentally?) recently featured an article about no-till farming, which reduces fertilizer runoff.

So, how much agriculture is practiced in your state? How big an impact does fertilizer runoff have on your ecosystem? Consider asking your students to report on whether their families fertilize their lawns, and find out what your community is doing to deal with runoff into lakes and streams!

Spring still keeps happening slowly in Minnesota, and snow is still melting up north. Iowa and other big agricultural states to our south have experienced all their snow melt, though, and are beginning the farming season.

Here's a worksheet that's pretty well inappropriate to the academic year -- no one is doing rate of change right now in calculus or precalculus! But it's written, so I may as well share. Again, it's about nitrate and nitrite runoff into the Raccoon River in Iowa. Spring is a good time to fertilize soil, but the runoff that's happening during the first snow melt is actually all from fertilizer applied last summer.

Average Change: Nitrates in the Raccoon River

The semester is coming to a close. Just a few more weeks of class and it's over. I'm working, as slowly as the spring, on some new worksheets about White Bear Lake water levels and about bee ecology. I learned today that Michelle Obama keeps bees near the White House garden. They're fascinating creatures!

More later... just a few final exams to go 🙂

Did you know that raccoons wash their food when near a body of water? I love the image. I don't even know if raccoons live near the Raccoon River in Iowa anymore. But I do know where to find real-time nitrate and nitrite monitoring data for the Raccoon River.

Nitrate is NO3 and nitrite is NO2. They both occur naturally in soil and are also vitally important components of fertilizer. Fertilizer, of course, is necessary for the high-yield agriculture practiced in US states like Iowa. The difficulty is that nitrate and nitrite are highly water soluble. They're only useful to a plant if they're available to the plant at the right time in its growth cycle. If the soil is too dry for it to sink in and get to the roots of the plants or the plant doesn't grow due to bad weather, then excess fertilizer is left on the ground and runs off in the rain.

An interesting time to look at nitrate/nitrite runoff is as the snow is melting in the fields of Iowa. Fertilizer hasn't been applied for a season, so all that is left is the runoff from last year's application. It's often not raining yet, so the only water for runoff comes from snowmelt. Daily temperature fluctuations rule the amount of runoff each day for a few days.

So here's a graph-reading worksheet: it's not calculus, and is perhaps more focused on high-school or junior-high skills, but these are always worth a reminder....

Precalc: Nitrates in the Raccoon River

It's been a while. First set of midterms written, given, and graded. Spring may (?) be coming to Minnesota. Ski trips taken. Spring break coming.

I've been working on this nitrate run-off project for a while. Learning about the problem of nitrite and nitrate runoff from agriculture -- mostly from fertilizers -- has been a non-linear process! I've heard reports on the radio about the problems nitrate runoff causes, not only for drinking water in towns in Minnesota and Iowa, but in the dead zone it is causing in the Gulf of Mexico. I read some papers as well, looking for data and ideas tractable for calculus worksheets. Finally I found some real-time data tracking nitrate levels in Iowa rivers, including the Racoon River. Since Iowa is so heavily agricultural, nitrate levels are a significant problem for drinking water treatment plants.

This is the perfect time of year to look at nitrate levels because the spring thaw is either here now or coming soon. Over the winter, farmers did not fertilize -- that would be silly! -- but the spring thaw means a lot of water from snowmelt and precipitation washing over fields and into rivers and streams, bringing with it the leftover nitrate from last year's fertilization. There are some interesting things to see in the data: when temperatures are hovering around freezing, the daily freeze-thaw cycle can often be seen in the nitrate levels measured by the monitors.

It's not easy to model daily nitrate runoff because it depends so much on daily temperature, precipitation, level of snowmelt, and other factors that can change quickly. On the other hand, we can look at data over a period of time and use calculus to understand some of the factors involved. Now that I've wrestled the time and date formatting of the real-time data into compliance using the R programming language, I can make you some beautiful graphs and present some numerical integration worksheets estimating nitrate runoff as well as some graph interpretation worksheets asking students to come up with physical explanations for the data they see presented.

Coming soon....