Tomatoes with a side of Precalculus

At 7:32 this morning, I emailed Pierce, a junior, this photo of his project:

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Sad Tomatoes, 2016.

Pierce, 7:38: NOOOOOO
Me, 9:29: Google what the issue is with droopy plants?
Pierce, 10:34: It was not enough watering. Found the problem with the sprinklers. Will explain when I next see you.

Not the type of conversation you might expect between a teacher and Honors Precalculus student. Wait, Precalculus?

I described our first STEM project – DIY Aeroponics – to visitors from St. Joseph High School (Trumbull, CT) on Thursday morning. Aeroponic growing is a method of suspending plants in the air and spraying them with a nutrient-rich solution in lieu of planting them in soil. This method is already economically advantageous enough that there are hydroponic farms sprouting up around the United States. We decided to try small-scale aeroponics with our students. The visiting assistant principal was interested, but skeptical. She described her own math classes, which weren’t much different than the ones she observes as an admin at her school. “I always asked when I was ever going to use this, and I still don’t know.”

In mid-August, I started growing tomatoes in my 900 square-foot apartment. On the upstairs floor of the loft, there is an awkward space where a tenant might put a desk. Instead, I have a 27-gallon reservoir pumping filtered tap water through sprinklers which spray the root systems of my plants, which started from seeds and the tallest parts of which are two feet tall.

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I’ve spent time collecting data about my plants and looking for patterns. Much like good writing, pattern recognition is easily identifiable in students, but hard for them to improve. Data on its own is difficult to interpet; instead, we often graph it and look for a relationship. Talented math students can easily differentiate one curve from another, even if parts may seem similar.

When I researched how to grow tomatoes indoors, I paid particular attention to what I needed to do to the water. Different plants grow in different soil, so the water additives need to mimic the nutrients your plants would absorb outside. If the pH of the water indoors fluctuates too much, the plants cannot absorb the potassium, nitrates, and other ions from the reservoir.

In the 24 hours after my first few weekly water changes, I found that the pH was rising well above the 6.5 maximum recommended for tomatoes. Why? It seems that the ten gallons I was using should have been twenty. Here’s a more recent graph:

It took twice as long for me to hit 6.5 and it stabilized shortly after. Still high, but better. My hypothesis is that pH correlates directly to how much nutrient solution is in the water; as the plants absorb what they need, the pH rises. I could verify this by testing the levels of, for example, potassium ions in the water. I also might need to just add more plant food.

Those “natural exponent” graphs and those crazy A, B, and C values? Weeks of required material in Precalculus. So are trigonometric graphs:

The temperature of the water in the reservoir rises and falls with the temperature of my apartment. However, temperature should decrease exponentially, like your coffee: quickly at first, and then more slowly as it approaches room temperature. So why isn’t it? I still haven’t figure this out yet. 

The visiting team from Trumbull told us that they were impressed with the way our students articulated the purpose of their work. They asked where we came up with the ideas for these projects. We get this question often. 

Part of it is interest; honestly, Dana and I thought it would be fun to try and that we would find math in the physics of fluid dynamics (how fluids move) and optics (the study of light). I thought other data would come from tracking the height of the plants or the pattern at which the leaves grow. Based on the data presented here, there are even better options. 

I began growing tomatoes inside as work. I’ve since grown quite attached to them and I care enough to figure out how they work. If Pierce is any indication, the students will, too.

 More photos of my aeroponic tomato plants:

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One Response to Tomatoes with a side of Precalculus

  1. mark hines says:

    Wonderful thinking around the ways to model the behavior of your plants – exciting data!

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