For years, Oceanside High School math teacher Rocio Saborido has heard students pose an eternal question about the arcane figures and symbols they struggle to master in her classes: “When will I ever use this?”
Saborido found an answer in something many of them already had in their hands — energy drinks.
Saborido, 45, had her work published in the September issue of “Mathematics Teacher: Learning and Teaching PK-12,” a peer-reviewed journal published by the National Council of Teachers of Mathematics. Her article, “Caffeine, Energy Drinks, and Exponential Functions,” explores how teachers can use students’ everyday caffeine consumption to teach concepts including exponential decay, half-life and infinite geometric series.
The lesson grew out of a challenge Saborido encountered early in her career in Oceanside, which began in 2003. “I would teach this concept of half-life,” she recalled. “And I've been using the examples from the textbook, and a lot of the examples had to do with radioactive decay. And it was just something the kids couldn't relate to.”
Students could manipulate the formulas, she said, but they didn’t necessarily understand what those formulas represented.
At the same time, Saborido began noticing more students coming to class with energy drinks. Surely she could relate the concept of a half-life to the effects of caffeine, she thought.
“These kids are drinking energy drinks, and they really have no idea what they're drinking,” she said. “These are two ideas that I can merge together so they can learn the math, and they can learn something important about their health.”
Saborido earned a degree in math with a minor in secondary education from CUNY Queens College in 2003, and a master’s in math education there in 2007. She became a National Board-certified teacher in 2011, and renewed her certification in 2020. She has developed her caffeine-focused half-life lessons over the past 14 years, and refined them with students and presented them at conferences at her alma mater before eventually turning the work into an article.
In it, she describes two hands-on activities that use caffeine to make abstract mathematical concepts tangible. In one activity, students model the caffeine content of an 80-milligram serving of Red Bull. Two cups of water represent the bloodstream, while drops of food coloring represent caffeine. Students repeatedly remove about half of the mixture and replace it with clear water, modeling the process of caffeine being metabolized.
The exercise gives students a visual representation of half-life — the amount of time required for half of a substance to be metabolized, or decay.
Saborido doesn’t initially tell students how long caffeine’s half-life is. Instead, she lets them work through the problem before revealing that, assuming a five-hour half-life, the stimulative effects of 80 milligrams of Red Bull take roughly 35 hours to dissipate.
“That also introduces to them the concept of exponential decay,” Saborido said.
The lesson often leads to surprised reactions from students. “There’s the reaction of, ‘Oh, wow, I learned about half-life in [chemistry], but now it makes sense,’” she said. “A lot of them don’t realize how long it would take to get rid of 80 milligrams of caffeine from your body.”
That curiosity is exactly what Saborido hopes to encourage.
The National Council of Teachers of Mathematics emphasizes the importance of helping students recognize and apply mathematics outside the classroom, and her article connects those principles to a familiar part of students’ lives.
“Because a lot of the math they learn feels very abstract — like, ‘This has nothing to do with me’ — but a lot of it is directly related to their lives and they just don't know,” she said.
“The more they can realize how math is present in their lives, and how they can use math to reason through their lives and solve real problems within their lives,” Saborido added, “it just gives them more of a sense of purpose.”
Having her lessons published by the NCTM was particularly meaningful. “The fact that they saw that it was something important and worthy of publishing was such an honor,” she said.
The response has already reached beyond Oceanside. Saborido said that a teacher in Japan recently emailed her after trying the lesson in her own classroom. “I was like, wow, kids in so many different places can maybe benefit from this idea that I had,” she said.
Saborido credits her National Board certification with encouraging her to continue examining and improving her teaching techniques. The certification, she said, emphasizes reflection and a continued effort to improve instruction.
“I could easily just have kept teaching it that way,” she said of her original half-life lessons. “But National Board certification … says something like, no, you need to try to do better with this.”
The goal, Saborido said, isn’t simply for students to memorize a formula, but to understand what the math means — and recognize how it can help them make sense of the world around them.
