One Stone High School: Embracing the Role of Learner

At One Stone, we’re working to integrate real life issues into all of our academic work, math included. The case study below highlights an example of how our coaches and students work together to explore issues as they arise, which lends itself to relevant and timely study. In this example, One Stone students Jadon Chen and Dylan Baker and One Stone coach Dr. Celeste Bolin visited the Ada County Landfill as part of “The Lab,” a science course offered by Celeste. The Lab was a collaborative experience with the major goal of inspiring students to get their hands dirty, tinker, and garner enthusiasm about using scientific methods to drive inquiry-based investigations.  At the landfill, Jadon, Dylan, and Celeste became interested in the lifespan of the landfill and when, exactly, the landfill might be full.

This story is an example of how we’re uniting math with other disciplines. We believe that by incorporating math into multiple courses, students can understand math as a powerful problem-solving tool.

Jadon: When you think of your town’s dump, do you imagine a big, smelly pile of rotting garbage? Because that’s exactly what I thought until I visited the Ada County Landfill in October of 2018. The entire structure of the landfill was really interesting—things like lining the base of the landfill with 6-feet of clay and a moldable plastic to prevent groundwater contamination had never crossed my mind before. It turns out the landfill is very clean and requires a lot of science, thought, and planning.

Celeste: When we visited the site, the deputy director of the landfill, Theresa Rademacher, shared a few facts about where our local garbage goes, and the one that stuck out the most to many students was that the landfill is, in fact, going to fill up!  The information presented was that in 79 years, the remaining 300 acres of usable landfill would be used up. Even more shocking was the fact that this estimate was based on a 1% growth in garbage produced, but in 2018, Boise saw an 8% growth in garbage. Forbes Magazine headline declared that Boise is the fastest-growing large metro area in the U.S (March, 2018).

Jadon: I found this problem to be very interesting because of how applicable it was to the real world, which was something that I felt a lot of math and science classes had been missing in the past. My friend Dylan and I worked to find the landfill’s spatial longevity to verify the timeline the manager at the landfill gave us.  The reason that this was an interesting project was that Boise's growth rate had become much higher in the last year than the rate of growth they had used as their standard for calculating the necessary landfill area. This made me think that we’d have to find a solution in my lifetime for not having a functional landfill in Boise anymore. This realization made me think about how much longer this resource would be available to us, and led me to start developing my equation.    

Celeste: Each student came back to One Stone headquarters from the landfill excited about different ways to think about what they learned. Some students decided to follow recycling initiatives and really understand the new use of orange bags to sort our plastics. Others wanted to understand where we could take recycling locally, devastated by the high energy cost of shipping recyclables out of Boise. One young woman wanted to actually measure the BPA in certain plastics. Dylan and Jadon wanted to know how many years we might have remaining if the prediction was based on 8% growth rather than 1% growth. This last project was by far the most challenging and required a level of mathematics and organization beyond what Dylan, Jadon, and myself had completed. With the help of Dr. Sion Ledbetter, a fellow academic coach at One Stone specializing in mathematics, we undertook to fact-check this problem and make a prediction if growth in Boise continues as it has in the past year.

Jadon: We first had to find the average amount of garbage produced by each person in Ada County and calculate the county's population.  We learned from the director of the landfill that the average person creates about 1 ton of garbage each year, and the population of Ada County is about 457,000. We also knew that the landfill had 300 remaining acres available for garbage.  I had to reach out to Theresa to find out some more information to tackle this problem, including the allowable height of the garbage in this area, which was 100 feet or about 33 yards. I did some research and found out that 1,300 pounds of garbage can be compacted into a cubic yard, according to the South Carolina Department of Health and Environmental Control. We had to find the landfill’s remaining space by converting its acreage and height limit to cubic yards (ref).  From here, we made the following calculations:

1. Convert 457,000 tons of garbage produced per year in Ada County to pounds.

457,000 tons x (2000 lbs/ton)  = 914,000,000 lbs per year

2.  Convert pounds to cubic yards.

914,000,000 lbs /(1300 lbs in a cubic yard) = 703, 077 cubic yards

3. Estimate the cubic yards of each acre in the landfill.

We know an acre is 4,840 square yards.

X^2 = 4840 square yards

X = 69.57 yd ~70 yd

We also knew it could get 33 yards high, so we calculated the cubic yards.

33 x 70 x 70 = 161,700 cubic yards in each acre

4. Now we had to figure out how many acres of the landfill are used per year.

703, 077 total cubic yards per year / (161,700 cubic yards/acre ) =  4.34 acres are used a year

5. The final step is to divide the remaining acres by the acres used each year.

300 acres / (4.34 acres used/year) = 69.12 years

This is very close to the 79 year estimate we got from the director! So what if we did this calculation assuming we were actually making more than 1 ton per person, instead making 8% more, which would be 1.08 tons of garbage per person per year.

We estimated 457,000 people x 1.08 tons of garbage per person = 493,560 tons.

This time, we came up with 63.8 years, which is around 15 years less than the estimate from the landfill and about 5 years less than our calculation. And it doesn’t even account for the population growth!

Celeste: The most impactful things about this project were the collaboration between Jadon and Dylan, the co-learning with coaches and students, and the investment the students had in understanding and solving a real-world question. It was inspiring to see that as the problem got more complex and we made mistakes, the students became much more invested as opposed to giving up. It was also great to be involved in a modeling of working relationships in problem solving. There was communication between Jadon and Dylan, between them and I, between them and the landfill director, and between myself, them, and another coach that was all necessary to complete this project. I also believe the lack of a “right answer” gave them increased confidence, curiosity, and stamina to stick with approaching the problem in the most simplified way that would approximate what they wanted to know. I also saw their appreciation for how relevant application of math to real world scenario made it so worthwhile to stick with.

Jadon: I thought that the math behind this problem was very interesting. I had also never worked on a math problem that was so easily applied to the real world. The only resources we needed were information from the people working at the landfill and help from Celeste and Sion with developing how to explore this problem and make reasonable estimates. The main thing I appreciated about this project was that I saw my coaches as peers. I had an equality of voice and input on the project. It was the first time I was working on a problem with a coach that was learning along with us. This process allowed for much more ideation in the way that we approached this problem, since no one had the right answers.

Advice I might have for other students is to seek out meaningful mentors—people willing to grow alongside you. This experience changed my perspective of math because it was an applicable use of my skills that had real world relevance. I wasn’t solving a fake or theoretical problem about Tony buying pineapples at the grocery store. Who’s Tony and why am I concerned about his pineapples? I am, however, concerned about my local community and if we’ll have to live in garbage.

Click here to read the companion post to this piece by Sarah Galasso of Carnegie Learning.